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.
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, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of the time-dependent Schrödinger equation that provides a comprehensive framework for analyzing the system's quantum properties. To characterize the nonclassical features of the radiation field, we examine photon number distribution, second-order correlation function 𝑔2(0), squeezing properties, and Mandel's 𝑄𝑀 parameter. These properties reveal significant insights into the quantum statistical behaviour of the field and its deviation from classicality under different interaction regimes. In addition, we quantify the atom-atom entanglement using linear entropy which captures the mixedness of the atomic subsystem and elucidates the interplay between atom-atom interactions. The results highlight the crucial role of nonlinear interactions and the Stark shift in shaping the quantum correlations and nonclassical phenomena of the system.
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.
Abstract In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.
In this paper, we present some properties through two two-level atoms interacting with a two-mode quantized cavity field. We study this system in the presence of detuning parameter, Kerr nonlinearity, Stark shift, relative phase and intensity-dependent atoms-field coupling. Also, the coupling parameter is modulated to be time dependent. The exact solution of this model is given by using the Schrődinger equation when the atoms and the field are initially prepared in superposition states and coherent states, respectively. We employed the results to calculate some aspects such as linear entropy, total atomic inversion and cross-correlation function.
In the present communication, we consider the problem of two quantum systems with the Kerr-like medium nonlinearity. The system is cast form of an interaction between two operators of the form su(1,1) Lie algebra and su(2) Lie algebra. We obtain the wave function via the evolution operator where we use the Heisenberg equations of motion to derive the constants of motion. We discuss the atomic inversion. It is found that the Kerr-like medium decreases the amplitude and increases the fluctuations. Also we consider different types of squeezing, it is shown that the entropy squeezing is pronounced in the second quadrature, but it shows a small amount in the first quadrature. For the variance squeezing, a small amount occurs in the presence of the Kerr-like medium. However, the normal squeezing occurs in the first quadrature where the squeezing is sensitive to both the Kerr-like medium parameter and the initial state. Furthermore, the degree of entanglement is examined through the linear entropy. It is shown that the function decreases besides rapid fluctuations. The correlation function displays nonclassical behavior in addition to an increase in the amplitude of the fluctuations.
In this paper, to study the effects of a nonlinear medium on the atom–field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as our nonlinear optical phenomena, and with the use of its algebra, we show that it can be considered as a deformed oscillator as well as a deformed su(2) algebra. Then we construct the associated two-mode nonlinear coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom–field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we study the effect of the nonlinear medium on the occupation probabilities of the atomic levels and consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider the photon distribution, correlation function, Mandel parameters of the field, von Neumann entropy, and also the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of the two modes is clarified.