Single-mode Cavity Field Research Articles

Analytical and numerical analysis of the atom–field dynamics in non-stationary cavity QED

We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field–atom coupling on the photon generation from vacuum via the dynamical Casimir effect.

ENTANGLING TWO MULTIATOM CLUSTERS VIA A SINGLE-MODE THERMAL FIELD

We consider a system consisting of two multiple two-level-atom clusters simultaneously interacting with a single-mode cavity field. Entanglement of the two clusters is investigated by use of the negativity measure. We find that the entanglement can be not only induced by a thermal field but also enhanced by increasing the mean thermal photon number.

ENTANGLEMENT OF A TWO-LEVEL ATOM INTERACTING WITH A NEW STRUCTURE OF A GENERALIZED NONLINEAR STARK SHIFT VIA Ξ CONFIGURATION

The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.

Quantum correlations between identical and unidentical atoms in a dissipative environment

We have studied the dynamics of quantum correlations such as entanglement, Bell nonlocality and quantum discord between identical and unidentical atoms interacting with a single-mode cavity field and subject to cavity decay. The effect of single-atom detuning, cavity decay rate and initial preparation of the atoms on the corresponding correlation measures have been investigated. It is found that even under strong dissipation, time evolution can create high quantum discord while entanglement and Bell nonlocality stay zero for an initially separable state. Quantum discord increases while entanglement decreases in a certain time period under dissipation for the initial state that both atoms are in the excited state if the qubits are identical. For some types of initial states, cavity decay is shown to drive the system to a stationary state with high entanglement and quantum discord.

Phase transitions and Heisenberg limited metrology in an Ising chain interacting with a single-mode cavity field

We investigate the thermodynamics of a combined Dicke and Ising model that exhibits a rich phenomenology arising from the second-order and quantum phase transitions from the respective models. The partition function is calculated using mean-field theory, and the free energy is analyzed in detail to determine the complete phase diagram of the system. The analysis reveals both first- and second-order Dicke phase transitions into a super-radiant state, and the cavity mean field in this regime acts as an effective magnetic field, which restricts the Ising chain dynamics to parameter ranges away from the Ising phase transition. Physical systems with first-order phase transitions are natural candidates for metrology and calibration purposes, and we apply filter theory to show that the sensitivity of the physical system to temperature and external fields reaches the 1/N Heisenberg limit.

Dynamics of a degenerate Fermi gas in a one-dimensional optical lattice coupled to a cavity

We systematically study the dynamics of a one-dimensional degenerate Fermi gas in an optical-lattice potential coupled to a single-mode cavity field. We derive an effective model to study the nonperturbative effect caused by the cavity field. Our numerical results show that due to the addition of the optical-lattice potential, the system undergoes second-order transition to a bistable density-wave steady state, where the atoms form a density wave and the cavity field is bistable. In addition, the coherent oscillating behavior of the cavity photon number can be observed. We also present a feasible experimental protocol to realize these phenomena, which may be beneficial for future quantum-information applications.

General formalism of the interaction of a single-mode cavity field with a four-level atom

In this paper, we study a general model for an atomic system described by a four-level atom and one mode of the radiation field. The model describes multi-photon processes and includes possible forms of nonlinearities of both the field and the intensity-dependent coupling. The general forms for the constants of motion of the considered atomic system are obtained. We used the Schrodinger equation in solving this problem. The wave function is obtained when the atom is prepared initially in a superposition coherent state. Some of the statistical aspects which are related to this atomic system are calculated. Also, the effect of the Kerr medium on the dynamics of a four-level W -type atom one-mode system are examined.

Quantum Entanglement and Nonlocality Properties of Two-Mode Squeezed Thermal States in a Common-Reservoir Model

We study a system consisting of two identical non-interacting single-mode cavity fields coupled to a common vacuum environment and provide general, explicit, and exact solutions to its master equation by means of the characteristic function method. We analyze the entanglement dynamics of two-mode squeezed thermal state in this model and show that its entanglement dynamics is strongly determined by the two-mode squeezing parameter and the purity. In particular, we find that two-mode squeezed thermal state with the squeezing parameter is extremely fragile and almost does not survive in a common vacuum environment. We investigate the time evolution of nonlocality for two-mode squeezed thermal state in such an environment. It is found that the evolved state loses its nonlocality in the beginning of the evolution, but after a time, the revival of nonlocality can occur.

Quantum trajectory model for photon detectors and optoelectronic devices

We consider a single-mode optical cavity field with simultaneous dissipative and amplifying couplings to a reservoir via a two-state system. In previous works, the reservoir has either solely absorbed energy (detector setup) or added energy (amplifying setup) to the cavity. In this work, we allow both interactions simultaneously and derive a reduced dynamic model for the optical field. Our model includes four physical parameters: the field-two-state system coupling γ, the excitation and de-excitation couplings of the two-state system to the reservoir λA and λD, respectively, and the mirror losses of the cavity C. We show that, depending on the parameters, our setup can operate as a detector, a light-emitting diode or a laser. We also consider single-photon subtraction and addition schemes based on beam splitters and calculate the output fields and the probabilities of the subtraction and addition events. Furthermore, we discuss which are the parameter regimes in which our model is equivalent to beam splitter-based schemes.

System mixedness as a contributor to entanglement in the Jaynes–Cummings model

The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber–Lachs state were investigated in the framework of the Jaynes–Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.

Asymptotic mean excitation numbers due to anti-rotating term (AMENDART) in Markovian circuit QED

We study the cavity field's and atomic asymptotic mean excitation numbers due to anti-rotating term (AMENDART) in the circuit Quantum Electrodynamics (circuit QED) system, composed of a two-level atom and a single cavity field mode, subject to Markovian damping and dephasing mechanisms. We show that the AMENDART are above the thermal values, and their behavior is analyzed analytically and numerically for typical parameters in circuit QED implementations described by the Rabi Hamiltonian. We point out that "parasitic elements" such as other cavity modes or eventual off-resonant atoms, also contribute substantially to AMENDART.

GENERATION OF THE NON-CLASSICAL STATES OF THE QUANTIZED CAVITY FIELD IN THE INTERACTION WITH TRAPPED EQUIDISTANT THREE-LEVEL ION

The interaction between the laser cooled and trapped equidistant three-level atom (ion) and the quantized cavity field is investigated. The dipole moment matrix transition elements between the adjacent atomic energy levels d12 and d23 are assumed to be different. This model generalizes the problem of the pair of indistinguishable two-level atoms interacting with the squeezed vacuum which is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements. The exact analytical solution for the atom-field state-vector is found in the case in which at the initial moment t = 0, the single-mode cavity field is supposed to be in the squeezed vacuum state. With the help of this solution, the quantum-statistical and squeezing properties of the radiation field are studied. The obtained results are compared with those for the single two-level atom model. It should be noted that in the proposed model, the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one. The two limiting cases are analyzed. In the first limiting case in which d12 → d23 the quantum-statistical properties of the single-mode cavity field resemble those for the pair of indistinguishable two-level atoms. In the second one d12 → 0 the quantum-statistical and squeezing features of the proposed model are similar with those for the single two-level atom model.

Dynamics of Entanglement between Moving Four-Level Atom and Single Mode Cavity Field

In this paper we are interested in studying the entanglement between a single four-level ladder-type atom interacting with one-mode cavity field when the atomic motion is taken into account. The exact solution of the model is obtained by using Schrodinger equation for a specific initial conditions. The field entropy of this system is investigated in the non-resonant case. The effects of the detuning parameter and the atomic motion on the entanglement degree are examined. These investigations show that both of the detuning and the atomic motion play important roles in the evolution of the von Neumann entropy and atomic populations. Finally, conclusions and some features are given.

Entanglement properties of an ultracold atom interacting with a cavity quantized electromagnetic field

We study the temporal evolution of the properties of a two-level atom coupled to a single-mode cavity field without dissipation with its center-of-mass motion quantized in one dimension. It is shown that, starting with a separable state, genuine tripartite entangled states can be generated under resonance conditions of the light frequency and atom transition frequency in the cold regime. The onset of Rabi oscillations is analyzed and explicit predictions for properties like emission probability and dispersions for the center-of-mass position and momenta are given for resonance and detuned conditions. Transmission-resonance effects on entanglement and other properties are also analyzed. Comparisons with the semiclassical adiabatic approximation predictions are also made.

Simple schemes for generation of W-type multipartite entangled states and realization of quantum-information concentration

We propose simple schemes for generating W-type multipartite entangled states in cavity quantum electrodynamics (CQED). Our schemes involve a largely detuned interaction of Λ-type three-level atoms with a single-mode cavity field and a classical laser, and both the symmetric and asymmetric W states can be created in a single step. Our schemes are insensitive to both the cavity decay and atomic spontaneous emission. With the above system, we also propose a scheme for realizing quantum-information concentration which is the reverse process of quantum cloning. In this scheme, quantum-information originally coming from a single qubit, but now distributed into many qubits, is concentrated back to a single qubit in only one step.

Role of the counter-rotating terms in the creation of entanglement between two atoms

The problem of the creation of entanglement exclusively from the presence of the counter-rotating terms in the interaction Hamiltonian between two atoms and a single-mode cavity field is studied. The time evolution of the concurrence between the atoms is discussed for two different initial separable states and arbitrary strengths of the coupling constants of the atoms to the cavity mode. We show that a transient entanglement can be created between the atoms only if the counter-rotating terms are taken into account in the interaction Hamiltonian. The source of the entanglement is identified, and the entanglement features are explained in terms of the properties of the reduced density operator of the atoms. In particular, we find that the main source of the entanglement is in the two-photon coherence induced by the counter-rotating terms that cause two-photon transitions through virtual states.

How ‘cold’ can a Markovian dissipative cavity QED system be?

We consider the cavity quantum electrodynamics (QED) system described by the Rabi Hamiltonian, composed of a two-level atom and a single cavity field mode, subject to Markovian damping and dephasing mechanisms. It is shown that without the rotating wave approximation the asymptotic mean photon number and the atomic excitation probability are above the thermal values due to the anti-resonant term in the Rabi Hamiltonian, and are always greater than zero. These quantities are evaluated approximately for two different master equations and compared to exact numerical results, showing good agreement. We discuss the origin of this phenomenon and show that it also persists for an empty dissipative cavity if one uses a quite general form of the Markovian master equation.

Thermal Entanglement of the Two-Qubit Heisenberg Spin Chain Coupled to a Single-Mode Cavity Field

Thermal entanglement of a two-qubit Heisenberg spin chain coupled to a single-mode cavity field is investigated. It is found that (1) thermal entanglement without the rotating-wave approximation (RWA) is explicitly smaller than that obtained with the RWA, which means that the counter-rotating terms have a large impact on thermal entanglement, therefore they cannot be neglected; (2) the case (ω≪Ω) is more beneficial for enhancing thermal entanglement than the resonance case (ω=Ω), the near-resonant case (ω≈Ω) and the case (ω≫Ω); (3) for thermal entanglement, there is a competition process between the exchange coupling J (the direct-coupling between the two two-level atoms) and the coupling constant g (which deduces the indirect effect between the two two-level atoms); the critical value of g increases with the spin coupling strength J.

Tunable electromagnetically induced transparency and absorption with dressed superconducting qubits

Electromagnetically induced transparency and absorption (EIT and EIA) are usually demonstrated using three-level atomic systems. In contrast to the usual case, we theoretically study the EIT and EIA in an equivalent three-level system: a superconducting two-level system (qubit) dressed by a single-mode cavity field. In this equivalent system, we find that both the EIT and the EIA can be tuned by controlling the level-spacing of the superconducting qubit and hence controlling the dressed system. This tunability is due to the dressed relaxation and dephasing rates which vary parametrically with the level-spacing of the original qubit and thus affect the transition properties of the dressed qubit and the susceptibility. These dressed relaxation and dephasing rates characterize the reaction of the dressed qubit to an incident probe field. Using recent experimental data on superconducting qubits (charge, phase, and flux qubits) to demonstrate our approach, we show the possibility of experimentally realizing this proposal.

Unified quantum jump superoperator for optical fields from the weak- to the strong-coupling limit

We derive a generalized quantum jump superoperator that can be used in the quantum trajectory description of single photon detectors, light-emitting diodes (LEDs), and lasers. Our model describes an optical single-mode cavity field coupled to a reservoir through a two-state quantum system and includes three physical parameters: the coupling of the field to the two-state system, the coupling of the two-state system to the reservoir, and the cavity loss rate. In this setup, the two-state system can act as a photodetector or as an energy-adding mechanism. In the first case, we assume that the reservoir acts as a damping mechanism for an ideal cavity and derive reduced field operators describing the photon detection events. Our model coincides with the commonly known quantum trajectory based photon counting models at the weak- and strong-coupling limits and is, furthermore, also applicable between their validity regimes. In the second case, we assume that the reservoir injects energy into a lossy cavity through the two-state system. Again we derive the reduced field operators describing photon creation events into the lossy cavity. We show that this setup can act as an LED or as a laser depending on the strength of the injection. We also investigatemore » how the setup operates at the close proximity of the lasing threshold.« less