Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable deep-learning approach that would enable the rapid prediction of spatial densities for strongly correlated systems in arbitrary potentials. In this work, we present a straightforward scheme, where we learn to predict densities using convolutional neural networks trained on random potentials. While we demonstrate this approach in 1D and 2D lattice models using data from numerical techniques like Quantum Monte Carlo, it is directly applicable as well to training data obtained from experimental quantum simulators. We train networks that can predict the densities of multiple observables simultaneously and that can predict for a whole class of many-body lattice models, for arbitrary system sizes. We show that our approach can handle well the interplay of interference and interactions and the behaviour of models with phase transitions in inhomogeneous situations, and we also illustrate the ability to solve inverse problems, finding a potential for a desired density.
Certification of Genuine Multipartite Entanglement with General and Robust Device-independent Witnesses
Chao Zhang,
Wen-Hao Zhang,
Pavel Sekatski,
Jean-Daniel Bancal,
Michael Zwerger,
Peng Yin,
Gong-Chu Li,
Xing-Xiang Peng,
Lei Chen, et al.
Physical Review Letters
129
190503
(2022)
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Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
Theory of Laser-Assisted Nuclear Excitation by Electron Capture
The interplay of x-ray ionization and atomic and nuclear degrees of freedom is investigated theoretically in the process of laser-assisted nuclear excitation by electron capture. In the resonant process of nuclear excitation by electron capture, an incident electron recombines into a vacancy in the atomic shell with simultaneous nuclear excitation. Here we investigate the specific scenario in which the free electron and the required atomic shell hole<br>are generated by an x-ray free electron laser pulse. We develop a theoretical description based on the Feshbach projection operator formalism and consider numerically experimental scenarios at the SACLA x-ray free electron laser. Our numerical results for excitation of the 29.2 keV nuclear state in <sub>229</sub>Th and the 14.4 keV Mössbauer transition in <sub>57</sub>Fe show low excitation rates but strong enhancement with respect to direct two photon nuclear excitation.
Nonreciprocal and chiral single-photon scattering for giant atoms
Yao-Tong Chen,
Lei Du,
Lingzhen Guo,
Zhihai Wang,
Yan Zhang,
Yong Li,
Jin-Hui Wu
Communications Physics
5
215
(2022)
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Quantum optics with giant atoms has provided a new paradigm to study photon scatterings. In this work, we investigate the nontrivial single-photon scattering properties of giant atoms being an effective platform to realize nonreciprocal and chiral quantum optics. For two-level giant atoms, we identify the condition for nonreciprocal transmission: the external atomic dissipation is further required other than the breaking of time-reversal symmetry by local coupling phases. Especially, in the non-Markovian regime, unconventional revival peaks periodically appear in the reflection spectrum. To explore more interesting scattering behaviors, we extend the two-level giant-atom system to Δ-type and ∇ -type three-level giant atoms coupled to double waveguides with different physical mechanisms to realize nonreciprocal and chiral scatterings. Our proposed giant-atom structures have potential applications of high-efficiency targeted routers that can transport single photons to any desired port deterministically and circulators that can transport single photons between four ports in a cyclic way.
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. Feedback-based 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 quantum-non-demolition 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.
Topological phonon transport in an optomechanical system
Hengjiang Ren,
Tirth Shah,
Hannes Pfeifer,
Christian Brendel,
Vittorio Peano,
Florian Marquardt,
Oskar Painter
Nature Communications
13
3476
(2022)
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Recent advances in cavity-optomechanics 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 small-scale optomechanical circuits capable of on-chip 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 cavity-optomechanical elements. Using sensitive, spatially resolved optical read-out 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 non-reciprocal elements may be implemented. Owing to the broadband character of the topological channels, the control of the flow of heat-carrying phonons, albeit at cryogenic temperatures, may also be envisioned.
Deep Learning of Quantum Many-Body Dynamics via Random Driving
Naeimeh Mohseni,
Thomas Fösel,
Lingzhen Guo,
Carlos Navarrete-Benlloch,
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 quantummany-body system, where the training is based purely on monitoring expectation values of observables under random driving. The trained recurrent network is able to produce accurate predictions for driving 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 learn the 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 many-body 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 times longer than those it has been trained on, as well as to the infinite-system-size limit.
TMM-Fast: A Transfer Matrix Computation Package for Multilayer Thin-Film Optimization: tutorial
Alexander Luce,
Ali Mahdavi,
Florian Marquardt,
Heribert Wankerl
Journal of the Optical Society of America A-Optics Image Science and Vision
39
(6)
1007-1013
(2022)
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Achieving the desired optical response from a multilayer thin-film structure over a broad range of wavelengths and angles of incidence can be challenging. An advanced thin-film structure can consist of multiple materials with different thicknesses and numerous layers. Design and optimization of complex thin-film structures with multiple variables is a computationally heavy problem that is still under active research. To enable fast and easy experimentation with new optimization techniques, we propose the Python package Transfer Matrix Method - Fast (TMM-Fast), which enables parallelized computation of reflection and transmission of light at different angles of incidence and wavelengths through the multilayer thin film. By decreasing computational time, generating datasets for machine learning becomes feasible, and evolutionary optimization can be used effectively. Additionally, the subpackage TMM-Torch allows us to directly compute analytical gradients for local optimization by using PyTorch Autograd functionality. Finally, an OpenAI Gym environment is presented, which allows the user to train new reinforcement learning agents on the problem of finding multilayer thin-film configurations.
Observing polarization patterns in the collective motion of nanomechanical arrays
Juliane Doster,
Tirth Shah,
Thomas Fösel,
Philipp Paulitschke,
Florian Marquardt,
Eva Weig
Nature Communications
13
2478
(2022)
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In recent years, nanomechanics has evolved into a mature field, with wide-ranging 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 two-dimensional 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.
Ising machines: Hardware solvers for combinatorial optimization problems
Naeimeh Mohseni,
Peter McMahon,
Tim Byrnes
Nature Reviews Physics
4
363-379
(2022)
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Ising machines are hardware solvers that aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because any problem in the complexity class NP can be formulated as an Ising problem with only polynomial overhead, and thus a scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications. We survey the status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors and digital hardware accelerators; dynamical systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses.
Modern applications of machine learning in quantum sciences
Anna Dawid,
Julian Arnold,
Borja Requena,
Alexander Gresch,
Marcin Płodzień,
Kaelan Donatella,
Kim Nicoli,
Paolo Stornati,
Rouven Koch, et al.
In this book, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.
Directional emission of white light via selective amplification of photon recycling and Bayesian optimization of multi-layer thin films
Heribert Wankerl,
Christopher Wiesmann,
Laura Kreiner,
Rainer Butendeich,
Alexander Luce,
Sandra Sobczyk,
Maike Lorena Stern,
Elmar Wolfgang Lang
Over the last decades, light-emitting diodes (LED) have replaced common light bulbs in almost every application, from flashlights in smartphones to automotive headlights. Illuminating nightly streets requires LEDs to emit a light spectrum that is perceived as pure white by the human eye. The power associated with such a white light spectrum is not only distributed over the contributing wavelengths but also over the angles of vision. For many applications, the usable light rays are required to exit the LED in forward direction, namely under small angles to the perpendicular. In this work, we demonstrate that a specifically designed multi-layer thin film on top of a white LED increases the power of pure white light emitted in forward direction. Therefore, the deduced multi-objective optimization problem is reformulated via a real-valued physics-guided objective function that represents the hierarchical structure of our engineering problem. Variants of Bayesian optimization are employed to maximize this non-deterministic objective function based on ray tracing simulations. Eventually, the investigation of optical properties of suitable multi-layer thin films allowed to identify the mechanism behind the increased directionality of white light: angle and wavelength selective filtering causes the multi-layer thin film to play ping pong with rays of light.
These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University, though the first draft was created for a previous course I taught at the University of Erlangen-Nuremberg in Germany. It has been designed for students who have only had basic training on quantum mechanics, and hence, the course is suited for people at all levels. The notes are a work in progress, meaning that some proofs and many figures are still missing. However, I've tried my best to write everything in such a way that a reader can follow naturally all arguments and derivations even with these missing bits. Quantum optics treats the interaction between light and matter. We may think of light as the optical part of the electromagnetic spectrum, and matter as atoms. However, modern quantum optics covers a wild variety of systems, including superconducting circuits, confined electrons, excitons in semiconductors, defects in solid state, or the center-of-mass motion of micro-, meso-, and macroscopic systems. Moreover, quantum optics is at the heart of the field of quantum information. The ideas and experiments developed in quantum optics have also allowed us to take a fresh look at many-body problems and even high-energy physics. In addition, quantum optics holds the promise of testing foundational problems in quantum mechanics as well as physics beyond the standard model in table-sized experiments. Quantum optics is therefore a topic that no future researcher in quantum physics should miss.
Phase Space Crystal Vibrations: Chiral Edge States with Preserved Time-reversal Symmetry
Lingzhen Guo,
Vittorio Peano,
Florian Marquardt
Physical Review B
105
(9)
094301
(2022)
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Chiral transport along edge channels in Chern insulators represents the most robust version of topological transport, but it usually requires breaking of the physical time-reversal 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 phase-space crystal of atoms, which can be generated by periodic driving of a one-dimensional interacting quantum gas, we show that the resulting vibrational lattice waves have topological properties. Our work provides a new platform to study topological many-body physics in dynamical systems.
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Contact
Theory Division Prof. Florian Marquardt
Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
