Single-mode Radiation Field Research Articles

Effect of cavity leakage on time-dependent spectrum of two atoms Tavis-Cummings model

We study the atomic emission spectrum and cavity field spectrum of dipole–dipole coupled two atoms interacting with a single-mode radiation field in a non-ideal cavity. We solved the quantum master equation by a method that combined analytical analysis and numerical solution. The explicit expression of spectral peak position and numerical results of spectral structure are given for the atoms in entangled state and the field in vacuum initially. The results shown that the decay rate of cavity field has obvious influence on the intensity of spectra but a little effect on the spectral structure. The cavity dissipation makes also the measurement time an important factor in measuring spectral structure.

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.

F-deformed cavity mode coupled to a Λ-type atom in the presence of dissipation and Kerr nonlinearity

In this paper, the dynamics of a system consisting of a three-level atom, which interacts with a single-mode quantized field in a lossy cavity, is studied in the presence of the dependence of atom–field coupling and third-order nonlinear susceptibility on the intensity of light. The system contains a Λ -type atom coupled to a single-mode radiation field, with a degenerate multi-photon transition in the intensity-dependent regime. Also, the nonlinearity of the medium due to Kerr and intensity-dependent Kerr effects, and the detuning parameters are considered. Furthermore, to see the effects of dissipation such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom, a non-Hermitian Hamiltonian is introduced, which results in obtaining the state vector of the whole system by applying the time-dependent Schrödinger equation. Thereupon, the dynamics of entanglement, coherence, photon statistics, and quadrature squeezing are numerically investigated. In each case, the roles of the intensity-dependent nonlinearity function, Kerr and intensity-dependent Kerr nonlinearity, different sources of dissipation, and detuning parameters are discussed. The numerical results indicate that the nonclassicality can remarkably be revealed, and can appropriately be controlled via the above-mentioned effects. It can be found that the presence of dissipation not only does not weaken the physical properties but also can enhance and protect the nonclassicality of the system.

Symmetries in cavity models: Beyond the rotating wave approximation

The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics. The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian. Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity. Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ, is insufficient to draw the complete picture of the system. Instead, they support the relevance of U(1) symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics. Further exploring the U(1) and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators.

Entanglement dynamics of a dc SQUID interacting with a single-mode radiation field

In this work, we study the coupling between a superconducting device as a dc SQUID, simulated from an artificial atom with two degrees of freedom, and a single-mode radiation field for the information transference process. We demonstrate that the population transfer among the energy levels of the artificial atom yields entanglement dynamics, which leads to the generation of a pair of photons. Moreover, we show the quantum information transference between the internal modes of the superconducting device, initially in a maximally entangled state, and the radiation field. The artificial atom absorbs the photon, and the radiation field modes become entangled as quantum coherence is transmitted from the superconducting device to the photons. These results strengthen the applicability of superconducting devices for the transference of quantum information, contributing to promising applications in emerging quantum technologies.

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole-Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning.

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.

Time-Series and Network Analysis in Quantum Dynamics: Comparison with Classical Dynamics

Time-series analysis and network analysis are now used extensively in diverse areas of science. In this paper, we applythese techniques to quantum dynamics in an optomechanical system: specifically, the long-time dynamics of the mean photon number in an archetypal tripartite quantum system comprising a single-mode radiation field interacting with a two-level atom and an oscillating membrane. We also investigate a classical system of interacting Duffing oscillators which effectively mimics several of the features of tripartite quantum-optical systems. In both cases, we examine the manner in which the maximal Lyapunov exponent obtained from a detailed time-series analysis varies with changes in an appropriate tunable parameter of the system. Network analysis is employed in both the quantum and classical models to identify suitable network quantifiers which will reflect these variations with the system parameter. This is a novel approach towards (i) examining how a considerably smaller data set (the network) obtained from a long time series of dynamical variables captures important aspects of the underlying dynamics, and (ii) identifying the differences between classical and quantum dynamics.

Signal transmission and parameter measurement in quantum bits interacting with a single-mode radiation field

Quantum systems can display the quantum chaos characteristics under non-rotating wave approximation. Because of the complex multi-body effect, the inevitability of coupling with the environment and the existence of uncertainty relation, some parameters in quantum system are often uncertain. In order to determine the properties of quantum system, we need to accurately measure any parameters in the system. In this work, we first analyse the characteristics of quantum bits interacting with a single-mode radiation field. On this basis, we design a unique technique to accurately measure the uncertain parameter in the quantum bits. Finally, we complete the synchronization transmission of signal in quantum bits based on the sliding mode control technology.

Effects of postselected von Neumann measurement on the properties of single-mode radiation fields**Project supported by the National Natural Science Foundation of China (Grant No. 11865017) and the Introduction Program of High-Level Talents of Xinjiang Ministry of Science, China.

Postselected von Neumann measurement characterized by postselection and weak value has been found to possess potential applications in quantum metrology and solved plenty of fundamental problems in quantum theory. As an application of this new measurement technique in quantum optics and quantum information processing, its effects on the features of single-mode radiation fields such as coherent state, squeezed vacuum state and Schrödinger cat sate are investigated by considering full-order effects of unitary evolution. The results show that the conditional probabilities of finding photons, second-order correlation functions, Qm-factors and squeezing effects of those states after the postselected measurement is significantly changed are comparable with the corresponding initial pointer states.

Manipulating entanglement sudden death in two coupled two-level atoms interacting off-resonance with a radiation field: an exact treatment.

We study a model of two coupled two-level atoms (qubits) interacting off-resonance (at non-zero detuning) with a single mode radiation field. This system is of special interest in the field of quantum information processing (QIP) and can be realized in electron spin states in quantum dots or Rydberg atoms in optical cavities and superconducting qubits in linear resonators. We present an exact analytical solution for the time evolution of the system starting from any initial state. Utilizing this solution, we show how the entanglement sudden death (ESD), which represents a major threat to QIP, can be efficiently controlled by tuning atom-atom coupling and non-zero detuning. We demonstrate that while one of these two system parameters may not separately affect the ESD, combining the two can be very effective, as in the case of an initial correlated Bell state. However in other cases, such as a W-like initial state, they may have a competing impacts on ESD. Moreover, their combined effect can be used to create ESD in the system, as in the case of an anti-correlated initial Bell state. A clear synchronization between the population inversion collapse-revival pattern and the entanglement dynamics is observed at all system parameter combinations. Nevertheless, only for initial states that may evolve to ESD, the population inversion revival oscillations, where exchange of energy between the atoms and the field takes place, temporally coincide with the entanglement revival peaks, whereas the population collapse periods match the ESD intervals. The variation of the radiation field intensity has a clear impact on the duration of the ESD at any combination of the other system parameters.

New features of non-linear time-dependent two-level atoms

Abstract In this paper, two-level atoms interacting with a single-mode radiation field alongside important properties are presented. The model presented discusses multi-photon process and it has also a nonlinear Kerr-medium and Stark-shift. In addition, the coupling parameter is discussed in a time-dependent fashion. The results show that Stark-shift, time-dependent coupling parameter, and nonlinear Kerr-medium play significant roles regarding the evolution of the von-Neumann entropy and the system's geometric phases. We've used accessible parameters to examine these observations, and some new results are obtained. Remarkably, the geometric phase shows high sensitivity to any change of the considered parameters.

Non-Gaussian bosonic channels in the Tavis–Cummings model

The time evolution of two-level atoms interacting with a single-mode radiation field through the Tavis–Cummings Hamiltonian is studied from the perspective of channel action on the radiation mode. The operator sum representation for the channel in the situation of one atom interacting in resonance with the radiation mode, and two atoms interacting in resonance with the radiation mode, is obtained in the Fock basis. The notions of entanglement breaking, extremality, non-classicality and non-Gaussianity are explored using the obtained operator sum representation. It is shown that the respective channels are not entanglement breaking, are extremal and can generate both non-classicality and non-Gaussianity.

Evolution of Atomic Entanglement for Different Cavity-Field Statistics in Single-Mode Two-Photon Process

We study the evolution of entanglement for a pair of two-level Rydberg atoms passing one after another into an ideal cavity filled with a single mode radiation field. The atoms interact with the cavity field via two-photon transitions. The initial joint state of two atoms that enter the cavity one after the other is unentangled. Interactions intervened by the single mode cavity photon field brings out the final two-atom mixed entangled type state. We use the well known measure appropriate for the mixed states, i.e. the entanglement of formation to quantify the entanglement. We calculate the entanglement of formation of the joint two-atom state as a function of the Rabi angle, for the Fock state field, coherent field and thermal field respectively inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number has been discussed.

Generation of Nonclassical Light by Unsaturated Two-Photon Absorption

In this paper, we investigate the distribution statistics of photons in a single mode radiation field subjected to two-photon absorption (TPA) and the factors that contribute to squeezing and antibunching of photons, leading to the generation of nonclassical light. TPA is a nonlinear optical phenomenon in which the atoms interact with the light field by absorbing two photons simultaneously. The motivation to study TPA is the recent intense activity on nanocrystallites/quantum dots. Further, it is the only nonlinear optical phenomenon that can be analytically studied. The simultaneous occurrence of squeezing and antibunching is studied with small initial photon numbers by solving the master equation for TPA of a single mode radiation directly by numerical integration, without going through analytical procedure. The results are compared with those of analytical/numerical procedures available. Further, the discussion on the parameters of squeezing and antibunching for short-time (ST) as well as long-time is done comprehensively in the present work by taking up the ST approximation and summation of ST (SST) procedure along with the exact numerical method.

Dicke coupling by feasible local measurements at the superradiant quantum phase transition.

We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e., extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensemble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the quantum Fisher information (QFI) and show that optimal estimation of the coupling may be achieved by tuning the frequency of the radiation field to drive the system toward criticality. The scaling behavior of the QFI at the critical point is obtained explicitly upon exploiting the symplectic formalism for Gaussian states. We then analyze the performances of feasible detection schemes performed only on the radiation subsystem, namely homodyne detection and photon counting, and show that the corresponding Fisher informations (FIs) approach the global QFI in the critical region. We thus conclude that criticality is a twofold resource. On the one hand, global QFI diverges at the critical point, i.e., the coupling may be estimated with the arbitrary precision. On the other hand, the FIs of feasible local measurements (which are generally smaller than the QFI out of the critical region), show the same scaling of the global QFI; i.e., optimal estimation of coupling may be achieved by locally probing the system, despite its strongly interacting nature.

The progressive solutions for the Dicke Hamiltonian

A progressive diagonalization scheme for the Dicke Hamiltonian, which describes the interaction of N two-level atoms with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the ground state of the Dicke Hamiltonian with a finite number of atoms can be solved almost exactly by using a progressive diagonalization scheme that involves a one-variable equation at each step. The scheme is efficient for the lower part of the spectrum. Calculated results for ground-state energies, photon numbers, atomic inversions, fluctuations in the latter two quantities, entanglement measures, and Shanon information entropies at resonance points for some finite j cases as functions of the coupling parameter are given. These outcomes show significant changes in the photon number, atomic inversion, and their fluctuations near the critical point where the entanglement measure reaches its maximum value.

Interaction of a Λ-type three-level atom with a single-mode field without rotating wave approximation: perturbation theory approach

In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ-type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the ‘constant detuning’ with the ‘intensity-dependent detuning’ in the first order, and the ‘constant atom–field coupling’ with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.

Dynamics of an open quantum system interacting with a quantum environment

We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom–field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The Mandel Q parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).

Emission Spectrum Property of Modulated Atom-Field Coupling System

The emission spectrum of a two-level atom interacting with a single mode radiation field in the case of periodic oscillation coupling coefficient is investigated. A general expression for the emission spectrum is derived. The numerical results for the initial field in pure number stare are calculated. It is found that the effect of the coupling coefficient modulation on the spectral structure is very obvious in the case of a low modulation frequency and larger amplitude when the initial field is vacuum, which is potentially useful for exploring a modulated light source.

Phonon effect on the quantum phase of a radiation field interacting with a tunneling-coupled quantum-dot molecule

A full quantum theory is adopted to derive the differential equations satisfied by the state of a system that is composed of an electron tunneling-coupled quantum-dot molecule interacting with a single-mode radiation field. The phase of the field is calculated by the Pegg-Barnett quantum phase formalism under the initial condition of a coherent-state field and the tunneling excited state or ground state for the quantum-dot molecule. Phase distribution and fluctuation of the field are analyzed, the influence of interaction between phonons and the quantum-dot molecule on the Pegg-Barnett quantum phase is investigated, and the phase distribution is compared with the Husimi phase distribution of the field. Results indicate that temperature can have a marked impact on the phase evolution. The existence of phonons suppresses the field phase distribution and fluctuation in the case when the quantum dot molecule is initially in the tunneling-excited state, while it enhances the diffusion and fluctuation of the field phase in the case when the quantum dot molecule is initially in the ground state. The Husimi phase distribution and the Pegg-Barnett phase distribution agree with each other fairly well in our study.