We introduce the problem of three types of interaction between an N-level quantum system and a two-level atom where three coupling parameters are involved. The system can be deduced from the Heisenberg chain. The canonical transformation is used to remove two coupling parameters from the system and consequently it is reduced to atom–atom interaction. The wave function is calculated using the evolution operator and hence we have managed to obtain the expectation value of some dynamical operators. During our study of the atomic inversion we noted that the collapses period is shifted up when we take the effect of λ2 into consideration. While it is shifted up and down in the presence of λ3. The atomic angle plays a crucial role for controlling the degree of entanglement. For the variance squeezing we noted that the coupling parameter λ2 shows amounts of squeezing more than the case of λ3. Similar behavior is noted for the entropy squeezing.
We introduce the problem of three types of interaction between an N-level quantum system and a two-level atom where three coupling parameters are involved. The system can be deduced from the Heisenberg chain. The canonical transformation is used to remove two coupling parameters from the system and consequently it is reduced to atom–atom interaction. The wave function is calculated using the evolution operator and hence we have managed to obtain the expectation value of some dynamical operators. During our study of the atomic inversion we noted that the collapses period is shifted up when we take the effect of λ2 into consideration. While it is shifted up and down in the presence of λ3. The atomic angle plays a crucial role for controlling the degree of entanglement. For the variance squeezing we noted that the coupling parameter λ2 shows amounts of squeezing more than the case of λ3. Similar behavior is noted for the entropy squeezing.
In this paper, we study the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter. The SU(1, 1) algebra is used to represent the combination of the interacting modes. A canonical transformation is used to cast the Hamiltonian into a tangible form. The solution of the Schrodinger equation for the wave function is given analytically. Using this solution we discuss numerically the atomic inversion, the degree of entanglement through the linear entropy and the variance entropy for chosen values of the detuning and coupling parameters. It is shown that the atomic inversion can be controlled through the rotation angle α and the atomic angle θ as well as the Bargmann index k. The degree of entanglement is affected by both α and θ in addition to the ratio ϵ. Variance squeezing is sensitive to changes in the atomic and the phase angles besides the parameter k. For entropy squeezing, the effective parameters are α, θ and k.
Using the adiabatic elimination we have managed to deal with the problem of the interaction between a single three-level atom and |N| two-level non-interacting atoms. The adiabatic elimination is used to obtain the effective Hamiltonian that describes a nonlinear interaction in the form of a Stark-like shift between a two-level atom and su|(2)N| two-level atoms. The time evolution operator is calculated in the presence of a Stark-like shift and the detuning parameters. The time-dependent wave function is determined through the evolution operator and consequently the density matrix is obtained. We adopt an initial wave function for the |N| two-level atoms that takes into account the structural degeneracies occurring in the system and thus generalize the atomic coherent state. The phenomenon of the collapses and revivals of the atomic population inversion for different values of the Stark shift parameters is considered. The degree of entanglement is also investigated and discussed, where the linear entropy is used. Finally we examine the variance squeezing for the system for different values of the involved parameters. It is shown that different values of the Stark shift parameters lead to different observations of the squeezing in the quadratures.
The problem of two two-level atoms in interaction with a nondegenerate parametric amplifier is considered. The analytical solution of the wavefunction is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement, as well as the variance and entropy squeezing are discussed. In our analysis, we assumed that the atomic systems are in the excited states and the fields in the squeezed-pair coherent state. It has been shown that the coupling parameter, λ3 (the coupling between the two fields), gets more effective for the case in which the q-parameter is not equal to zero. Also for a strong coupling parameter λ3 the superstructure phenomenon can be observed. In the meantime, as we increase the value of the coupling parameter, the entanglement between the atoms and the fields gets stronger. Also it has been shown that in the presence of the parametric amplifier term, the system never reaches the pure state except during revival periods.
We have four systems, each of them contains N-atoms, and each atom of them consists of two levels, and all of them interact with an atom consisting of three levels. Moreover, the atom is also related to the systems by coupling parameters that are time-dependent. By considering particular conditions, the exact solution for the wave function is realized. Then we survey the atomic population inversion in addition to the normalized correlation functions. We examine the influence of many parameters on the previous statistical aspects. We deduce from the conclusions that the behavior of the correlation function is affected by the existence of the time-dependent coupling parameters between spins. We prove that changing the values of the coupling parameters between spins λk, the parameters ε, and the quantum numbers Nγ enables us to control the correlated behavior in addition to the atomic population. So, we can control this model through these parameters.
We have four systems, each of them contains N-atoms, and each atom of them consists of two levels, and all of them interact with an atom consisting of three levels. Moreover, the atom is also related to the systems by coupling parameters that are time-dependent. By considering particular conditions, the exact solution for the wave function is realized. Then we survey the atomic population inversion in addition to the normalized correlation. We examine the influence of many parameters on the previous statistical aspects. We deduce from the conclusions that the behavior of the correlation function is affected by the existence of the time-dependent coupling parameters between spins. We prove that changing the values of the coupling parameters between spins λk, the parameters ε, and the quantum numbers Nγ enables us to control the correlated behavior in addition to the atomic population. So, we can control this model through these parameters.
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.