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 field-theoretic 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.
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 field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange 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 energy-momentum tensor and determine the continuity equations relating ``energy'' and ``momentum'' of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order 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.
Quantum state transfer via acoustic edge states in a 2D optomechanical array
Marc-Antoine 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 solid-state spin qubits are coupled to the acoustic modes ofa two-dimensional array of optomechanical(OM)nano cavities. Previous studies of coupled OMcavities have shown that in the presence of strong optical drivingfields, the interplay between thephoton-phonon interaction and their respective inter-cavity hopping allows the generation oftopological phases of sound and light. In particular, the mechanical modes can enter a Chern insulatorphase where the time-reversal 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 high-fidelity 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 silicon-vacancy 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
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 Cramer-Rao bound. In addition,when probed collectively, these ancillas may exhibit superlinear scalings of the Fisher information, especiallyfor weak system-ancilla 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 high-fidelity 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 shortcuts-to-adiabaticity 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 super-position 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: double-wellinterference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and en-tanglement generation and read-out of nanomechanical oscillators.
Kommt der künstliche Physiker?
Thomas Fösel,
Florian Marquardt,
Talitha Weiß
Physik in unserer Zeit
50
(5)
220-227
(2019)
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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 non-Hermitian operators characterized by complex eigenvalues and not normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism which enables us to extend the popular Rayleigh-Schrödinger perturbation theory to the case of electromagnetic Debye's potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first- and second-order 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.
Non-exponential 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 time-delay for the field to propagate across the giant atom, giving rise to non-Markovian dynamics4. We demonstrate the non-Markovian character of the giant atom in the frequency spectrum as well as non-exponential 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 time-dependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise self-consistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phonon-assisted photon tunneling. We study open, one-dimensional 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 Fano-type 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 Fano-peak 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 bias-current 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 Tavis-Cummings model with modified boundary conditions between the cavity and transmission-line 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
We demonstrate the use of shortcuts to adiabaticity protocols for initialisation, readout, and coherent control of dressed states generated by closed-contour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their two-level 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 bi-directionality 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 coherence-protected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing.
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.
Contact
Theory Division Prof. Florian Marquardt
Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
