Single Mode Of Electromagnetic Field Research Articles

Dissipative phase transition in an open Tavis–Cummings model with a two-photon drive

We investigate the steady-state quantum phases and associated collective phenomena of an open Tavis–Cummings (TC) model driven by a two-photon source. The standard (non-dissipative) TC model describes the quantum phases of an ensemble of N q two-level quantum emitters interacting with a single-mode electromagnetic field. The interplay among coherent driving, dissipation, and dipole interactions of the open TC model results in emergent collective phenomena, leading to a dissipative or non-equilibrium phase transition from the normal to the superradiant phase. We solve the Liouvillian equation analytically using the semi-classical mean-field approximation. We carry out stability analysis of the steady-state phases and determine the phase boundary. The use of Holstein–Primakoff transformation in the thermodynamic limit reduces the system to an effective coupled-oscillator model, the solution of which yields collective modes.

Quantum Advantage of Binary Discrete Modulations for Space Channels

We assume information is discrete-modulated over coherent states of the single-mode electromagnetic field and transmitted over space quantum channels. In this work, we provide a comparison of quantum detection with classical detection for communication using on-off keying (OOK) and binary phase shift keying (BPSK) for illustrative system parameters for LEO, MEO and GEO satellites. To do so, we assume an attenuation-only (pure-loss) channel and compute the Shannon capacities for the following detection methods: classical (shot-noise limited) single-photon and coherent detectors as well as optimal quantum hypothesis-testing (Helstrom) detection. As in classical system engineering design, we also obtain theoretical references for comparison, namely, Shannon capacities and Holevo bounds for the ideal Gaussian optical channel. Our results show the ranges of transmitted power and orbital heights for which either classical or quantum detection is optimal, thus providing useful insights into design guidelines and operations of future space communication systems. We also obtain the remarkable result that the BPSK Holevo bound achieves the ultimate quantum capacity of the considered channel.

Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to N-atom Dicke model in the Coulomb gauge

In the present paper we show that the Hamiltonian describing the resonant interaction of N two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a simple basis set of states. This allows one to find an analytical approximation for the eigenvectors and eigenvalues of the system, which interpolates the numerical solution in a broad range of the coupling constant values. For the first time, we show that the energy spectrum of Dicke model (DM) as a function of N (with ) satisfies the simple scaling relation. In addition, the introduced basis states provide a regular way of calculating the corrections and estimating the convergence to the exact numerical solution. Analytical approximations and numerical results describing the energy spectrum are valid for both quantum Rabi model (N = 1) and DM for atoms.

Entanglement Entropy Analysis in Dicke's Model Quantum System

Entanglement is a property of interacting particles in a quantum system. The measure of the interaction can be known by looking for the entanglement entropy value in the system. The quantum system used in this study is the Dicke model quantum system which consists of a single-mode electromagnetic radiation field and a two-level N-atom. This study aims to determine the influence of the coupling constant on entanglement entropy and system dynamics. Simulation of system dynamics is carried out with the Quantum Toolbox in Python (QuTiP) module. The simulation results show that the coupling constant has a significant effect on the entanglement entropy value. The greater the value of the coupling constant used, the entanglement entropy value increases. In addition, there is a maximum entanglement entropy value for N greater than one. The coupling constant also affects the dynamics of the system, that is, the greater the value of the coupling constant, the more quantum states can be accessed by atoms.

Nonclassical properties of a deformed atom-cavity field state

We analyse here a nonclassical state produced by an atom-cavity field interaction. The two-level atom is passed through the single-mode electromagnetic cavity field. By deforming the field operators and introducing nonlinearity to the classic Jaynes–Cummings model, we explore the system in respect of a nonlinear Hamiltonian. Assuming that the atom is in an excited state and the field is in a coherent state initially, the analytic expression for the state vector of the entire system state vector is obtained. With the help of the derived state vector, we calculate the photon number distribution, Mandel's parameter, Wigner function, anti-bunching, squeezing properties and Q function etc.

Dynamics of entanglement in coherent states, entangled SchrÖdinger cat state and distribution function

We exploit the dynamics of entangled system between a harmonic oscillator and a single mode electromagnetic field as two harmonic oscillators, to examine quantum entanglement in coherent states. Through the Schrödinger cat state, we compute analytically its distribution function. Then, we check graphically the evolution of entanglement and the distribution function for two particular cases: the first is defined by two harmonic oscillators in quantum motion in a Paul trap; here whatever the quantum state , the system is at most entangled. The second case is visualised by two harmonic oscillators with a perturbative force, in that case, by varying the displacement numbers of the coherent states, the quantum entanglement and the distribution function present a similar evolution and they reach very large values. Comparing the two models: in the first, the dynamics of quantum entanglement exhibits a multi-frequency lines behaviour while in the second model, it shows an exponential behaviour.

Collective enhancement in dissipative quantum batteries

We study a quantum battery made out of N nonmutually interacting qubits coupled to a dissipative single electromagnetic field mode in a resonator. We quantify the charging energy, ergotropy, transfer rate, and power of the system, showing that collective enhancements are still present despite losses, and can even increase with dissipation. Moreover, we observe that a performance deterioration due to dissipation can be reduced by scaling up the battery size. This is useful for experimental realizations when controlling the quality of the resonator and the number of qubits are limiting factors.

On the interaction between Λ-type five-level atom and one-mode squeezed coherent field

This article investigates the effect of the detuning interaction parameters of a single-mode electromagnetic field with a five-level Λ-type. The differential system is solved in the presence of detuning parameter under the initial conditions when the atom and field are prepared in an excited and squeezed state, respectively. The non-classical properties of the field initially in the squeezed coherent states based on the evolution of the second-order correlation function. The study of entanglement between parts of a quantum system is done through the von Neumann entropy. We analyze the effect of the squeeze and detuning parameters on the dynamics of some field aspects and non-local correlation. The results obtained from this study show that the detuning parameter has an essential impact on the field properties.

Regimes of cavity QED under incoherent excitation: From weak to deep strong coupling

The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.

Beyond the Tavis-Cummings model: Revisiting cavity QED with ensembles of quantum emitters

The interaction of an ensemble of $N$ two-level atoms with a single mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by $g_N = \sqrt{N} \bar{g}_1$, where $\bar{g}_1$ is the ensemble-averaged single-atom coupling strength. Formerly, this model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into non-cavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive atoms. We show that the predictions of our model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.

Lamb shift statistics in mesoscopic quantum ensembles

Ensembles of two-level systems interacting with a single-mode electromagnetic field are increasingly being used for the development of quantum information processors and mesoscopic quantum devices. These systems are characterized by a set of energy-level hybridizations, split by Lamb shifts, that occur when the ensemble and field mode interact coherently with high cooperativity. For high dimensions simulating system dynamics while including the complete set of Lamb shifts is generally intractable. We present a compact description of Lamb shift statistics and behavior across all collective angular momentum and excitation subspaces of the ensemble without resorting to overly restrictive approximations of the state space. We also calculate the averaged effective Lamb shift weighted over the degeneracies of these subspaces to connect our results to experiments.

Engineering non-classical correlation and teleportation with Robust fidelity using Jaynes–Cummings model

In this paper, we propose a model to describe the geometry of quantum correlations and entanglement through their distinct physical significance in quantum information processing and modern communications. However, geometric discord, using trace, Hilbert–Schmidt distances, and entanglement of formation, is engineered to be a well-defined non-classical correlation measure of an atomic field system. It consists of employing Jaynes–Cummings model to study the interaction between an excited atom at two levels and a single electromagnetic field mode inside an electrodynamic cavity in two cases, namely resonance and non-resonance. In fact, the dynamics of these measures depends decisively on the atom-field initial parameters where, importantly, the field parameters can be specified as control settings to implement an optimal teleportation protocol. The obtained results reveal that the behaviors of teleported geometric quantum discord and entanglement are similar to those displayed for maximum fidelity in terms of fully entanglement fraction. Therefore, since fidelity always exceeds the classical limit, one can design a quantum teleportation scheme with robust fidelity superior to any conventional communication protocol.

Comparison of the mean field and Bohmian semi-classical approximations to the Rabi model

Bohmian mechanics is an alternative to standard quantum mechanics that does not suffer from the measurement problem. While it agrees with standard quantum mechanics concerning its experimental predictions, it offers novel types of approximations not suggested by the latter. Of particular interest are semi-classical approximations, where part of the system is treated classically. Bohmian semi-classical approximations have been explored before for systems without electromagnetic interactions. Here, the Rabi model is considered as a simple model involving light-matter interaction. This model describes a single mode electromagnetic field interacting with a two-level atom. As is well-known, the quantum treatment and the semi-classical treatment (where the field is treated classically rather than quantum mechanically) give qualitatively different results. We analyze the Rabi model using a different semi-classical approximation based on Bohmian mechanics. In this approximation, the back-reaction from the two-level atom onto the classical field is mediated by the Bohmian configuration of the two-level atom. We find that the Bohmian semi-classical approximation gives results comparable to the usual mean field one for the transition between ground and first excited state. Both semi-classical approximations tend to reproduce the collapse of the population inversion, but fail to reproduce the revival, which is characteristic of the full quantum description. Also an example of a higher excited state is presented where the Bohmian approximation does not perform so well.

Von Neumann entropy in a dispersive cavity

We study the von Neumann entropy of the partial trace of a system of 2 two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single-mode electromagnetic field in the cavity. We make a contrast of this entanglement entropy with the spin squeezing property of the system. We find a close relationship between this von Neumann entropy and the spin squeezing of the system. We observe that this entanglement entropy attains its maximum value when the spin squeezing in the system goes to its maximum and is zero when the spin squeezing in the system vanishes.

Supersymmetric approach to the interaction of a V-type three-level atom with a single mode of electromagnetic field via multi-photon transitions

The interaction of a V-type three-level atom with a single mode of electromagnetic field via multi-photon transitions is analytically solved via supersymmetric unitary operator approach. We have constructed the corresponding supersymmetric generators and performed the diagonalization of the Hamiltonian of the atomic system. The time evolution of the atom-field wave functions is derived in an exact form. We studied some quantum effects of the considered system, namely the evolution of both the second-order correlation function of the radiation field and the quasi-probability distribution Q-function is investigated. We conclude that the used method of solution is very simple and can be applied on a variety of similar atomic systems.

Experimental realization of the classical Dicke model

We report the experimental implementation of the Dicke model in the semiclassical approximation, which describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is managed by making use of two non-linearly coupled active, synthetic LC circuits, implemented by means of analog electrical components. The simplicity and versatility of our platform allows us not only to experimentally explore the coexistence of regular and chaotic trajectories in the Dicke model but also to directly observe the so-called ground-state and excited-state ``quantum'' phase transitions. In this analysis, the trajectories in phase space, Lyapunov exponents and the recently introduced Out-of-Time-Order-Correlator (OTOC) are used to identify the different operating regimes of our electronic device. Exhaustive numerical simulations are performed to show the quantitative and qualitative agreement between theory and experiment.

Influence of Stark-shift on quantum coherence and non-classical correlations for two two-level atoms interacting with a single-mode cavity field

An exact analytic solution for two two-level atoms coupled with a multi-photon single-mode electromagnetic cavity field in the presence of the Stark shift is derived. We assume that the field is initially prepared in a coherent state and the two atoms are initially prepared in excited state. Considering the atomic level shifts generated by the Stark shift effect, the dynamical behavior of both quantum coherence (QC) measured using a quantum Jensen–Shannon divergence and of quantum correlations captured by quantum discord (QD) are investigated. It is shown that the intensity-dependent Stark-shift in the cavity and the number of coherent state photons plays a key role in enhancing or destroying both QC and QD during the process of intrinsic decoherence. We remarked that increasing the Stark-shift parameters, the frequencies of the transition for the mode of the cavity field, and photons number destroy both the amount of QC and QD and affected their periodicity. More importantly, QC and QD exhibit similar behavior and both show a revival phenomenon. We believe that the present work shows that the quantum information protocols based on physical resources in optical systems could be controlled by adjusting the Stark-shift parameters.

Sudden death of entanglement induced by a minimal thermal environment

We study the dynamics of two interacting two-level systems (qubits) having one of them isolated and the other coupled to a single mode electromagnetic field in a thermal state. The field plays the role of a small environment, in contrast to the usual approach of modelling an environment via a thermal reservoir with many degrees of freedom. We find the analytical solution of the proposed model, which allows us to investigate the consequences of the coupling to the small environment on characteristic quantum features of the two-qubit system. We study the time evolution of quantum entanglement and coherence, verifying the dependence on the relevant coupling constants as well as the influence of the effective temperature of the environment. Interestingly, we find that both sudden death and sudden birth of entanglement may occur in such a simple system. We also discuss a different partition, in which the isolated qubit is considered to be coupled to a composite environment, constituted by the other qubit plus the field mode.

Quantum Fisher Information: Probe to Measure Fractional Evolution

We develop an analytical solution of fractional Schrodinger equation to explain the interaction between a two-level atom and a single electromagnetic field mode inside a cavity. Based on this solution, two different cases are discussed; the first one reflects the standard Jaynes Cummings model, while the second solution gives rise to a wave equation for a dipole interacted with a field in semi-classical sense. By controlling different parameters inside cavity, the estimation degree in terms of quantum Fisher information is investigated. The obtained results show that the precision estimation increases as the detuning decreases and number of photons inside cavity increases. Moreover robust estimation is obtained for the standard Jaynes Cummings model. To measure the amount of information, a comparative study between von Neumann entropy and quantum Fisher information show the same behavior. As a result, we conclude that quantum Fisher information may detect entanglement of the interacted atom-field system.

Maximal trace distance between isoenergetic bosonic Gaussian states

We locate the set of pairs $(\rho_{1},\rho_{2})$ of Gaussian states of a single mode electromagnetic field that exhibit maximal trace distance subject to the energy constraint $\langle a^{\dagger}a \rangle_{\rho_{1}}=\langle a^{\dagger}a \rangle_{\rho_{2}} = E$. Any such pair allows to achieve the minimum possible error in the task of binary distinguishability of two single mode, isoenergetic Gaussian quantum signals. In particular, we show that the logarithm of the minimal error probability for distinguishing two maximally trace distant, isoenergetic Gaussian states scales as $-E^{2}$, less than the achievable scaling of the minimal error probability for distinguishing, e.g., a pair of isoenergetic Heisenberg-Weyl coherent states with energy $E$ or a pair of isoenergetic quadrature squeezed states with energy $E$. For the case of a field consisting of $M>1$ modes, we locate the set of pairs of maximally trace distant isoenergetic, isocovariant Gaussian states. These results have basic applications in the theory of continuous variable quantum communications with Gaussian states of light.