An analytical solution is obtained when the Kerr medium and Stark shift are considered as nonlinear interaction terms to the system containing two-qubit and two-mode electromagnetic field from the parametric amplifier. Dynamics of the population inversion, cavity–qubit and qubit–qubit entanglements are analyzed under the unitary cavity–qubit interaction, the Kerr medium and the Stark shift. The population inversion of a qubit presents periodic revivals and collapses. The results show that the entanglement and the population inversion as well as the inversion have the same stable intervals, that is, the collapse intervals. It is found that the Kerr medium and the Stark shift may lead to reduction of the periods and the amplitudes of the population inversion and the cavity–qubit/qubit–qubit entanglement. The deteriorated qubit–qubit/cavity–qubit entanglement and the population inversion, due to the Kerr medium, may be increased by increasing the Stark shift and vice versa.
An analytical solution is obtained when the Kerr medium and Stark shift are considered as nonlinear interaction terms to the system containing two-qubit and two-mode electromagnetic field from the parametric amplifier. Dynamics of the population inversion, cavity–qubit and qubit–qubit entanglements are analyzed under the unitary cavity–qubit interaction, the Kerr medium and the Stark shift. The population inversion of a qubit presents periodic revivals and collapses. The results show that the entanglement and the population inversion as well as the inversion have the same stable intervals, that is, the collapse intervals. It is found that the Kerr medium and the Stark shift may lead to reduction of the periods and the amplitudes of the population inversion and the cavity–qubit/qubit–qubit entanglement. The deteriorated qubit–qubit/cavity–qubit entanglement and the population inversion, due to the Kerr medium, may be increased by increasing the Stark shift and vice versa.
In this paper, the effects of the field damping and Kerr-like medium on a system of a four-level atom in the [Formula: see text]-type interacting nonlinearly with a two-mode field are studied. Analytical solution of the system of differential equations resulting from the Schrödinger equation is obtained. The effects of detuning parameters, Kerr-like parameter, coupling function and damping rate are discussed for atomic population inversion, the second-order correlation function, Shannon information entropy, and linear entropy. Under justifiable all conditions, extreme entanglement states may appear periodically with the evolution of time. The arrival of the quantum system to a pure state can be controlled by variations of the Kerr medium and the damping parameters. The results also exhibit that the periods of strong and weak entanglement between the parts of the system are achieved during the periods of collapses and revivals of the atomic population inversion. Moreover, the photon distribution changes from non-classical to classical by increasing the damping rate.
A quantum cavity filled with a nonlinear medium (Kerr like medium) and contains a 2-mode field interacting with time dependence of 2-qubit is investigated. Part of the two qubits interact in the form of an amplifier, while the other is in the form of a ladder. The constants of motion are calculated by using the Heisenberg differential equation. Moreover, the analytical solution is calculated by solving the Schrodinger differential equations. Some statistical quantities are calculated to identify the features of the proposed model. The effective of the nonlinear term on the phenomena of collapse and revival are discussed through atomic population. The amount of entanglement between the quantum subsystem, whether it is between the 2-qubit and the cavity field, or between the 2-qubit together are calculated using the linear entropy and the concurrence. The results indicated that there is a superstructure between the atomic population and the linear entropy, concurrence. The intensity of oscillations decreases for the entanglement between the field and the two qubits when the Kerr like medium of the Hamiltonian system is included. The nonclassical distribution of the quantum system decreases after taking Kerr like medium into account.
In this paper, the entanglement between two qubits that exist in two distinct cavities which are connected by an optical fiber is investigated by using the concurrence, while two-photon transitions and Kerr medium effect are also considered. Each cavity contains a qubit and a single-mode quantized field. The appearance of entanglement between the two qubits in the separate cavities originates from the presence of optical fiber. The obtained numerical results of the considered system show that, if the Kerr medium is large enough, the initial values of entanglement between the two qubits (which may have the maximum possible value, i.e. 1) can be approximately protected from the large amplitude fluctuations, so that acceptable stability is created. Also, qubit-field coupling and detuning effects are investigated and it is observed that symmetric coupling results in more stability of entanglement. Eventually, atomic population inversion is also studied and it is observed that it is controllable by considering different parameters.
An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom–field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.
Recalling that counter rotating terms (CRTs) in atom–field interaction are not always ignorable, particularly in the strong coupling regimes of atom–field systems, in this paper we are going to study the interaction between two qubits (two-level atoms) with a two-mode field in a high quality cavity by considering CRTs while the dipole–dipole (D–D) interaction is also taken into account. Indeed, by performing an appropriate dynamical Hamiltonian associated with the Jaynes–Cummings and anti-Jaynes–Cummings terms, as well as the D–D interaction for the system, we solve the corresponding time-dependent Schrödinger equation with specific initial conditions for atoms and field. In the continuation, concurrence, as an appropriate measure of the degree of entanglement of the two qubits, and atomic population inversion of the qubits, as the rate of energy exchange between atoms and field, are evaluated. Meanwhile, we investigate the influence of CRTs and D–D interaction (as well as other involved parameters in the model interaction) on the mentioned quantities. Our numerical results indicate that collapse-revival phenomenon can be observed in the absence of D–D interaction with or without rotating wave approximation, however, CRTs cause an increase or decrease in the number of collapse-revivals in a finite interval of time, depending on the chosen parameters. In fact, by entering the D–D interaction term, this phenomenon is destroyed and the time behaviour of the quantities experiences irregular oscillations. Noticing that the initial field is considered in the vacuum state, the occurrence of collapse-revival in the population inversion of the two qubits is an interesting feature of this work. As is shown, the degree of entanglement and atomic population inversion of the qubits can generally be tuned, and the death of entanglement can be prevented, both by adjusting the evolved parameters in the model.
In this paper, we explore the atomic population inversion and entanglement dynamics of a quantum system consisting of three identical two-level atoms interacting with a single-mode cavity field. The cavity is surrounded by a Kerr medium exhibiting f-deformed Kerr nonlinearity, and we consider a degenerate multi-photon transition in the nonlinear regime. The study systematically analyzes the effects of intensity-dependent coupling, detuning, Kerr nonlinearity, f-deformed Kerr nonlinearity, and multi-photon transition on the nonclassical properties of the system. Our results show that the Kerr and f-deformed Kerr nonlinearities significantly influence the atomic inversion dynamics, leading to phenomena such as collapse and revival, with distinct behaviors observed under varying detuning parameters. Furthermore, entanglement dynamics between the atoms and cavity mode are enhanced under intensity-dependent coupling and nonlinearity. The detuning parameter generally reduces entanglement but has a less pronounced effect in the two-photon transition case, where entanglement is notably enhanced. The study provides valuable insights into controlling quantum correlations in multi-atom systems, with potential applications in quantum information processing, computing, and communication.