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Physica Scripta

Nonclassical properties of the integrability condition of the time-dependent SU(2) quantum system

M. Sebawe Abdalla, Eied Mahmoud Khalil

Published Sep 20, 2011• 3 citations
Publisher

Abstract

In this paper, we treat the problem of the multi-photon Tavis–Cummings classically, where the effect of time-dependence takes place. Under certain integrability conditions the time-dependent wave function in the Schrodinger picture is obtained. Some statistical properties of the system are discussed based on the solution for the equations of motion in the Heisenberg picture. Using the atomic coherent state as a basis, the phenomenon of squeezing is observed in the quadrature variances Fx and Fy; however, it was pronounced in the quadrature Fy. The phenomenon of squeezing is also reported for the usual atomic state case where squeezing is only observed in the first quadrature Fx. An examination of the correlation function using the atomic state showed us that the system is sensitive to variation in the integrability parameter β. The nonclassical effect is also found to be pronounced for small values of the parameter β.

DOI
10.1088/0031-8949/84/04/045010

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In this paper, we treat the problem of the multi-photon Tavis–Cummings classically, where the effect of time-dependence takes place. Under certain integrability conditions the time-dependent wave function in the Schrodinger picture is obtained. Some statistical properties of the system are discussed based on the solution for the equations of motion in the Heisenberg picture. Using the atomic coherent state as a basis, the phenomenon of squeezing is observed in the quadrature variances Fx and Fy; however, it was pronounced in the quadrature Fy. The phenomenon of squeezing is also reported for the usual atomic state case where squeezing is only observed in the first quadrature Fx. An examination of the correlation function using the atomic state showed us that the system is sensitive to variation in the integrability parameter β. The nonclassical effect is also found to be pronounced for small values of the parameter β.
We investigate the quantum statistics of three time-dependent coupled oscillators in the presence of multiphoton processes. The system is connected with the two-atom multiphoton Tavis-Cummings model. The solution of the Heisenberg equations of the motion is obtained in a compact form. We assume that the modes are initially prepared in coherent states, and we discuss nonclassical phenomena (squeezing and sub-Poissonian behavior). Further, we examine the joint quasi-distribution functions as well as photon-number distribution and its factorial moments. The system has shown that the nonclassical effect is apparent in compound modes (1,3) and (2,3). Moreover, the superstructure phenomenon is observed when the photon transition is increased.
In this paper we introduce a Hamiltonian model which represents the interaction between SU (1, 1) and SU (2) quantum systems. The Heisenberg equations of motion are invoked to derive the exact time-dependent dynamical operators. The phenomena of the collapse and revival are observed for the intermediate states, however, for a large value of the excitation number m . It is also shown that the phenomenon of squeezing is observed in the intermediate state. Moreover, it is sensitive to the variation in the coupling parameter λ, the detuning parameter Δ, as well as in the Bargmann index k . The examination of the correlation function shows that the system displays anti-bunching for all periods of time except for a large value of the excitation number when k = 3/4. Our discussion for the variance squeezing also shows that the phenomenon of squeezing is pronounced in the quadrature variances for the odd parity case when the detuning parameter is large.
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.
By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ≫ 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).
Some nonclassical features, including photon antibunching, atomic squeezing and quantum collapse-revival phenomenon, were numerically studied in the vacuum field Jaynes–Cummings model (JCM). The influence of the initial atomic coherence on these features was discussed. It is shown that the squeezing can appear only if the atom is initially prepared in the coherent state, and photon antibunching can occur if the atom is initially in the excited state or the coherent one. The effect of the virtual-photon field was studied in JCM without the rotating-wave approximation (RWA). We have shown that even under the condition in which RWA is considered to be valid, there are significant effects on the nonc1assical features due to the interference between the virtual-photon processes and the real-photon processes. Quantum dynamics of JCM without RWA was also studied. We showed that regular dynamical behavior is exhibited in the cases rather close to the integrable limits, and irregular dynamical behavior is presented in the cases far from the integrable limits; in addition, all the nonclassical features disappear in the cases far from the integrable limits.
In this manuscript, the phenomenon of time dependence is treated using the integral property of a model consisting of interaction of an atom with a cavity in which a bi-mode field of an amplifier type. The exact solution is obtained through the Schrodinger equation, followed by the wave function characteristic of the proposed system. The effect of both the deformed pair coherent states and the time dependence on some statistical quantities are studied. The phenomena of revival and collapse are studied by computing the atomic inversion. Moreover, the entanglement between the parts of the quantum system is studied, and the periods of squeezing are determined by entropy squeezing and variance squeezing. The results are also compared and statistical quantities linked together.