Quantum Optical Model Research Articles

The Jaynes–Cummings model: 60 years and still counting

2023 marked the 60th anniversary of the Jaynes–Cummings model, a foundational model in quantum optics. Over the years, its importance has expanded beyond traditional light–matter interaction systems, such as cavity QED. This special issue presents a collection of articles that showcase the evolution of the model’s applications, blending traditional topics with contemporary developments.

Spacing distribution for quantum Rabi models * *Dedicated to Mr. Hiromichi Shinohara, who was instrumental in establishing NTT-IFM, on his 70th birthday.

The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the Z2 -symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies and recent theoretical results, we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter, reflecting the hidden symmetry of the AQRM. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge.

The 1 + 2 vector DKP oscillator as a pseudo-Hermitian model of quantum optics

The 1 + 2 vector DKP oscillator as a pseudo-Hermitian model of quantum optics

Designing Variational Ansatz for Quantum‐Enabled Simulation of Non‐Unitary Dynamical Evolution ‐ An Excursion into Dicke Supperradiance

AbstractAdaptive Variational Quantum Dynamics (AVQD) algorithms offer a promising approach to providing quantum‐enabled solutions for systems treated within the purview of open quantum dynamical evolution. In this study, the unrestricted‐vectorization variant of AVQD is employed to simulate and benchmark various non‐unitarily evolving systems. Exemplification of how construction of an expressible ansatz unitary and the associated operator pool can be implemented to analyze examples such as the Fenna–Matthews–Olson complex (FMO) and even the permutational invariant Dicke model of quantum optics. Furthermore, an efficient decomposition scheme is shown for the ansatz used, which can extend its applications to a wide range of other open quantum system scenarios in near future. In all cases the results obtained are in excellent agreement with exact numerical computations that bolsters the effectiveness of this technique. The successful demonstrations pave the way for utilizing this adaptive variational technique to study complex systems in chemistry and physics, like light‐harvesting devices, thermal, and opto‐mechanical switches, to name a few.

Spectral quasi-clustering estimates for certain semiregular systems

We show a quasi-clustering result for a subclass of the class of Semiregular Metric Globally Elliptic Systems (SMGES) including certain quantum optics models (such as Jaynes-Cummings and its generalizations) which describe light-matter interaction. More precisely, we show that for the class of systems with polynomial coefficients we consider, the spectrum concentrates within the union of intervals (not necessarily disjoint, but at most intersecting in an a priori finite number) centered at a sequence determined in terms of invariants of the (total) symbol and width decreasing as the centers go to infinity.

Quantum simulation of an extended Dicke model with a magnetic solid

The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO3, where the role of atoms (photons) is played by Er3+ spins (Fe3+ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Dimensional reduction in quantum optics

One-dimensional quantum optical models usually rest on the intuition of large-scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially resulting in the violation of (3+1)-dimensional Maxwell's theory. Here, we provide a rigorous foundation for this approximation by means of the light-matter interaction. We show how the quantized electromagnetic field can be decomposed—exactly—into an infinite number of living on a lower-dimensional subspace and containing the entirety of the spectrum when studying axially symmetric setups, such as with an optical fiber, a laser beam, or a waveguide. The approximation then corresponds to a truncation in the number of such subfields that in turn, when considering the interaction with for instance an atom, corresponds to a modification to the atomic spatial profile. We explore under what conditions the standard approach is justified and when corrections are necessary in order to account for the dynamics due to the neglected spatial dimensions. In particular we examine what role vacuum fluctuations and structured laser modes play in the validity of the approximation. Published by the American Physical Society 2024

Classical, semiclassical, and quantum-optical models for an x-ray planar cavity with electronic resonance

Classical, semiclassical, and quantum-optical models for an x-ray planar cavity with electronic resonance

On sampling determinantal and Pfaffian point processes on a quantum computer

DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since then, they have been widely used as models and subsampling tools in statistics and computer science. Most applications require sampling from a DPP, and given their quantum origin, it is natural to wonder whether sampling a DPP on a quantum computer is easier than on a classical one. We focus here on DPPs over a finite state space, which are distributions over the subsets of {1,…,N} parametrized by an N × N Hermitian kernel matrix. Vanilla sampling consists in two steps, of respective costs O(N3) and O(Nr2) operations on a classical computer, where r is the rank of the kernel matrix. A large first part of the current paper consists in explaining why the state-of-the-art in quantum simulation of fermionic systems already yields quantum DPP sampling algorithms. We then modify existing quantum circuits, and discuss their insertion in a full DPP sampling pipeline that starts from practical kernel specifications. The bottom line is that, with P (classical) parallel processors, we can divide the preprocessing cost by P and build a quantum circuit with O(Nr) gates that sample a given DPP, with depth varying from O(N) to O(rlogN) depending on qubit-communication constraints on the target machine. We also connect existing work on the simulation of superconductors to Pfaffian point processes (PfPP), which generalize DPPs and would be a natural addition to the machine learner’s toolbox. In particular, we describe ‘projective’ PfPPs, the cardinality of which has constant parity, almost surely. Finally, the circuits are empirically validated on a classical simulator and on 5-qubit IBM machines.

Dynamics Reflects Quantum Phase Transition of Rabi Model

As the simplest and most fundamental model describing the interaction between light and matter, a breakdown in the rotating wave approximation of the Rabi model leads to phase transition versus coupling strength when the frequency of the qubit greatly surpasses that of the oscillator. In addition to the phase transition revealed in the ground state, we show that the dynamics of physical quantities can reflect such a phase transition for this model. In addition to the excitation of the bosonic field in the ground state, we show that the witness of inseparability (entanglement), mutual information, quantum Fisher information, and the variance of cavity quadrature can be employed to detect the phase transition in quench. We also reveal the negative impact of temperature on checking the phase transition by quench. This model can be implemented using trapped ions, superconducting artificial atoms coupled bosonic modes, and quantum simulations. By reflecting the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit, this work offers an idea to explore phase transitions by nonequilibrium process for open quantums.

Quantum chaos in the Dicke model and its variants

Recently, the out-of-time-ordered correlator (OTOC) has gained much attention as an indicator of quantum chaos. In the semi-classical limit, its exponential growth rate resembles the classical Lyapunov exponent. The quantum–classical correspondence has been supported for the one-body chaotic systems as well as realistic systems with interactions, as in the Dicke model, a model of multi-two-level atoms and cavity field interactions. To this end, we calculate the OTOC for different variations of the Dicke model in an open quantum system setting. The connection between the superradiant phase transition of the Dicke model and the OTOC is studied. Further, we establish a relation between the OTOC and the second-order coherence function. This becomes important for the experimental studies of the OTOC and quantum chaos in the models of quantum optics.

Improving quantum state transfer: correcting non-Markovian and distortion effects

Quantum state transfer is a key operation for quantum information processing. The original pitch-and-catch protocols rely on flying qubits or single photons with engineered wavepacket shapes to achieve a deterministic, fast and high-fidelity transfer. Yet, these protocols overlook two important factors, namely, the distortion of the wavepacket during the propagation and non-Markovian effects during the emission and reabsorption processes due to time-dependent controls. Here we address both difficulties in a general quantum-optical model and propose a correction strategy to improve quantum state transfer protocols. Including non-Markovian effects in our theoretical description, we show how to derive control pulses that imprint phases on the wavepacket that compensate the distortion caused by propagation. Our theoretical results are supported by detailed numerical simulations showing that a suitable correction strategy can improve state transfer fidelities up to three orders of magnitude.

Experimental observation of phase transitions of a deformed Dicke model using a reconfigurable, bi-parametric electronic platform

We experimentally study the infinite-size limit of the Dicke model of quantum optics with a parity-breaking deformation strength that couples the system to an external bosonic reservoir. We focus on the dynamical consequences of such symmetry breaking, which makes the classical phase space asymmetric with non-equivalent energy wells. We present an experimental implementation of the classical version of the deformed Dicke model using a state-of-the-art bi-parametric electronic platform. Our platform constitutes a playground for studying representative phenomena of the deformed Dicke model in electrical circuits with the possibility of externally controlling parameters and initial conditions. In particular, we investigate the dynamics of the ground state, various phase transitions and the asymmetry of the energy wells as a function of the coupling strength gamma and the deformation strength alpha in the resonant case. Additionally, to characterize the various behavior regimes, we present a two-dimensional phase diagram as a function of the two intrinsic system parameters. The onset of chaos is also analyzed experimentally. Our findings provide a clear connection between theoretical predictions and experimental observations, demonstrating the usefulness of our bi-parametric electronic setup.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics.

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Quantum battery based on dipole-dipole interaction and external driving field.

The Dicke model is a fundamental model in quantum optics, which describes the interaction between quantum cavity field and a large ensemble of two-level atoms. In this work, we propose an efficient charging quantum battery achieved by considering an extension Dicke model with dipole-dipole interaction and an external driving field. We focus on the influence of the atomic interaction and the driving field on the performance of the quantum battery during the charging process and find that the maximum stored energy exhibits a critical phenomenon. The maximum stored energy and maximum charging power are investigated by varying the number of atoms. When the coupling between atoms and cavity is not very strong, compared to the Dicke quantum battery, such quantum battery can achieve more stable and faster charging. In addition, the maximum charging power approximately satisfies a superlinear scaling relation P_{max}∝βN^{α}, where the quantum advantage α=1.6 can be reached via optimizing the parameters.

Plasmonic volcano-like fiber-optic probe for Raman enhancement.

Light-matter interaction is a fascinating topic extensively studied from classical theory, based on Maxwell's equations, to quantum optics. In this study, we introduce a novel, to the best of our knowledge, silver volcano-like fiber-optic probe (sensor 1) for surface-enhanced Raman scattering (SERS). We employ the emerging quasi-normal mode (QNM) method to rigorously calculate the Purcell factor for lossy open system responses, characterized by complex frequencies. This calculation quantifies the modification of the radiation rate from the excited state e to ground state g. Furthermore, we use and extend a quantum mechanical description of the Raman process, based on the Lindblad master equation, to calculate the SERS spectrum for the plasmonic structure. A common and well-established SERS probe, modified by a monolayer silver nanoparticle array, serves as a reference sensor (sensor 2) for quantitatively predicting the SERS performance of sensor 1 using quantum formalism. The predictions show excellent consistency with experimental results. In addition, we employ the FDTD (finite-difference time-domain) solver for a rough estimate of the all-fiber Raman response of both sensors, revealing a reasonable range of SERS performance differences compared to experimental results. This research suggests potential applications in real-time, remote detection of biological species and in vivo diagnostics. Simultaneously, the developed FDTD and quantum optics models pave the way for analyzing the response of emitters near arbitrarily shaped plasmonic structures.

Chiral Polaritonics: Analytical Solutions, Intuition, and Use.

Preferential selection of a given enantiomer over its chiral counterpart has become increasingly relevant in the advent of the next era of medical drug design. In parallel, cavity quantum electrodynamics has grown into a solid framework to control energy transfer and chemical reactivity, the latter requiring strong coupling. In this work, we derive an analytical solution to a system of many chiral emitters interacting with a chiral cavity similar to the widely used Tavis-Cummings and Hopfield models of quantum optics. We are able to estimate the discriminating strength of chiral polaritonics, discuss possible future development directions and exciting applications such as elucidating homochirality, and deliver much needed intuition to foster the newly flourishing field of chiral polaritonics.

Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media

The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. Here we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge-fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges commonly used in quantum optics. We also consider gauge conditions with explicit time dependence, enabling us to unambiguously introduce additional phenomenologically time-dependent light-matter interactions in any gauge. Our results allow one to derive rigorous nonrelativistic models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant model of photodetection.

Charging performance of quantum batteries based on intensity-dependent Dicke model

Recently, quantum battery based on various physical models from quantum optics model to spin model and its enhancement of charging performance have attracted increasing interest. It has been demonstrated that quantum entanglement is beneficial to the speedup of work extraction. In this paper, by an exact diagonalization approach, we investigate the charging performance of the field intensity-dependent Dicke model (also called intensity-dependent Dicke model) quantum battery, which consists of <i>N</i> qubits collectively interacting with a single-mode cavity. The considered intensity-dependent Dicke model is a generalized Dicke model with a nonlinear-coupling fashion and different weights of energy conserved term and non-conserved term. Firstly, we consider the influences of energy non-conserved term (also called anti-rotating wave term) on the maximum stored energy and maximum charging power in quantum battery. It is shown that the maximum stored energy is not very sensitive to the increase of the weight of energy non-conserved term, but the maximum charging power undergoes a significant change with the increase of the weight of energy non-conserved term. We also show that the maximum charging power increases monotonically with the increase of coupling constant between qubits and cavity, but the maximum stored energy is not monotonically related to the increase of coupling constant. Then, we further examine in detail the characteristics of the maximum stored energy, charging time, energy quantum fluctuation and maximum charging power in the quantum battery under the same weight between energy conserved term and non-conserved term. By comparing the charging performances of quantum battery based on the single-photon-Dicke model with those based on the two-photon-Dicke model, we find that the performances, specifically, the charging time and maximum charging power of the intensity-dependent Dicke quantum battery are better than those of single-photon Dicke quantum battery, but weaker than those of two-photon Dicke quantum battery. Of particular interest is that the relationship of maximum charging power with large quantum cell number in intensity-dependent Dicke quantum battery has the same form as that in the two-photon Dicke quantum battery, i.e. their maximum values of charging power are both proportional to the large quantum cell number squared, specifically, <inline-formula><tex-math id="M1">\begin{document}$ P_{\mathrm{max}}^{\mathrm{ID}}\propto N^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M1.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ P\mathrm{_{max}^{2ph}}\propto N^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M2.png"/></alternatives></inline-formula>, which are consistent with the upper bound given by the paper (Gyhm J, Šafránek D, Rosa D <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevLett.128.140501"> 2022 <i>Phys. Rev. Lett.</i> <b>128</b> 140501</ext-link>). It is worthwhile to mention that Dou et al. (Dou F Q, Zhou H, Sun J A <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevA.106.032212"> 2022 <i>Phys. Rev. A</i> <b>106</b> 032212</ext-link>) showed that using the quantum advantage of maximum charging power in the quantum battery based on cavity Heisenberg-spin-chain model <inline-formula><tex-math id="M5">\begin{document}$ P\mathrm{_{max}}\propto N^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M5.png"/></alternatives></inline-formula> can be obtained. Therefore, this study of the charging performance based on the intensity-dependent Dicke quantum battery may provide an alternative approach to the further research on quantum battery.

Measurement-device-independent quantum key distribution with passive time-dependent source side channels

While measurement-device-independent (MDI) quantum key distribution (QKD) allows two trusted parties to establish a shared secret key from a distance without needing to trust a central detection node, their quantum sources must be well characterized, with side channels at the source posing the greatest loophole to the protocol's security. In this paper, we identify a time-dependent side channel in a common polarization-based QKD source that employs a Faraday mirror for phase stabilization. We apply a recently developed numerical proof technique [Phys. Rev. A 99, 062332 (2019)] to quantify the sensitivity of the secret key rate to the quantum optical model for the side channel, and to develop strategies to mitigate the information leakage. In particular, we find that the MDI three-state and BB84 protocols, while yielding the same key rate under ideal conditions, have diverging results in the presence of a side channel, with BB84 proving more advantageous. While we consider only a representative case example, we expect the strategies developed and key rate analysis method to be broadly applicable to other leaky sources.