Jaynes-Cummings Model Research Articles

Memory-induced weak dissipation in fractional-time-derivative quantum Lindblad-based model

Modeling the interaction between a quantum system and its environment is crucial for practical quantum technologies. The Lindblad master equation is the simplest equation to understand this interaction. In this paper, we have extended the traditional Lindblad equation by fractionalizing its time derivative to account for the memory-induced dissipation. Using this approach, we show weak dissipation of selected quantum systems can be reproduced by this proposed time-fractional Lindblad equation without introducing any specific dissipation terms in the model. By varying the order of the time-fractional Lindblad equation without dissipation terms, we can reproduce the results with good agreements to three tested cases: (a) dissipative Rabi oscillation, (b) dissipative Ising model, and (c) collapse and revival in the Jaynes–Cumming model. We believe this proposed time-fractional Lindblad equation may be a useful modeling tool to characterize weakly dissipative quantum systems in practical quantum technologies, especially if the complex dissipation mechanism is not completely known from the traditional approaches.

Hamiltonian Monodromy via spectral Lax pairs

Hamiltonian Monodromy is the simplest topological obstruction to the existence of global action-angle coordinates in a completely integrable system. We show that this property can be studied in a neighborhood of a focus-focus singularity by a spectral Lax pair approach. From the Lax pair, we derive a Riemann surface which allows us to compute in a straightforward way the corresponding Monodromy matrix. The general results are applied to the Jaynes–Cummings model and the spherical pendulum.

Taming the Rotating Wave Approximation

The interaction between light and matter is one of the oldest research areas of quantum mechanics, and a field that just keeps on delivering new insights and applications. With the arrival of cavity and circuit quantum electrodynamics we can now achieve strong light-matter couplings which form the basis of most implementations of quantum technology. But quantum information processing also has high demands requiring total error rates of fractions of percentage in order to be scalable (fault-tolerant) to useful applications. Since errors can also arise from modelling, this has brought into center stage one of the key approximations of quantum theory, the Rotating Wave Approximation (RWA) of the quantum Rabi model, leading to the Jaynes-Cummings Hamiltonian. While the RWA is often very good and incredibly useful to understand light-matter interactions, there is also growing experimental evidence of regimes where it is a bad approximation. Here, we ask and answer a harder question: for which experimental parameters is the RWA, although perhaps qualitatively adequate, already not good enough to match the demands of scalable quantum technology? For example, when is the error at least, and when at most, 1%? To answer this, we develop rigorous non-perturbative bounds taming the RWA. We find that these bounds not only depend, as expected, on the ratio of the coupling strength and the oscillator frequency, but also on the average number of photons in the initial state. This confirms recent experiments on photon-dressed Bloch-Siegert shifts. We argue that with experiments reporting controllable cavity states with hundreds of photons and with quantum error correcting codes exploring more and more of Fock space, this state-dependency of the RWA is increasingly relevant for the field of quantum computation, and our results pave the way towards a better understanding of those experiments.

Pure Decoherence of the Jaynes–Cummings Model: Initial Entanglement with the Environment, Spin Oscillations and Detection of Non-Orthogonal States

A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson degrees of freedom. The study demonstrates that the potential applicability of the Jaynes–Cummings model in detecting non-orthogonal bosonic states is preserved in the presence of pure decoherence.

Behaviour of large eigenvalues for the asymmetric quantum Rabi model

We prove that the spectrum of the asymmetric quantum Rabi model consists of two eigenvalue sequences ( E m + ) m = 0 ∞ , ( E m − ) m = 0 ∞ , satisfying a two-term asymptotic formula with error estimate of the form O ( m − 1 / 4 ), when m tends to infinity.

Manipulating chiral photon generation from plasmonic nanocavity-emitter hybrid systems: from weak to strong coupling

Abstract By confining light into a deep subwavelength scale to match the characteristic dimension of quantum emitters, plasmonic nanocavities can effectively imprint the light emission with unique properties in terms of intensity, directionality, as well as polarization. In this vein, achiral quantum emitters can generate chiral photons through coupling with plasmonic nanocavities with either intrinsic or extrinsic chirality. As an important metric for the chiral-photon purity, the degree of circular polarization (DCP) is usually tuned by various scattered factors such as the nanocavity design, the emitter type, and the coupling strategy. The physical mechanisms of the chiral photon generation, especially when plasmons and emitters step into the strong coupling regime, are less explored. In this paper, we extended the coupled-oscillator and Jaynes–Cummings models to their chiral fashion to account for the above factors within a single theoretical framework and investigated the chiroptical properties of a plasmonic nanocavity-emitter hybrid system from weak to strong coupling. It was demonstrated that both the circular differential scattering and prominent scattering DCP rely on the intrinsic chirality generated by breaking the mirror symmetry with the emitter, and is thereby tunable by the coupling strength. However, the luminescence DCP (as high as 87 %) is closely related to the extrinsic chirality of the bare nanocavity and independent of the coupling strength. The results thus reveal two different physical mechanisms of generating chiral photons in scattering and luminescence. Our findings provide a theoretical guideline for designing chiral photon devices and contribute to the understanding of chiral plasmon-emitter interaction.

Invariant approach to the driven Jaynes-Cummings model

We investigate the dynamics of the driven Jaynes-Cummings model, where a two-level atom interacts with a quantized field and both, atom and field, are driven by an external classical field. Via an invariant approach, we are able to transform the corresponding Hamiltonian into the one of the standard Jaynes-Cummings model. Subsequently, the exact analytical solution of the Schrödinger equation for the driven system is obtained and employed to analyze some of its dynamical variables.

Sudden change of the photon output field marks phase transitions in the quantum Rabi model

The experimental observation of quantum phase transitions predicted by the quantum Rabi model in quantum critical systems is usually challenging due to the lack of signature experimental observables associated with them. Here, we describe a method to identify the dynamical critical phenomenon in the quantum Rabi model consisting of a three-level atom and a cavity at the quantum phase transition. Such a critical phenomenon manifests itself as a sudden change of steady-state output photons in the system driven by two classical fields, when both the atom and the cavity are initially unexcited. The process occurs as the high-frequency pump field is converted into the low-frequency Stokes field and multiple cavity photons in the normal phase, while this conversion cannot occur in the superradiant phase. The sudden change of steady-state output photons is an experimentally accessible measure to probe quantum phase transitions, as it does not require preparing the equilibrium state.

Persisting quantum effects in the anisotropic Rabi model at thermal equilibrium

Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this paper, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling. Published by the American Physical Society 2024

Bound states in continuum domain of double resonant ring metal metasurfaces

Metasurfaces have found extensive applications in microwave, terahertz, and optical range, serving different purposes such as filters, sensors, slow light devices, and nonlinear devices due to their distinctive electromagnetic response characteristics. Recent development requires metasurface devices to exhibit enhanced monochromaticity and stronger light interaction. Consequently, there is a growing interest in designing metasurfaces with high-quality factor (<i>Q</i>-factor) resonances, considering their crucial role in achieving sharp resonances through constructing bound states in the continuum (BIC) mode. The utilization of BIC has emerged as a prominent method of designing metasurfaces with high <i>Q</i>-factor resonances. Due to the fact that the changes in the structural parameters of metasurfaces can simultaneously affect the resonance of two components of q-BICs, it is difficult to achieve on-demand design of operating frequency, bandwidth, and <i>Q</i>-factor. In this work, we investigate a novel THz metasurfaces supporting q-BIC resonance. We optimize the geometric parameters of two split ring resonators (SRRs) to tailor the operating frequencies of intrinsic resonance, and tune the coupling between different resonance modes to form the q-BIC mode resonance. The dominant modes are demonstrated by the results of multipolar decomposition calculations of the electromagnetic field distributions and scattered power at different resonant operating frequencies. In <i>x</i>-polarized and <i>y</i>-polarized incident electromagnetic wave, the normalized coupling strength ratio between the two modes are calculated by Jaynes-Cummings model to be 0.54% (<i>x-</i>polarized) and 4.42% (<i>y-</i>polarized) respectively, which explains the law that the resonant frequency of different modes changes with the structural parameters of SRRs device. In order to analyze the refractive index sensing capabilities of our designed metasurfaces under the incident electromagnetic waves with different polarizations, we investigate the variations of the transmitted spectrum of the metasurface with refractive index of matters. The calculated results show that the sensitivity of the metasurface is 151 GHz/RIU when the incident wave is <i>y</i>-polarized and 108 GHz/RIU when the incident wave is <i>x</i>-polarized. We realize the effective control of the operating frequency, bandwidth, and <i>Q</i>-factor of the q-BIC mode resonance in the transmission spectrum of the metasurface, which provides a new idea for the practical designing of terahertz metasurfaces with high <i>Q</i>-factor.

Inside the Jaynes–Cummings sum

It is shown that the atomic inversion in the Jaynes–Cummings model has an exact representation as an integral over the Hankel contour. For a field in a coherent state, the integral is evaluated using the saddle point method. The trajectories of saddle points as a function of time are on the branches of the multi-valued Lambert function. All of them start at the initial moment of time, but make the maximum contribution to the inversion at different times. If the collapse and the first revival are clearly distinguished, then subsequent revivals are determined by the comparable contributions of several trajectories.

Jaynes–Cummings model in a weak gravitational wave background

Working in the framework of the linearized theory, we analyze the influence of a weak gravitational wave on the dynamics of the Jaynes–Cummings model, describing the interaction between a two-level quantum system and the electromagnetic field in a cavity. We show that the gravitational wave induces a small, time-dependent modulation in the generalized Rabi frequency Ω of the system. Such a modulation has the same frequency as the incoming gravitational wave. We also find that the atomic inversion acquires a similar time-dependent modulation. After a pulse of the electromagnetic driving field in the cavity, an atomic population N 0, previously prepared in its excited state, ends showing a small unbalance between the excited and the de-excited atoms. The unbalance amplitude is proportional to HN 0, with H being the gravitational strain. We briefly comment about possible astrophysical implications.

On the two-photon quantum Rabi model at the critical coupling strength

On the two-photon quantum Rabi model at the critical coupling strength

Identifying unbound strong bunching and the breakdown of the rotating wave approximation in the quantum Rabi model

Identifying unbound strong bunching and the breakdown of the rotating wave approximation in the quantum Rabi model

Unique Steady-State Squeezing in a Driven Quantum Rabi Model

Unique Steady-State Squeezing in a Driven Quantum Rabi Model

Quantum phase transition of the Jaynes-Cummings model

Quantum phase transition of the Jaynes-Cummings model

Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations.

The first numerically exact simulation of a full ab initio molecular quantum system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the ground state but is quickly lost already in the deep cryogenic regime. This is in contrast to predictions from the Jaynes-Cummings model, which is the standard starting point to model collective strong-coupling chemistry phenomenologically. Moreover, we find that the fluctuations of matter remain modified by the quantum nature of the thermal and vacuum-field fluctuations for significant temperatures, e.g., at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) have implications for the understanding and control of polaritonic chemistry and materials science, since a semiclassical theoretical description of light-matter interaction becomes reasonable, but the typical (classical) canonical equilibrium assumption for the nuclear subsystem remains violated. This opens the door for quantum fluctuation-induced stochastic resonance phenomena under vibrational strong coupling, which have been suggested as a plausible theoretical mechanism to explain the experimentally observed resonance phenomena in the absence of periodic driving that has not yet been fully understood.

Unconventional photon blockade in the two-photon Jaynes–Cummings model with two-frequency cavity drivings and atom driving

In a two-frequency cavity driving and atom driving atom-cavity system, we find the photon blockade effect. In a truncated eigenstates space, we calculate the zero-delay second-order correlation function of the cavity mode analytically and obtain an optimal condition for the photon blockade. By including three transition pathways, we find that higher excitations of the cavity mode can be further suppressed and the zero-delay second-order correlation function can be reduced additionally. Based on the master equation, we simulate the system evolution and find that the analytical solutions match well with the numerical results. Our scheme is robust with small fluctuations of parameters and may be used as a new type of single photon source.

Thermal states of two identical two-level atoms interacting with the single-mode fields of the Arik–Coon and Biedenharn–Macfarlane q-oscillators

We consider the Jaynes–Cummings models (JCMs) of two identical two-level atoms interacting with a single mode of the Arik–Coon and Biedenharn–Macfarlane [Formula: see text]-boson fields in a cavity. It is shown that there is a constant of motion, so-called the total number of excitation, which leads to decomposition of the total Hilbert space of [Formula: see text]-deformed system into three invariant subspaces. So, we have the block diagonal structure with three blocks as the Hamiltonian matrices. The exact energy spectrum and eigenstates of the [Formula: see text]-deformed models are obtained by diagonalizing each block. Assuming that the cavity fields and atoms are in thermal equilibrium, the partition function and thermal density matrix of the models are calculated. Finally, the influence of deformation parameters of the Arik–Coon and Biedenharn–Macfarlane [Formula: see text]-oscillator light fields at low-temperatures on the entropy and internal energy of the Jaynes–Cummings models as well as on the atom–atom entanglement via the concurrence measure is analyzed.

Cavity-Modified Chemiluminescent Reaction of Dioxetane.

Chemiluminescence is a thermally activated chemical process that emits a photon of light by forming a fraction of products in the electronic excited state. A well-known example of this spectacular phenomenon is the emission of light in the firefly beetle, where the formation of a four-membered cyclic peroxide compound and subsequent dissociation produce a light-emitting product. The smallest cyclic peroxide, dioxetane, also exhibits chemiluminescence but with a low quantum yield as compared to that of firefly dioxetane. Employing the strong light-matter coupling has recently been found to be an alternative strategy to modify the chemical reactivity. In the presence of an optical cavity, the molecular degrees of freedom greatly mix with the cavity mode to form hybrid cavity-matter states called polaritons. These newly generated hybrid light-matter states manipulate the potential energy surfaces and significantly change the reaction dynamics. Here, we theoretically investigate the effects of a strong light-matter interaction on the chemiluminescent reaction of dioxetane using the extended Jaynes-Cummings model. The cavity couplings corresponding to the electronic and vibrational degrees of freedom have been included in the interaction Hamiltonian. We explore how the cavity alters the ground- and excited-state path energy barriers and reaction rates. Our results demonstrate that the formation of excited-state products in the dioxetane decomposition process can be either accelerated or suppressed, depending on the molecular orientation with respect to the cavity polarization.