This page lists all publications from the MPL theory division, starting in 2016, including all independent subgroups. For individual publication lists, please see those of the Marquardt Group, Krenn Group and Kunst Group.
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in NonHermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately describe the evolution of nonHermitian systems when encircling an exceptional point. This allows us to use the recently proposed Magnusbased strategy for control to design fast nonreciprocal, topological operations whose fidelity error is orders of magnitude smaller than their much slower adiabatic counterparts.
Arbitrary optical wave evolution with Fourier transforms and phase masks
Victor LopézPastor, Jeff S. Lundeen, Florian Marquardt
A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a constructive proof that it is possible to realize a multiport universal interferometer on N modes with a succession of 6N Fourier transforms and 6N+1 phase masks, for any even integer N. Furthermore, we provide an algorithm to find the correct succesion of Fourier transforms and phase masks to realize a given arbitrary unitary transformation. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.
Design of quantum optical experiments with logic artificial intelligence
Logic artificial intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and be solved by checking their satisfiability (SAT). Recently, SAT solvers have become a sophisticated and powerful computational tool capable, among other things, of solving longstanding mathematical conjectures. In this work, we propose the use of logic AI for the design of optical quantum experiments. We show how to map into a SAT problem the experimental preparation of an arbitrary quantum state and propose a logicbased algorithm, called Klaus, to find an interpretable representation of the photonic setup that generates it. We compare the performance of Klaus with the stateoftheart algorithm for this purpose based on continuous optimization. We also combine both logic and numeric strategies to find that the use of logic AI improves significantly the resolution of this problem, paving the path to develop more formalbased approaches in the context of quantum physics experiments.
Observing polarization patterns in the collective motion of nanomechanical arrays
Juliane Doster, Tirth Shah, Thomas Fösel, Florian Marquardt, Eva Weig
In recent years, nanomechanics has evolved into a mature field, with wideranging impact from sensing applications to fundamental physics, and it has now reached a stage which enables the fabrication and study of ever more elaborate devices. This has led to the emergence of arrays of coupled nanomechanical resonators as a promising field of research, serving as model systems to study collective dynamical phenomena such as synchronization or topological transport. From a general point of view, the arrays investigated so far represent scalar fields on a lattice. Moving to a scenario where these could be extended to vector fields would unlock a whole host of conceptually interesting additional phenomena, including the physics of polarization patterns in wave fields and their associated topology. Here we introduce a new platform, a twodimensional array of coupled nanomechanical pillar resonators, whose orthogonal vibration directions encode a mechanical polarization degree of freedom. We demonstrate direct optical imaging of the collective dynamics, enabling us to analyze the emerging polarization patterns and follow their evolution with drive frequency.
Deep recurrent networks predicting the gap evolution in adiabatic quantum computing
Naeimeh Mohseni, Carlos NavarreteBenlloch, Tim Byrnes, Florian Marquardt
One of the main challenges in quantum physics is predicting efficiently the dynamics of observables in manybody problems out of equilibrium. A particular example occurs in adiabatic quantum computing, where finding the structure of the instantaneous gap of the Hamiltonian is crucial in order to optimize the speed of the computation. Inspired by this challenge, in this work we explore the potential of deep learning for discovering a mapping from the parameters that fully identify a problem Hamiltonian to the full evolution of the gap during an adiabatic sweep applying different network architectures. Through this example, we find that a limiting factor for the learnability of the dynamics is the size of the input, that is, how the number of parameters needed to identify the Hamiltonian scales with the system size. We demonstrate that a long shortterm memory network succeeds in predicting the gap when the parameter space scales linearly with system size. Remarkably, we show that once this architecture is combined with a convolutional neural network to deal with the spatial structure of the model, the gap evolution can even be predicted for system sizes larger than the ones seen by the neural network during training. This provides a significant speedup in comparison with the existing exact and approximate algorithms in calculating the gap.
Learning Interpretable Representations of Entanglement in Quantum Optics Experiments using Deep Generative Models
Daniel FlamShepherd, Tony Wu, Xuemei Gu, Alba CerveraLierta, M. Krenn, Alan AspuruGuzik
Quantum physics experiments produce interesting phenomena such as interference or entanglement, which is a core property of numerous future quantum technologies. The complex relationship between a quantum experiment's structure and its entanglement properties is essential to fundamental research in quantum optics but is difficult to intuitively understand. We present the first deep generative model of quantum optics experiments where a variational autoencoder (QOVAE) is trained on a dataset of experimental setups. In a series of computational experiments, we investigate the learned representation of the QOVAE and its internal understanding of the quantum optics world. We demonstrate that the QOVAE learns an intrepretable representation of quantum optics experiments and the relationship between experiment structure and entanglement. We show the QOVAE is able to generate novel experiments for highly entangled quantum states with specific distributions that match its training data. Importantly, we are able to fully interpret how the QOVAE structures its latent space, finding curious patterns that we can entirely explain in terms of quantum physics. The results demonstrate how we can successfully use and understand the internal representations of deep generative models in a complex scientific domain. The QOVAE and the insights from our investigations can be immediately applied to other physical systems throughout fundamental scientific research.
Channel discord and distortion
WeiWei Zhang, Yuval R. Sanders, Barry C. Sanders
New Journal of Physics (23)
083025
(2021)

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Discord, originally notable as a signature of bipartite quantum correlation, in fact can be nonzero
classically, i.e. arising from noisy measurements by one of the two parties. Here we redefine
classical discord to quantify channel distortion, in contrast to the previous restriction of classical
discord to a state, and we then show a monotonic relationship between classical (channel) discord
and channel distortion. We show that classical discord is equivalent to (doubly stochastic) channel
distortion by numerically discovering a monotonic relation between discord and totalvariation
distance for a bipartite protocol with one party having a noiseless channel and the other party
having a noisy channel. Our numerical method includes randomly generating doubly stochastic
matrices for noisy channels and averaging over a uniform measure of input messages. Connecting
discord with distortion establishes discord as a signature of classical, not quantum, channel
distortion.
Perturbation theory of nearly spherical dielectric optical resonators
Julius Gohsrich, Tirth Shah, Andrea Aiello
Physical Review A
104(2)
023516
(2021)

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Dielectric spheres of various sizes may sustain electromagnetic whisperinggallery modes resonating at optical frequencies with very narrow linewidths. Arbitrary small deviations from the spherical shape typically shift and broaden such resonances. Our goal is to determine these shifted and broadened resonances. A boundarycondition perturbation theory for the acoustic vibrations of nearly circular membranes was developed by Rayleigh more than a century ago. We extend this theory to describe the electromagnetic excitations of nearly spherical dielectric cavities. This approach permits us to avoid dealing with decaying quasinormal modes. We explicitly find the frequencies and the linewidths of the optical resonances for arbitrarily deformed nearly spherical dielectric cavities, as power series expansions by a small parameter, up to and including secondorder terms. We thoroughly discuss the physical conditions for the applicability of perturbation theory.
Optical signatures of the coupled spinmechanics of a levitated magnetic microparticle
Vanessa Wachter, Victor A. S. V. Bittencourt, Shangran Xie, Sanchar Sharma, Nicolas Joly, Philip Russell, Florian Marquardt, Silvia ViolaKusminskiy
We propose a platform that combines the fields of cavity optomagnonics and levitated optome
chanics in order to control and probe the coupled spinmechanics of magnetic dielectric particles. We theoretically study the dynamics of a levitated Faradayactive dielectric microsphere serving as an optomagnonic cavity, placed in an external magnetic field and driven by an external laser. We find that the optically driven magnetization dynamics induces angular oscillations of the particle with low associated damping. Further, we show that the magnetization and angular motion dynamics
can be probed via the power spectrum of the outgoing light. Namely, the characteristic frequencies attributed to the angular oscillations and the spin dynamics are imprinted in the light spectrum by two main resonance peaks. Additionally, we demonstrate that a ferromagnetic resonance setup with an oscillatory perpendicular magnetic field can enhance the resonance peak corresponding to
the spin oscillations and induce fast rotations of the particle around its anisotropy axis.
Deep Reinforcement Learning for Quantum State Preparation with Weak Nonlinear Measurements
Riccardo Porotti, Antoine Essig, Benjamin Huard, Florian Marquardt
Quantum control has been of increasing interest in recent years, e.g. for tasks like state initialization and stabilization. Feedbackbased strategies are particularly powerful, but also hard to find, due to the exponentially increased search space. Deep reinforcement learning holds great promise in this regard. It may provide new answers to difficult questions, such as whether nonlinear measurements can compensate for linear, constrained control. Here we show that reinforcement learning can successfully discover such feedback strategies, without prior knowledge. We illustrate this for state reparation in a cavity subject to quantumnondemolition detection of photon number, with a simple linear drive as control. Fock states can be produced and stabilized at very high fidelity. It is even possible to reach superposition states, provided the measurement rates for different Fock states can be controlled as well.
Analytic Design of Accelerated Adiabatic Gates in Realistic Qubits: General Theoryand Applications to Superconducting Circuits
F Setiawan, Peter Groszkowski, Hugo Ribeiro, Aashish A Clerk
Shortcuts to adiabaticity (STA) is a general methodology for speeding up adiabatic quantumprotocols, and has many potential applications in quantum information processing. Unfortunately,analytically constructing STAs for systems having complex interactions and more than a few levelsis a challenging task. This is usually overcome by assuming an idealized Hamiltonian (e.g., only alimited subset of energy levels are retained, and the rotatingwave approximation (RWA) is made).Here, we develop ananalyticapproach that allows one to go beyond these limitations. Our methodis general and results in analyticallyderived pulse shapes that correct both nonadiabatic errorsas well as nonRWA errors. We also show that our approach can yield pulses requiring a smallerdriving power than conventional nonadiabatic protocols. We show in detail how our ideas can beused to analytically design highfidelity singlequbit “tripod” gates in a realistic superconductingfluxonium qubit.
Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels
A large set of recent experiments has been exploring topological transport in bosonic systems,e.g. of photons or phonons. In the vast majority, timereversal symmetry is preserved, and bandstructures are engineered by a suitable choice of geometry, to produce topologically nontrivialbandgaps in the vicinity of highsymmetry points. However, this leaves open the possibility oflargequasimomentum backscattering, destroying the topological protection. Up to now, it has beenunclear what precisely are the conditions where this effect can be sufficiently suppressed. In thepresent work, we introduce a comprehensive semiclassical theory of tunneling transitions in momentum space, describing backscattering for one of the most important system classes, based on thevalley Hall effect. We predict that even for a smooth domain wall effective scattering centres developat locations determined by both the local slope of the wall and the energy. Moreover, our theoryprovides a quantitative analysis of the exponential suppression of the overall reflection amplitudewith increasing domain wall smoothness.
Rapid Exploration of Topological Band Structures using Deep Learning
Vittorio Peano, Florian Sapper, Florian Marquardt
Physical Review X
11(2)
021052
(2021)

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The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explore and optimize band structures and to classify their topological characteristics for arbitrary unitcell geometries. In this work, we show how deep learning can address this challenge. We introduce an approach where a neural network first maps the geometry to a tightbinding model. The tightbinding model encodes not only the band structure but also the symmetry properties of the Bloch waves. This allows us to rapidly categorize a large set of geometries in terms of their band representations, identifying designs for fragile topologies. We demonstrate that our method is also suitable to calculate strong topological invariants, even when (like the Chern number) they are not symmetry indicated. Engineering of domain walls and optimization are accelerated by orders of magnitude. Our method directly applies to any passive linear material, irrespective of the symmetry class and space group. It is general enough to be extended to active and nonlinear metamaterials.
Machine Learning and Quantum Devices
Florian Marquardt
SciPost Physics (21)
10.21468
(2021)

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These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation, image classification, convolutional networks and autoencoders.The second part is about advanced techniques like reinforcement learning (for discovering control strategies), recurrent neural networks (for analyzing timetraces), and Boltzmann machines (for learning probability distributions). In the third lecture, we discuss first recent applications to quantum physics, with an emphasis on quantum information processing machines. Finally, the fourth lecture is devoted to the promise of using quantum effects to accelerate machine learning.
Renormalized Mutual Information for Artificial Scientific Discovery
Leopoldo Sarra, Andrea Aiello, Florian Marquardt
Physical Review Letters
126
200601
(2021)

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We derive a welldefined renormalized version of mutual information that allows to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation relevant for feature extraction, where the goal is to produce a lowdimensional effective description of a highdimensional system. Our approach enables the discovery of collective variables in physical systems, thus adding to the toolbox of artificial scientific discovery, while also aiding the analysis of information flow in artificial neural networks.
Phase Space Crystal Vibrations: Chiral Edge States with Preserved Timereversal Symmetry
Chiral transport along edge channels in Chern insulators represents the most robust version of topological transport, but it usually requires breaking of the physical timereversal symmetry. In this work, we introduce a different mechanism that foregoes this requirement, based on the combination of the symplectic geometry of phase space and interactions. Starting from a honeycomb phasespace crystal of atoms, which can be generated by periodic driving of a onedimensional interacting quantum gas, we show that the resulting vibrational lattice waves have topological properties. Our work provides a new platform to study topological manybody physics in dynamical systems.
Error suppression in adiabatic quantum computing with qubit ensembles
Naeimeh Mohseni, Marek Narozniak, Alexey N Pyrkov, Valentin Ivannikov, Jonathan P Dowling
npj Quantum Information
7(71)
(2021)

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Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an errorprotected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards errorcorrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensembleensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by meanfield theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.
Deep Learning of Quantum ManyBody Dynamics via Random Driving
Naeimeh Mohseni, Thomas Fösel, Lingzhen Guo, Carlos NavarreteBenlloch, Florian Marquardt
Neural networks have emerged as a powerful way to approach many practical problems in quantumphysics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantummanybody system, where the training isbased purely on monitoring expectation values of observablesunder random driving. The trained recurrent network is able to produce accurate predictions fordriving trajectories entirely different than those observed during training. As a proof of principle,here we train the network on numerical data generated from spin models, showing that it can learnthe dynamics of observables of interest without needing information about the full quantum state.This allows our approach to be applied eventually to actual experimental data generated from aquantum manybody system that might be open, noisy, or disordered, without any need for a detailedunderstanding of the system. This scheme provides considerable speedup for rapid explorations andpulse optimization. Remarkably, we show the network is able to extrapolate the dynamics to timeslonger than those it has been trained on, as well as to the infinitesystemsize limit.
Microsphere kinematics from the polarization of tightly focused nonseparable light
Stefan BergJohansen, Martin Neugebauer, Andrea Aiello, Gerd Leuchs, Peter Banzer, Christoph Marquardt
Optics Express
29(8)
1242912439
(2021)

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Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica 2(10), 864 (2015)]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the farfield polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polarization measurements only, we
demonstrate position sensing of a Mie particle in three dimensions. Our work extends the concept of back focal plane interferometry and highlights the potential of polarization analysis in optical tweezers employing structured light.
Quantum circuit optimization with deep reinforcement learning
Thomas Fösel, Murphy Yuezhen Niu, Florian Marquardt, Li Li (李力)
A central aspect for operating future quantum computers is quantum circuit optimization, i.e., the search for efficient realizations of quantum algorithms given the device capabilities. In recent years, powerful approaches have been developed which focus on optimizing the highlevel circuit structure. However, these approaches do not consider and thus cannot optimize for the hardware details of the quantum architecture, which is especially important for nearterm devices. To address this point, we present an approach to quantum circuit optimization based on reinforcement learning. We demonstrate how an agent, realized by a deep convolutional neural network, can autonomously learn generic strategies to optimize arbitrary circuits on a specific architecture, where the optimization target can be chosen freely by the user. We demonstrate the feasibility of this approach by training agents on 12qubit random circuits, where we find on average a depth reduction by 27% and a gate count reduction by 15%. We examine the extrapolation to larger circuits than used for training, and envision how this approach can be utilized for nearterm quantum devices.
Selflearning Machines based on Hamiltonian Echo Backpropagation
A physical selflearning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for selflearning in any timereversible Hamiltonian system. We illustrate the training of such a selflearning machine numerically for the case of coupled nonlinear wave fields.
Floquet theory for temporal correlations and spectra in timeperiodic open quantum systems: Application to squeezed parametric oscillation beyond the rotatingwave approximation
Carlos NavarreteBenlloch, Rafael Garcés, Naeimeh Mohseni, German J. de Valcarcel
Physical Review A
103(2)
023713
(2021)

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Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to selfpulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantumstatistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute twotime correlations and corresponding spectral densities of timeperiodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory, we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into oneperiod duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a twodimensional temporal domain that is treated as a chessboard with oneperiod × oneperiod cells. This technique avoids cumulative numerical errors as well as efficiently saving computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically driven oscillator (degenerate parametric oscillator) below threshold and far away from rotatingwave approximation conditions, which is a relevant scenario for modern lowfrequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotatingwave approximation.
Engineering Fast HighFidelity Quantum Operations With Constrained Interactions
Thales Figueiredo Roque, Aashish A Clerk, Hugo Ribeiro
npj Quantum Information
7
28
(2021)

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Understanding how to tailor quantum dynamics to achieve a desired evolution is a crucial problemin almost all quantum technologies. We present a very general method for designing highefficiencycontrol sequences that are always fully compatible with experimental constraints on available interactions and their tunability. Our approach reduces in the end to finding control fields by solvinga set of timeindependent linear equations. We illustrate our method by applying it to a numberof physicallyrelevant problems: the strongdriving limit of a twolevel system, fast squeezing in aparametrically driven cavity, the leakage problem in transmon qubit gates, and the acceleration ofSNAP gates in a qubitcavity system.
2020
Oscillating bound states for a giant atom
Lingzhen Guo, Anton Frisk Kockum, Florian Marquardt, Göran Johannson
Physical Review Research
2(4)
043014
(2020)

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We investigate the relaxation dynamics of a single artificial atom interacting, via multiple coupling points, with a continuum of bosonic modes (photons or phonons) in a onedimensional waveguide. In the nonMarkovian regime, where the traveling time of a photon or phonon between the coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the atom, we find that a boson can be trapped and form a stable bound state. As a key discovery, we further find that a persistently oscillating bound state can appear inside the continuous spectrum of the waveguide if the number of coupling points is more than two since such a setup enables multiple bound modes to coexist. This opens up prospects for storing and manipulating quantum information in larger Hilbert spaces than available in previously known bound states.
Spatial localization and pattern formation in discreteoptomechanical cavities and arrays
Joaquín RuizRivas, Giuseppe Patera, Carlos NavarreteBenlloch, Eugenio Roldán, German de Valcarcel
New Journal of Physics
22
093076
(2020)

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We investigate theoretically the generation of nonlinear dissipative structures in optomechanical(OM) systems containing discrete arrays of mechanical resonators. We consider both hybridmodels in which the optical system is a continuous multimode field, as it would happen in an OMcavity containing an array of micromirrors, and also fully discrete models in which eachmechanical resonator interacts with a single optical mode, making contact with Ludwig andMarquardt (2013Phys.Rev.Lett.101, 073603). Also, we study the connections between both typesof models and continuous OM models. While all three types of models merge naturally in the limitof a large number of densely distributed mechanical resonators, we show that the spatiallocalization and the pattern formation found in continuous OM models can still be observed for asmall number of mechanical elements, even in the presence of finitesize effects, which we discuss.This opens new venues for experimental approaches to the subject.
Manybody dephasing in a trappedion quantum simulator
Harvey B. Kaplan, Lingzhen Guo, Wen Lin Tan, Arinjoy De, Florian Marquardt, Guido Pagano, Christopher Monroe
Physical Review Letters
125(1218)
120605
(2020)

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How a closed interacting quantum manybody system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable longrange interacting transversefield Ising Hamiltonian realized with a trappedion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finitesize system of spin1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spinspin coupling, which enables analytical predictions for the longtime nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of manybody dephasing.
Observation of concentrating paraxial beams
Andrea Aiello, Martin Paúr, Bohumil Stoklasa, Zdeněk Hradil, Jaroslav Řeháček, Luis L SánchezSoto
OSA Continuum
3(9)
10.1364/OSAC.400410
23872394
(2020)

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We report the first, to the best of our knowledge, observation of concentrating paraxialbeams of light in a linear nondispersive medium. We have generated this intriguing class of lightbeams, recently predicted by one of us, in both one and twodimensional configurations. As wedemonstrate in our experiments, these concentrating beams display unconventional features, suchas the ability to strongly focus in the focal spot of a thin lens like a plane wave, while keepingtheir total energy finite.
Topological phonon transport in an optomechanical system
Hengjiang Ren, Tirth Shah, Hannes Pfeifer, Christian Brendel, Vittorio Peano, Florian Marquardt, Oskar Painter
Recent advances in cavityoptomechanics have now made it possible to use light not just as a passive measuring device of mechanical motion, but also to manipulate the motion of mechanical objects down to the level of individual quanta of vibrations (phonons). At the same time, microfabrication techniques have enabled smallscale optomechanical circuits capable of onchip manipulation of mechanical and optical signals. Building on these developments, theoretical proposals have shown that larger scale optomechanical arrays can be used to modify the propagation of phonons, realizing a form of topologically protected phonon transport. Here, we report the observation of topological phonon transport within a multiscale optomechanical crystal structure consisting of an array of over 800 cavityoptomechanical elements. Using sensitive, spatially resolved optical readout we detect thermal phonons in a 0.325−0.34GHz band traveling along a topological edge channel, with substantial reduction in backscattering. This represents an important step from the pioneering macroscopic mechanical systems work towards topological phononic systems at the nanoscale, where hypersonic frequency (≳GHz) acoustic wave circuits consisting of robust delay lines and nonreciprocal elements may be implemented. Owing to the broadband character of the topological channels, the control of the flow of heatcarrying phonons, albeit at cryogenic temperatures, may also be envisioned.
Probing the TavisCummings level splitting with intermediatescale superconducting circuits
Ping Yang, Jan David Brehm, Juha Leppäkangas, Lingzhen Guo, Michael Marthaler, Isabella Boventer, Alexander Stehli, Tim Wolz, Alexey V. Ustinov, et al.
Physical Review Applied (14)
024025
(2020)

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We demonstrate the local control of up to eight twolevel systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual twolevel system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, being the hallmark of the TavisCummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states is limited by reduced signal visibility, and if uncalibrated by offresonance shifts of subcomponents. Our work demonstrates control and readout of quantum coherent mesoscopic multiqubit system of intermediate scale under conditions of noise.
Kinetics of ManyBody Reservoir Engineering
Hugo Ribeiro, Florian Marquardt
Physical Review Research
2(3)
033231
(2020)

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Recent advances illustrate the power of reservoir engineering in applications to manybody systems, such as quantum simulators based on superconducting circuits. We present a frameworkbased on kinetic equations and noise spectra that can be used to understand both the transientand longtime behavior of many particles coupled to an engineered reservoir in a numberconservingway. For the example of a bosonic array, we show that the nonequilibrium steady state can beexpressed, in a wide parameter regime, in terms of a modified BoseEinstein distribution with anenergydependent temperature.
Condensed matter physics in time crystals
Lingzhen Guo, Pengfei Liang
New Journal of Physics (22)
075003
(2020)

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Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous timetranslation symmetry in static systems is proved impossible for the equilibrium state, the discrete timetranslation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the socalled Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the manybody physics from the interplay of symmetrybroken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research.
Efficient cavity control with SNAP gates
Thomas Fösel, Stefan Krastanov, Florian Marquardt, Liang Jiang
Microwave cavities coupled to superconducting qubits have been demonstrated to be a promising platform for quantum information processing. A major challenge in this setup is to realize universal control over the cavity. A promising approach are selective numberdependent arbitrary phase (SNAP) gates combined with cavity displacements. It has been proven that this is a universal gate set, but a central question remained open so far: how can a given target operation be realized efficiently with a sequence of these operations. In this work, we present a practical scheme to address this problem. It involves a hierarchical strategy to insert new gates into a sequence, followed by a cooptimization of the control parameters, which generates short highfidelity sequences. For a broad range of experimentally relevant applications, we find that they can be implemented with 3 to 4 SNAP gates, compared to up to 50 with previously known techniques.
The sounds of science—a symphony for many instruments and voices
Gerianne Alexander, Roland E Allen, Anthony Atala, Warwick P Bowen, Alan A Coley, John B Goodenough, Mikhail I Katsnelson, Eugene V Koonin, Mario Krenn, et al.
Physical Review Research (2)
013201
(2020)

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Synchronization of weaklycoupled nonlinear oscillators is a ubiquitous phenomenon that has been observedacross the natural sciences. We study the dynamics of optomechanical arrays—networks of mechanically compliant structures that interact with the radiation pressure force—which are driven to selfoscillation. Thesesystems offer a convenient platform to study synchronization phenomena and have potential technological applications. We demonstrate that this system supports the existence of longlived chimera states, where parts ofthe array synchronize whilst others do not. Through a combined numerical and analytical analysis we show thatthese chimera states can only emerge in the presence of disorder.
Maxwell's lesser demon: A Quantum Engine Driven by Pointer Measurements
Stella Seah, Stefan Nimmrichter, Valerio Scarani
Physical Review Letters
124
100603

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We discuss a selfcontained spinboson model for a measurementdriven engine, in which a demongenerates work from random thermal excitations of a quantum spin via measurement and feedbackcontrol. Instead of granting it full direct access to the spin state and to Landauer’s erasure strokes foroptimal performance, we restrict this lesser demon’s action to pointer measurements, i.e. random orcontinuous interrogations of a damped mechanical oscillator that assumes macroscopically distinctpositions depending on the spin state. The engine could reach simultaneously high output powersand efficiencies and can operate in temperature regimes where quantum Otto engines would fail.
Quench dynamics in onedimensional optomechanical arrays
Sadegh Raeisi, Florian Marquardt
Physical Review A
101(2)
023814
(2020)

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Nonequilibrium dynamics induced by rapid changes of external parameters is relevant for a widerange of scenarios across many domains of physics. For waves in spatially periodic systems, quencheswill alter the bandstructure and generate new excitations. In the case of topological bandstructures,defect modes at boundaries can be generated or destroyed when quenching through a topologicalphase transition. Here, we demonstrate that optomechanical arrays are a promising platform forstudying such dynamics, as their bandstructure can be tuned temporally by a control laser. Westudy the creation of nonequilibrium optical and mechanical excitations in 1D arrays, including abosonic version of the SuSchriefferHeeger model. These ideas can be transferred to other systemssuch as driven nonlinear cavity arrays.
Nonreciprocal topological phononics in optomechanical arrays
Claudio Sanavio, Vittorio Peano, André Xuereb
Physical Review B
101(8)
085108
(2020)

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We propose a platform for robust and tunable nonreciprocal phonon transport based on arrays of optomechanical microtoroids. In our approach, timereversal symmetry is broken by the interplay of photonic spinorbit coupling, engineered using a stateoftheart geometrical approach, and the optomechanical interaction. We demonstrate the topologically protected nature of this system by investigating its robustness to imperfections. This type of system could find application in phononbased information storage and signalprocessing devices.
Nonlinear dynamics of weakly dissipative optomechanical systems
Thales Figueiredo Roque, Florian Marquardt, Oleg M. Yevtushenko
New Journal of Physics (22)
013049
(2020)

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Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular and chaotic dynamics in this important regime. To analyze the dynamical attractors, we have extended the "Generalized Alignment Index" method to dissipative systems. We show that, even when chaotic motion is absent, the dynamics in the weakly dissipative regime is extremely sensitive to initial conditions. We argue that reducing dissipation allows chaotic dynamics to appear at a substantially smaller driving strength and enables various routes to chaos. We identify three generic features in weakly dissipative classical optomechanical nonlinear dynamics: the NeimarkSacker bifurcation between limit cycles and limit tori (leading to a comb of sidebands in the spectrum), the quasiperiodic route to chaos, and the existence of transient chaos.
Deterministic generation of hybrid highN N00N states with Rydberg ions trapped in microwave cavities
Naeimeh Mohseni, Carlos NavarreteBenlloch, Shahpoor Saeidian, Jonathan P Dowling
Physical Review A
101(1)
013804
(2020)

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Trapped ions are among the most promising platforms for quantum technologies. They are atthe heart of the most precise clocks and sensors developed to date, which exploit the quantumcoherence of a single electronic or motional degree of freedom of an ion. However, future highprecision quantum metrology will require the use of entangled states of several degrees of freedom.Here we propose a protocol capable of generating highN00N states where the entanglement is sharedbetween the motion of a trapped ion and an electromagnetic cavity mode, a socalled ‘hybrid’configuration. We prove the feasibility of the proposal in a platform consisting of a trapped ionexcited to its circularRydbergstate manifold, coupled to the modes of a highQ microwave cavity.This compact hybrid architecture has the advantage that it can couple to signals of very differentnature, which modify either the ion’s motion or the cavity modes. Moreover, the exact same setupcan be used right after the statepreparation phase to implement the interferometer required forquantum metrology.
2019
Field theory of monochromatic optical beams I. classical fields
Andrea Aiello
Journal of Optics
22(1)
014001
(2019)

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We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a fieldtheoretic point of view. We introduce appropriate timeindependent Lagrangian densities for which the EulerLagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energymomentum tensor and determine the continuity equations relating ``energy'' and ``momentum'' of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful firstorder Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.
Field theory of monochromatic optical beams II. Classical and quantum paraxial fields
Andrea Aiello
Journal of Optics
22(1)
014002
(2019)

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This work is the second part of an investigation aiming at the study of optical wave equations from a fieldtheoretic point of view. Here, we study classical and quantum aspects of scalar fields satisfying the paraxial wave equation. First, we determine conservation laws for energy, linear and angular momentum of paraxial fields in a classical context. Then, we proceed with the quantization of the field. Finally, we compare our result with the traditional ones.
Quantum state transfer via acoustic edge states in a 2D optomechanical array
MarcAntoine Lemonde, Vittorio Peano, Peter Rabl, Dimitris G Angelakis
New Journal of Physics
21
113030
(2019)

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We propose a novel hybrid platform where solidstate spin qubits are coupled to the acoustic modes ofa twodimensional array of optomechanical(OM)nano cavities. Previous studies of coupled OMcavities have shown that in the presence of strong optical drivingfields, the interplay between thephotonphonon interaction and their respective intercavity hopping allows the generation oftopological phases of sound and light. In particular, the mechanical modes can enter a Chern insulatorphase where the timereversal symmetry is broken. In this context, we exploit the robust acoustic edgestates as a chiral phononic waveguide and describe a state transfer protocol between spin qubitslocated in distant cavities. We analyze the performance of this protocol as a function of the relevantsystem parameters and show that a highfidelity and purely unidirectional quantum state transfer canbe implemented under experimentally realistic conditions. As a specific example, we discuss theimplementation of such topological quantum networks in diamond based OM crystals where pointdefects such as siliconvacancy centers couple to the chiral acoustic channel via strain.
Collisional quantum thermometry
Stella Seah, Stefan Nimmrichter, Daniel Grimmer, Jader P. Santos, Valerio Scarini, Gabriel T. Landi
Physical Review Letters
123(18)
180602
(2019)

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We introduce a general framework for thermometry based on collisional models, where ancillas probe thetemperature of the environment through an intermediary system. This allows for the generation of correlatedancillas even if they are initially independent. Using tools from parameter estimation theory, we show through aminimal qubit model that individual ancillas can already outperform the thermal CramerRao bound. In addition,when probed collectively, these ancillas may exhibit superlinear scalings of the Fisher information, especiallyfor weak systemancilla interactions. Our approach sets forth the notion of metrology in a sequential interactionssetting, and may inspire further advances in quantum thermometry.
Almost thermal operations: inhomogeneous reservoirs
Angeline Shu, Yu Cai, Stella Seah, Stefan Nimmrichter, Valerio Scarini
Physical Review A
100(4)
042107
(2019)

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The resource theory of thermal operations explains the state transformations that are possible ina very specific thermodynamic setting: there is only one thermal bath, auxiliary systems can onlybe in the corresponding thermal state (free states), and the interaction must commute with the freeHamiltonian (free operation). In this paper we study the mildest deviation: the reservoir particlesare subject to inhomogeneities, either in the local temperature (introducing resource states) or inthe local Hamiltonian (generating a resource operation). For small inhomogeneities, the two modelsgenerate the same channel and thus the same state transformations. However, their thermodynamicsis significantly different when it comes to work generation or to the interpretation of the “secondlaws of thermal operations”.
Accelerated adiabatic quantum gates: optimizing speed versus robustness
Hugo Ribeiro, Aashish A. Clerk
Physical Review A
100(3)
032323
(2019)

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We develop new protocols for highfidelity single qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures with highly isolated logical states, where traditional approaches are problematic; a prime example are superconducting fluxonium qubits. By using an accelerated adiabatic protocol we can enforce the desired adiabatic evolution while having gate times that are comparable to the inverse adiabatic energy gap (a scale that is ultimately set by the amount of power used in the control pulses). By modelling the effects of decoherence, we explore the tradeoff between speed and robustness that is inherent to shortcutstoadiabaticity approaches.
Macroscopicity of quantum mechanical superposition tests via hypothesis falsification
Björn Schrinski, Stefan Nimmrichter, Benjamin A. Stickler, Klaus Hornberger
Physical Review A
100(3)
032111
(2019)

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We establish an objective scheme to determine the macroscopicity of quantum mechanical superposition tests, which is based on the Bayesian hypothesis falsification of macrorealistic modificationsof quantum theory. The measure uses the raw data gathered in an experiment, taking into accountall measurement uncertainties, and can be used to directly assess any conceivable quantum test.We determine the resulting macroscopicity for three recent tests of quantum physics: doublewellinterference of BoseEinstein condensates, LeggettGarg tests with atomic random walks, and entanglement generation and readout of nanomechanical oscillators.
Kommt der künstliche Physiker?
Thomas Fösel, Florian Marquardt, Talitha Weiß
Physik in unserer Zeit
50(5)
220227
(2019)

Journal
2016 besiegte das Computerprogramm AlphaGo einen der weltbesten Go‐Spieler. Damit rückte eine technische Revolution ins Bewusstsein der breiten Öffentlichkeit: Selbstlernende künstliche neuronale Netze sind zunehmend in der Lage, Menschen bei bestimmten Aufgaben zu schlagen. Zahlreiche Anwendungen, von der Bilderkennung bis zur automatischen Übersetzung, revolutionieren momentan die Technik – und auch Physik und Astronomie bieten viele potenzielle Einsatzmöglichkeiten. In der Astronomie können neuronale Netze das automatische Klassifizieren von Galaxien übernehmen. In der Statistischen Physik sind Magnetisierungsmuster von ferro‐ oder paramagnetischen Zuständen ein Beispiel. Ein anderes Beispiel ist die Suche nach Quantenfehler‐Korrekturstrategien in zukünftigen Quantencomputern. Unsere Forschung konnte zeigen, dass künstliche neuronale Netze mittels Reinforcement Learning hier bereits eigenständig neue Korrekturstrategien entwickeln können.
Perturbation theory of optical resonances of deformed dielectric spheres
Andrea Aiello, Jack G. E. Harris, Florian Marquardt
Physical Review A
100(2)
023837
(2019)

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We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of nonHermitian operators characterized by complex eigenvalues and not normalizable eigenfunctions. We avoid these difficulties using the KapurPeierls formalism which enables us to extend the popular RayleighSchrödinger perturbation theory to the case of electromagnetic Debye's potentials describing the light fields inside and outside the nearspherical dielectric object. We find analytical formulas, valid within certain limits, for the deformationinduced first and secondorder corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones finding full agreement.
Nonexponential decay of a giant artificial atom
Gustav Andersson, Baladitya Suri, Lingzhen Guo, Thomas Aref, Per Delsing
In quantum optics, light–matter interaction has conventionally been studied using small atoms interacting with electromagnetic fields with wavelength several orders of magnitude larger than the atomic dimensions1,2. In contrast, here we experimentally demonstrate the vastly different ‘giant atom’ regime, where an artificial atom interacts with acoustic fields with wavelength several orders of magnitude smaller than the atomic dimensions. This is achieved by coupling a superconducting qubit3 to surface acoustic waves at two points with separation on the order of 100 wavelengths. This approach is comparable to controlling the radiation of an atom by attaching it to an antenna. The slow velocity of sound leads to a significant internal timedelay for the field to propagate across the giant atom, giving rise to nonMarkovian dynamics4. We demonstrate the nonMarkovian character of the giant atom in the frequency spectrum as well as nonexponential relaxation in the time domain.
Dynamically Generated Synthetic Electric Fields for Photons
Petr Zapletal, Stefan Walter, Florian Marquardt
Physical Review A
100(2)
023804
(2019)

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Static synthetic magnetic fields give rise to phenomena including the Lorentz force and the quantum Hall effect even for neutral particles, and they have by now been implemented in a variety of physical systems. Moving towards fully dynamical synthetic gauge fields allows, in addition, for backaction of the particles' motion onto the field. If this results in a timedependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise selfconsistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phononassisted photon tunneling. We study open, onedimensional arrays, where synthetic magnetic fields are absent. However, we show that synthetic electric fields can be generated dynamically, which, importantly, suppress photon transport in the array. The generation of these fields depends on the direction of photon propagation, leading to a novel mechanism for a photon diode, inducing nonlinear nonreciprocal transport via dynamical synthetic gauge fields.
Resonance inversion in a superconducting cavity coupled to artificial atoms and a microwave background
Juha Leppäkangas, Jan David Brehm, Ping Yang, Lingzhen Guo, Michael Marthaler, Alexey V. Ustinov, Martin Weides
Physical Review A
99(6)
063804
(2019)

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We demonstrate how heating of an environment can invert the line shape of a driven cavity. We consider a superconducting coplanar cavity coupled to multiple artificial atoms. The measured cavity transmission is characterized by Fanotype resonances with a shape that is continuously tunable by bias current through nearby (magnetic flux) control lines. In particular, the same dispersive shift of the microwave cavity can be observed as a peak or a dip. We find that this Fanopeak inversion is possible due to a tunable interference between a microwave transmission through a background, with reactive and dissipative properties, and through the cavity, affected by biascurrent induced heating. The background transmission occurs due to crosstalk with the multiple control lines. We show how such background can be accounted for by a Jaynes or TavisCummings model with modified boundary conditions between the cavity and transmissionline microwave fields. A dip emerges when cavity transmission is comparable with background transmission and dissipation. We find generally that resonance positions determine system energy levels, whereas resonance shapes give information on system fluctuations and dissipation.
Initialisation of single spin dressed states using shortcuts to adiabaticity
Johannes Kölbl, Arne Barfuss, Mark Kasperczyk, Lucas Thiel, Aashish Clerk, Hugo Ribeiro, Patrick Maletinsky
Physical Review Letters
122(9)
090502
(2019)

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We demonstrate the use of shortcuts to adiabaticity protocols for initialisation, readout, and coherent control of dressed states generated by closedcontour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their twolevel counterparts can offer. Our state transfer protocols yield a transfer fidelity of ~ 99.4(2) % while accelerating the transfer speed by a factor of 2.6 compared to the adiabatic approach. We show bidirectionality of the accelerated state transfer, which we employ for direct dressed state population readout after coherent manipulation in the dressed state manifold. Our results enable direct and efficient access to coherenceprotected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing.
Classically Entangled Light
Andrew Forbes, Andrea Aiello, Bienvenu Ndagano
Progress in Optics
64
99153
(2019)

Book Chapter
The concept of entanglement is so synonymous with quantum mechanics that the prefix “quantum” is often deemed unnecessary; there is after all only quantum entanglement. But the hallmark of entangled quantum states is nonseparability, a property that is not unique to the quantum world. On the contrary, nonseparability appears in many physical systems, and pertinently, in classical vector states of light: classical entanglement? Here we outline the concept of classical entanglement, highlight where it may be found, how to control and exploit it, and discuss the similarities and differences between quantum and classical entangled systems. Intriguingly, we show that quantum tools may be applied to classical systems, and likewise that classical light may be used in quantum processes. While we mostly use vectorial structured light throughout the text as our example of choice, we make it clear that the concepts outlined here may be extended beyond this with little effort, which we showcase with a few selected case studies.
2018
Cavity optomagnonics with magnetic textures: coupling a magnetic vortex to light
Jasmin Graf, Hannes Pfeifer, Florian Marquardt, Silvia ViolaKusminskiy
Physical Review B
98(24)
241406
(2018)

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Optomagnonic systems, where light couples coherently to collective excitations in magnetically ordered solids, are currently of high interest due to their potential for quantum information processing platforms at the nanoscale. Efforts so far, both at the experimental and theoretical level, have focused on systems with a homogeneous magnetic background. A unique feature in optomagnonics is however the possibility of coupling light to spin excitations on top of magnetic textures. We propose a cavityoptomagnonic system with a non homogeneous magnetic ground state, namely a vortex in a magnetic microdisk. In particular we study the coupling between optical whispering gallery modes to magnon modes localized at the vortex. We show that the optomagnonic coupling has a rich spatial structure and that it can be tuned by an externally applied magnetic field. Our results predict cooperativities at maximum photon density of the order of C≈10−2 by proper engineering of these structures.
Reinforcement Learning with Neural Networks for Quantum Feedback
Thomas Fösel, Petru Tighineanu, Talitha Weiss, Florian Marquardt
Physical Review X
8(3)
031084
(2018)

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Artificial neural networks are revolutionizing science. While the most prevalent technique involves supervised training on queries with a known correct answer, more advanced challenges often require discovering answers autonomously. In reinforcement learning, control strategies are improved according to a reward function. The power of this approach has been highlighted by spectactular recent successes, such as playing Go. So far, it has remained an open question whether neuralnetworkbased reinforcement learning can be successfully applied in physics. Here, we show how to use this method for finding quantum feedback schemes, where a networkbased "agent" interacts with and occasionally decides to measure a quantum system. We illustrate the utility by finding gate sequences that preserve the quantum information stored in a small collection of qubits against noise. This specific application will help to find hardwareadapted feedback schemes for small quantum modules while demonstrating more generally the promise of neuralnetwork based reinforcement learning in physics.
Quantum nondemolition measurement of mechanical motion quanta
Luca Dellantonio, Oleksandr Kyriienko, Florian Marquardt, Anders S. Sørensen
Nature Communications
9
3621
(2018)

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The fields of optomechanics and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to make the detection of the mechanical mode occupation difficult, typically requiring the singlephoton strongcoupling regime. Here, we propose and analyse an electromechanical setup, which allows us to overcome this limitation and resolve the energy levels of a mechanical oscillator. We found that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.
Phonon Decoherence of Quantum Dots in Photonic Structures: Broadening of the ZeroPhonon Line and the Role of Dimensionality
Petru Tighineanu, C. L. Dreeßen, C. Flindt, P. Lodahl, A. S. Sorensen
Physical Review Letters
120(25)
257401
(2018)

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We develop a general microscopic theory describing the phonon decoherence of quantum dots and indistinguishability of the emitted photons in photonic structures. The coherence is found to depend fundamentally on the dimensionality of the structure resulting in vastly different performance for quantum dots embedded in a nanocavity (0D), waveguide (1D), slab (2D), or bulk medium (3D). In bulk, we find a striking temperature dependence of the dephasing rate scaling as T11 implying that phonons are effectively “frozen out” for T≲4 K. The phonon density of states is strongly modified in 1D and 2D structures leading to a linear temperature scaling for the dephasing strength. The resulting impact on the photon indistinguishability can be important even at subKelvin temperatures. Our findings provide a comprehensive understanding of the fundamental limits to photon indistinguishability in photonic structures.
Light polarization measurements in tests of macrorealism
Eugenio Roldan, Johannes Kofler, Carlos NavarreteBenlloch
Physical Review A
97
062117
(2018)

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According to the world view of macrorealism, the properties of a given system exist prior to and independent of measurement, which is incompatible with quantum mechanics. Leggett and Garg put forward a practical criterion capable of identifying violations of macrorealism, and so far experiments performed on microscopic and mesoscopic systems have always agreed with quantum mechanics. However, a macrorealist can always assign the cause of such violations to the perturbation that measurements effect on such small systems, and hence a definitive test would require using noninvasive measurements, preferably on macroscopic objects, where such measurements seem more plausible. However, the generation of truly macroscopic quantum superposition states capable of violating macrorealism remains a big challenge. In this work we propose a setup that makes use of measurements on the polarization of light, a property that has been extensively manipulated both in classical and quantum contexts, hence establishing the perfect link between the microscopic and macroscopic worlds. In particular, we use LeggettGarg inequalities and the criterion of no signaling in time to study the macrorealistic character of light polarization for different kinds of measurements, in particular with different degrees of coarse graining. Our proposal is noninvasive for coherent input states by construction. We show for states with welldefined photon number in two orthogonal polarization modes, that there always exists a way of making the measurement sufficiently coarse grained so that a violation of macrorealism becomes arbitrarily small, while sufficiently sharp measurements can always lead to a significant violation.
Quantum theory of continuum optomechanics
Peter Rakich, Florian Marquardt
New Journal of Physics
20
045005
(2018)

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We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavityoptomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a realspace picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. Among other examples, we analyze the 'strong coupling regime' of continuum optomechanics that may be accessible in future experiments.
Active locking and entanglement in type II optical parametric oscillators
Joaquín RuizRivas, Germán J. de Valcarcel, Carlos NavarreteBenlloch
New Journal of Physics
20
023004
(2018)

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Type II optical parametric oscillators are amongst the highestquality sources of quantumcorrelated light. In particular, when pumped above threshold, such devices generate a pair of bright orthogonallypolarized beams with strong continuousvariable entanglement. However, these sources are of limited practical use, because the entangled beams emerge with different frequencies and a diffusing phase difference. It has been proven that the use of an internal waveplate coupling the modes with orthogonal polarization is capable of locking the frequencies of the emerging beams to half the pump frequency, as well as reducing the phasedifference diffusion, at the expense of reducing the entanglement levels. In this work we characterize theoretically an alternative locking mechanism: the injection of a laser at half the pump frequency. Apart from being less invasive, this method should allow for an easier realtime experimental control. We show that such an injection is capable of generating the desired phase locking between the emerging beams, while still allowing for large levels of entanglement. Moreover, we find an additional region of the parameter space (at relatively large injections) where a mode with well defined polarization is in a highly amplitudesqueezed state.
Snowflake phononic topological insulator at the nanoscale
Christian Brendel, Vittorio Peano, Oskar Painter, Florian Marquardt
Physical Review B (Rapid Communications)
97(2)
020102
(2018)

Journal

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We show how the snowflake phononic crystal structure, which recently has been realized experimentally, can be turned into a topological insulator for mechanical waves. This idea, based purely on simple geometrical modifications, could be readily implemented on the nanoscale.
Scalable Ion Trap Architecture for Universal Quantum Computation by Collisions
We propose a scalable ion trap architecture for universal quantum computation, which is composed of an array of ion traps with one ion confined in each trap. The neighboring traps are designed capable of merging into one single trap. The universal twoqubit SWAP−−−−−−√ gate is realized by direct collision of two neighboring ions in the merged trap, which induces an effective spinspin interaction between two ions. We find that the collisioninduced spinspin interaction decreases with the third power of two ions' trapping distance. Even with a 200 μm trapping distance between atomic ions in Paul traps, it is still possible to realize a twoqubit gate operation with speed in 0.1 kHz regime. The speed can be further increased up into 0.1 MHz regime using electrons with 10 mm trapping distance in Penning traps.
2017
Cavity optomechanics in a levitated helium drop
L. Childress, M. P. Schmidt, A. D. Kashkanova, C. D. Brown, G. I. Harris, Andrea Aiello, Florian Marquardt, J. G. E. Harris
Physical Review A
96(6)
063842
(2017)

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We describe a proposal for a type of optomechanical system based on a drop of liquid helium that ismagnetically levitated in vacuum. In the proposed device, the drop would serve three roles: its optical whisperinggallery modes would provide the optical cavity, its surface vibrations would constitute the mechanical element, and evaporation of He atoms from its surface would provide continuous refrigeration. We analyze the feasibility of such a system in light of previous experimental demonstrations of its essential components: magnetic levitation of mmscale and cmscale drops of liquid He, evaporative cooling of He droplets in vacuum, and coupling to highquality optical whisperinggallery modes in a wide range of liquids. We find that the combination of these features could result in a device that approaches the singlephoton strongcoupling regime, due to the high optical quality factors attainable at low temperatures. Moreover, the system offers a unique opportunity to use optical techniques to study the motion of a superfluid that is freely levitating in vacuum (in the case of He4). Alternatively, for a normal fluid drop of He3, we propose to exploit the coupling between the drop's rotations and vibrations to perform quantum nondemolition measurements of angular momentum.
L lines, C points and Chern numbers: understanding band structure topology using polarization fields
Thomas Fösel, Vittorio Peano, Florian Marquardt
New Journal of Physics
19
115013
(2017)

Journal

PDF
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an important quantity in this field. Another example of topology, in polarization physics, are polarization singularities, called L lines and C points. By establishing a connection between these two theories, we develop a novel technique to visualize and potentially measure the Chern number: it can be expressed either as the winding of the polarization azimuth along L lines in reciprocal space, or in terms of the handedness and the index of the C points. For mechanical systems, this is directly connected to the visible motion patterns.
General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles
Carlos NavarreteBenlloch, Talitha Weiss, Stefan Walter, Germán J. de Valcarcel
Physical Review Letters
119(13)
133601
(2017)

Journal

PDF
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantumoptical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical longtime solution is time dependent, a most prominent example being spontaneous limitcycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (manybody) systems.
Unraveling beam selfhealing
Andrea Aiello, Girish S. Agarwal, Martin Paur, Bohumil Stoklasa, Zdenek Hradil, Jaroslav Rehacek, Pablo de la Hoz, Gerd Leuchs, Luis L. SanchezSoto
Optics Express
25(16)
1914719157
(2017)

Journal

PDF
We show that, contrary to popular belief, diffractionfree beams not only may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the selfreconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the selfreconstruction ability of a beam via a newly established degree of selfhealing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon ShackHartmann wave front reconstruction. We believe that these results can open new avenues in this field. (C) 2017 Optical Society of America
From KardarParisiZhang scaling to explosive desynchronization in arrays of limitcycle oscillators
Roland Lauter, Aditi Mitra, Florian Marquardt
Physical Review E
96(1)
012220
(2017)

Journal

PDF
Phase oscillator lattices subject to noise are one of the most fundamental systems in nonequilibrium physics. We have discovered a dynamical transition which has a significant impact on the synchronization dynamics in such lattices, as it leads to an explosive increase of the phase diffusion rate by orders of magnitude. Our analysis is based on the widely applicable KuramotoSakaguchi model, with local couplings between oscillators. For onedimensional lattices, we observe the universal evolution of the phase spread that is suggested by a connection to the theory of surface growth, as described by the KardarParisiZhang (KPZ) model. Moreover, we are able to explain the dynamical transition both in one and two dimensions by connecting it to an apparent finitetime singularity in a related KPZ lattice model. Our findings have direct consequences for the frequency stability of coupled oscillator lattices.Phase oscillator lattices subject to noise are one of the most fundamental systems in nonequilibrium physics. We have discovered a dynamical transition which has a significant impact on the synchronization dynamics in such lattices, as it leads to an explosive increase of the phase diffusion rate by orders of magnitude. Our analysis is based on the widely applicable KuramotoSakaguchi model, with local couplings between oscillators. For onedimensional lattices, we observe the universal evolution of the phase spread that is suggested by a connection to the theory of surface growth, as described by the KardarParisiZhang (KPZ) model. Moreover, we are able to explain the dynamical transition both in one and two dimensions by connecting it to an apparent finitetime singularity in a related KPZ lattice model. Our findings have direct consequences for the frequency stability of coupled oscillator lattices.
Synchronization of an optomechanical system to an external drive
Ehud Amitai, Niels Loerch, Andreas Nunnenkamp, Stefan Walter, Christoph Bruder
Physical Review A
95(5)
053858
(2017)

Journal

PDF
Optomechanical systems driven by an effective bluedetuned laser can exhibit selfsustained oscillations of the mechanical oscillator. These selfoscillations are a prerequisite for the observation of synchronization. Here, we study the synchronization of the mechanical oscillations to an external reference drive. We study two cases of reference drives: (1) an additional laser applied to the optical cavity; (2) a mechanical drive applied directly to the mechanical oscillator. Starting from a master equation description, we derive a microscopic Adler equation for both cases, valid in the classical regime in which the quantum shot noise of the mechanical selfoscillator does not play a role. Furthermore, we numerically show that, in both cases, synchronization arises also in the quantum regime. The optomechanical system is therefore a good candidate for the study of quantum synchronization.
Quantumcoherent phase oscillations in synchronization
Talitha Weiss, Stefan Walter, Florian Marquardt
Physical Review A
95(4)
041802
(2017)

Journal

PDF
Recently, several studies have investigated synchronization in quantummechanical limitcycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped and therefore incoherent. We show that there exist regimes of underdamped and even quantumcoherent phase motion, opening up new possibilities to study quantum synchronization dynamics. To this end, we investigate the Van der Pol oscillator (a paradigm for a selfoscillating system) synchronized to an external drive. We derive an effective quantum model which fully describes the regime of underdamped phase motion and additionally allows us to identify the quality of quantum coherence. Finally, we identify quantum limit cycles of the phase itself.
ManyParticle Dephasing after a Quench
Thomas Kiendl, Florian Marquardt
Physical Review Letters
118(13)
130601
(2017)

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After a quench in a quantum manybody system, expectation values tend to relax towards longtime averages. However, temporal fluctuations remain in the longtime limit, and it is crucial to study the suppression of these fluctuations with increasing system size. The particularly important case of nonintegrable models has been addressed so far only by numerics and conjectures based on analytical bounds. In this work, we are able to derive analytical predictions for the temporal fluctuations in a nonintegrable model (the transverse Ising chain with extra terms). Our results are based on identifying a dynamical regime of "manyparticle dephasing,"where quasiparticles do not yet relax but fluctuations are nonetheless suppressed exponentially by weak integrability breaking.
Pseudomagnetic fields for sound at the nanoscale
Christian Brendel, Vittorio Peano, Oskar J. Painter, Florian Marquardt
Proceedings of the National Academy of Sciences of the United States of America
114(17)
E3390E3395

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There is a growing effort in creating chiral transport of sound waves. However, most approaches so far have been confined to the macroscopic scale. Here, we propose an approach suitable to the nanoscale that is based on pseudomagnetic fields. These pseudomagnetic fields for sound waves are the analogue of what electrons experience in strained graphene. In our proposal, they are created by simple geometrical modifications of an existing and experimentally proven phononic crystal design, the snowflake crystal. This platform is robust, scalable, and wellsuited for a variety of excitation and readout mechanisms, among them optomechanical approaches.
Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering
Kejie Fang, Jie Luo, Anja Metelmann, Matthew H. Matheny, Florian Marquardt, Aashish A. Clerk, Oskar Painter
Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiationpressureinduced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break timereversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phasecorrelated laser light results in a synthetic magnetic flux, which, in combination with dissipative coupling to the mechanical bath, leads to nonreciprocal transport of photons with 35 dB of isolation. Additionally, optical pumping with bluedetuned light manifests as a particle nonconserving interaction between photons and phonons, resulting in directional optical amplification of 12 dB in the isolator throughdirection. These results suggest the possibility of using optomechanical circuits to create a more general class of nonreciprocal optical devices, and further, to enable new topological phases for both light and sound on a microchip.
Anderson localization of composite excitations in disordered optomechanical arrays
Thales Figueiredo Roque, Vittorio Peano, Oleg M. Yevtushenko, Florian Marquardt
New Journal of Physics
19
013006
(2017)

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Optomechanical (OMA) arrays are a promising future platform for studies of transport, manybody dynamics, quantum control and topological effects in systems of coupled photon and phonon modes. We introduce disordered OMA arrays, focusing on features of Anderson localization of hybrid photonphonon excitations. It turns out that these represent a unique disordered system, where basic parameters can be easily controlled by varying the frequency and the amplitude of an external laser field. We show that the twospecies setting leads to a nontrivial frequency dependence of the localization length for intermediate laser intensities. This could serve as a convincing evidence of localization in a nonequilibrium dissipative situation.
Noncritical generation of nonclassical frequency combs via spontaneous rotational symmetry breaking
Carlos NavarreteBenlloch, Giuseppe Patera, Germán J. de Valcarcel
Physical Review A
96(4)
043801
(2017)

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Synchronously pumped optical parametric oscillators (SPOPOs) are optical cavities driven by modelocked lasers, and containing a nonlinear crystal capable of downconverting a frequency comb to lower frequencies. SPOPOs have received a lot of attention lately because their intrinsic multimode nature makes them compact sources of quantum correlated light with promising applications in modern quantum information technologies. In this work we show that SPOPOs are also capable of accessing the challenging and interesting regime where spontaneous symmetry breaking confers strong nonclassical properties to the emitted light, which has eluded experimental observation so far. Apart from opening the possibility of studying experimentally this elusive regime of dissipative phase transitions, our predictions will have a practical impact, since we show that spontaneous symmetry breaking provides a specific spatiotemporal mode with large quadrature squeezing for any value of the system parameters, turning SPOPOs into robust sources of highly nonclassical light above threshold.
Linear and angular momenta in tightly focused vortex segmented beams of light
Martin Neugebauer, Andrea Aiello, Peter Banzer
Chinese Optics Letters
15(3)
030003
(2017)

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We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex threedimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex chargedependent relative shift of the energy density and linear momentum density.
2016
Topological phase transitions and chiral inelastic transport induced by
the squeezing of light
Vittorio Peano, Martin Houde, Christian Brendel, Florian Marquardt, Aashish A. Clerk
Nature Communications
7
10779
(2016)

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There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a wellknown fermionic singleparticle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by nontrivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particleconserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits.
Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the
3 dB Limit
C. U. Lei, A. J. Weinstein, J. Suh, E. E. Wollman, A. Kronwald, F. Marquardt, A. A. Clerk, K. C. Schwab
Physical Review Letters
117(10)
100801
(2016)

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We use a reservoir engineering technique based on twotone driving to generate and stabilize a quantum squeezed state of a micronscale mechanical oscillator in a microwave optomechanical system. Using an independent backactionevading measurement to directly quantify the squeezing, we observe 4.7±0.9 dB of squeezing below the zeropoint level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.
Topological Quantum Fluctuations and Traveling Wave Amplifiers
Vittorio Peano, Martin Houde, Florian Marquardt, Aashish A. Clerk
Physical Review X
6(4)
041026
(2016)

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It is now well established that photonic systems can exhibit topological energy bands. Similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is protected against backscattering. While it is understood how classical signals can propagate under these conditions, it is an outstanding important question how the quantum vacuum fluctuations of the electromagnetic field get modified in the presence of a topological band structure. We address this challenge by exploring a setting where a nonzero topological invariant guarantees the presence of a parametrically unstable chiral edge mode in a system with boundaries, even though there are no bulkmode instabilities. We show that one can exploit this to realize a topologically protected, quantumlimited traveling wave parametric amplifier. The device is naturally protected against both internal losses and backscattering; the latter feature is in stark contrast to standard traveling wave amplifiers. This adds a new example to the list of potential quantum devices that profit from topological transport.
Coupled spinlight dynamics in cavity optomagnonics
Silvia ViolaKusminskiy, Hong X. Tang, Florian Marquardt
Physical Review A
94(3)
033821
(2016)

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Experiments during the past 2 years have shown strong resonant photonmagnon coupling in microwave cavities, while coupling in the optical regime was demonstrated very recently for the first time. Unlike with microwaves, the coupling in optical cavities is parametric, akin to optomechanical systems. This line of research promises to evolve into a new field of optomagnonics, aimed at the coherent manipulation of elementary magnetic excitations in solidstate systems by optical means. In this work we derive the microscopic optomagnonic Hamiltonian. In the linear regime the system reduces to the wellknown optomechanical case, with remarkably large coupling. Going beyond that, we study the optically induced nonlinear classical dynamics of a macrospin. In the fastcavity regime we obtain an effective equation of motion for the spin and show that the light field induces a dissipative term reminiscent of Gilbert damping. The induced dissipation coefficient, however, can change sign on the Bloch sphere, giving rise to selfsustained oscillations. When the full dynamics of the system is considered, the system can enter a chaotic regime by successive period doubling of the oscillations.
Classical dynamical gauge fields in optomechanics
Stefan Walter, Florian Marquardt
New Journal of Physics
18
113029
(2016)

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Artificial gauge fields for neutral particles such as photons, recently attracted a lot of attention in various fields ranging from photonic crystals to ultracold atoms in optical lattices to optomechanical arrays. Here we point out that, among all implementations of gauge fields, the optomechanical setting allows for the most natural extension where the gauge field becomes dynamical. The mechanical oscillation phases determine the effective artificial magnetic field for the photons, and once these phases are allowed to evolve, they respond to the flow of photons in the structure. We discuss a simple threesite model where we identify four different regimes of the gaugefield dynamics. Furthermore, we extend the discussion to a twodimensional lattice. Our proposed scheme could for instance be implemented using optomechanical crystals.
Noiseinduced transitions in optomechanical synchronization
Talitha Weiss, Andreas Kronwald, Florian Marquardt
New Journal of Physics
18
013043
(2016)

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We study how quantum and thermal noise affects synchronization of two optomechanical limitcycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either inphase or antiphase. Taking into account the fundamental quantum noise, we find a regime where fluctuations drive transitions between these classical synchronization states. We investigate how this 'mixed' synchronization regime emerges from the noiseless system by studying the classicaltoquantum crossover and we show how the time scales of the transitions vary with the effective noise strength. In addition, we compare the effects of thermal noise to the effects of quantum noise.
Entanglement rate for Gaussian continuous variable beams
Zhi Jiao Deng, Steven J. M. Habraken, Florian Marquardt
New Journal of Physics
18
063022
(2016)

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We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators. This expression is especially useful for situations where the source emits an arbitrary frequency spectrum, e.g. when cavities are involved. To exemplify its meaning and potential, we apply it to a fourmode optomechanical setup that enables the simultaneous up and downconversion of photons from a drive laser into entangled photon pairs. This setup is efficient in that both the drive and the optomechanical up and downconversion can be fully resonant.
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