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Symmetry
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Symmetry in Quantum Optics Models
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Symmetry in Quantum Optics Models

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 July 2019) | Viewed by 26349

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Lucas Lamata

E-Mail Website
Guest Editor
Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41080 Sevilla, Spain
Interests: quantum optics; quantum information; theoretical physics; quantum simulations; trapped ion physics; superconducting circuits; entanglement classification; entanglement generation; quantum biomimetics; artificial intelligence; machine learning; embedding quantum simulators; penning traps; quantum photonics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Prototypical quantum optics models, such as for example the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models, are commonly analyzed with diverse techniques, including analytical exact solutions, mean-field theory, exact diagonalization, and the like. The analysis of these systems strongly depends on their symmetries, ranging, e.g., from a U(1) group in the Jaynes–Cummings model to a Z2 symmetry in the full-fledged quantum Rabi model.

In recent years, novel regimes of light–matter interactions, namely, the ultrastrong and deep-strong coupling regimes, have been attracting an increasing amount of interest. The quantum Rabi and Dicke models in these exotic regimes present new features, such as collapses and revivals of the population, bounces of photon-number wave packets, as well as the breakdown of the rotating-wave approximation. Symmetries also play an important role in these regimes and will additionally change depending on whether the few- or many-qubit systems considered have associated inhomogeneous or equal couplings to the bosonic mode.

Moreover, there is a growing interest in proposing and carrying out quantum simulations of these models in quantum platforms such as, e.g., trapped ions, superconducting circuits, and quantum photonics.

In this Special Issue, we intend to gather a series of articles related to symmetry in quantum optics models, possibly including, but not exclusively, the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models. We will also consider their generalizations to, e.g., inhomogeneous light–matter couplings, bias terms, time-dependent couplings, as well as all possible regimes of the light–matter interaction. We welcome papers on mathematical physics, related either to spectral analysis or time dynamics, as well as more applied articles with proposals for implementations of and/or experiments with these or related models in quantum platforms, such as trapped ions, superconducting circuits, and quantum photonics.

Prof. Dr. Lucas Lamata
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum Rabi model
  • Dicke model
  • Mathematical physics
  • Quantum simulations
  • Trapped ions
  • Superconducting circuits
  • Quantum photonics
  • Ultrastrong light–matter coupling regime

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Published Papers (6 papers)

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Editorial

Jump to: Research

2 pages, 152 KiB  
Editorial
Symmetry in Quantum Optics Models
by Lucas Lamata
Symmetry 2019, 11(10), 1310; https://doi.org/10.3390/sym11101310 - 18 Oct 2019
Cited by 1 | Viewed by 2176
Abstract
This editorial introduces the successful invited submissions [...] Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)

Research

Jump to: Editorial

13 pages, 1132 KiB  
Article
Symmetries in the Quantum Rabi Model
by Daniel Braak
Symmetry 2019, 11(10), 1259; https://doi.org/10.3390/sym11101259 - 9 Oct 2019
Cited by 35 | Viewed by 4788
Abstract
The quantum Rabi model is the simplest and most important theoretical description of light–matter interaction for all experimentally accessible coupling regimes. It can be solved exactly and is even integrable due to a discrete symmetry, the Z 2 or parity symmetry. All qualitative [...] Read more.
The quantum Rabi model is the simplest and most important theoretical description of light–matter interaction for all experimentally accessible coupling regimes. It can be solved exactly and is even integrable due to a discrete symmetry, the Z 2 or parity symmetry. All qualitative properties of its spectrum, especially the differences to the Jaynes–Cummings model, which possesses a larger, continuous symmetry, can be understood in terms of the so-called “G-functions” whose zeroes yield the exact eigenvalues of the Rabi Hamiltonian. The special type of integrability appearing in systems with discrete degrees of freedom is responsible for the absence of Poissonian level statistics in the spectrum while its well-known “Juddian” solutions are a natural consequence of the structure of the G-functions. The poles of these functions are known in closed form, which allows drawing conclusions about the global spectrum. Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
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16 pages, 1439 KiB  
Article
Behavior of Floquet Topological Quantum States in Optically Driven Semiconductors
by Andreas Lubatsch and Regine Frank
Symmetry 2019, 11(10), 1246; https://doi.org/10.3390/sym11101246 - 4 Oct 2019
Cited by 23 | Viewed by 4586
Abstract
Spatially uniform optical excitations can induce Floquet topological band structures within insulators which can develop similar or equal characteristics as are known from three-dimensional topological insulators. We derive in this article theoretically the development of Floquet topological quantum states for electromagnetically driven semiconductor [...] Read more.
Spatially uniform optical excitations can induce Floquet topological band structures within insulators which can develop similar or equal characteristics as are known from three-dimensional topological insulators. We derive in this article theoretically the development of Floquet topological quantum states for electromagnetically driven semiconductor bulk matter and we present results for the lifetime of these states and their occupation in the non-equilibrium. The direct physical impact of the mathematical precision of the Floquet-Keldysh theory is evident when we solve the driven system of a generalized Hubbard model with our framework of dynamical mean field theory (DMFT) in the non-equilibrium for a case of ZnO. The physical consequences of the topological non-equilibrium effects in our results for correlated systems are explained with their impact on optoelectronic applications. Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
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21 pages, 2740 KiB  
Article
Spin-Boson Model as A Simulator of Non-Markovian Multiphoton Jaynes-Cummings Models
by Ricardo Puebla, Giorgio Zicari, Iñigo Arrazola, Enrique Solano, Mauro Paternostro and Jorge Casanova
Symmetry 2019, 11(5), 695; https://doi.org/10.3390/sym11050695 - 20 May 2019
Cited by 12 | Viewed by 5910
Abstract
The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the [...] Read more.
The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms. Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
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20 pages, 3361 KiB  
Article
Parity-Assisted Generation of Nonclassical States of Light in Circuit Quantum Electrodynamics
by Francisco A. Cárdenas-López, Guillermo Romero, Lucas Lamata, Enrique Solano and Juan Carlos Retamal
Symmetry 2019, 11(3), 372; https://doi.org/10.3390/sym11030372 - 13 Mar 2019
Cited by 4 | Viewed by 4679
Abstract
We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of N extended cavities and an ultrastrongly coupled light–matter system. Under specific resonance conditions, our method generates, [...] Read more.
We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of N extended cavities and an ultrastrongly coupled light–matter system. Under specific resonance conditions, our method generates, in a deterministic manner, product states of uncorrelated photon pairs, Bell states, and W states in different modes on the extended cavities. Furthermore, the numerical simulations show that the generation scheme exhibits a collective effect which decreases the generation time in the same proportion as the number of extended cavity increases. Moreover, the entanglement encoded in the photonic states can be transferred towards ancillary two-level systems to generate genuine multipartite entanglement. Finally, we discuss the feasibility of our proposal in circuit quantum electrodynamics. This proposal could be of interest in the context of quantum random number generator, due to the quadratic scaling of the output state. Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
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10 pages, 1397 KiB  
Article
Quasiprobability Distribution Functions from Fractional Fourier Transforms
by Jorge A. Anaya-Contreras, Arturo Zúñiga-Segundo and Héctor M. Moya-Cessa
Symmetry 2019, 11(3), 344; https://doi.org/10.3390/sym11030344 - 7 Mar 2019
Cited by 3 | Viewed by 2950
Abstract
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript [...] Read more.
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript by showing a way in which the distribution we are introducing may be reconstructed by using atom-field interactions. Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
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