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Laser Physics

Quantum treatment for three waves mutually interacting with a single two-level atom

M. Sebawe Abdalla, A.‐S. F. Obada, Eied Mahmoud Khalil, M. M. A. Ahmed

Published Aug 22, 2014• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1054-660x/24/10/105205

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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.
In this paper, we study the interaction between a two-level atom and a three types of nonlinear interaction of two modes, two as a degenerate two photon and the third of the converter form. The solution to the Schrodinger equation is obtained exactly under a certain specific condition. By using this solution we discuss numerically the atomic inversion, the degree of entanglement through the atomic Wehrl entropy, the geometric phase entropy for chosen values of the detuning and coupling parameters. Statistical properties of the investigated system is discussed by the evolution of the Mandel parameter.
We consider the interaction between a two-level atom and a quantum system that consists of three electromagnetic fields. An analytic solution is provided for the wave function of a pairwise mutual interaction between a two-level atom and three modes using a frequency converter. SU(2) group generators are used to describe these field mode interactions. In addition, a canonical transformation is employed in order to convert the Hamiltonian model into a Jaynes–Cumming-like model, which is used to solve the Schrödinger equation. Statistical properties related to the atomic inversion, entanglement, and squeezing phenomena are discussed. Superstructure patterns and partial disentanglement, as well as squeezing swapping between quadratures, are displayed for selected parameters.
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.
A Hamiltonian, that describes the interaction between a two-level atom (su(2) algebra) and a system governed by su(1,1) Lie algebra besides two external interaction, is considered. Two canonical transformations are used, which results into removing the external terms and changing the frequencies of the interacting systems. The solution of the equations of motion of the operators is obtained and used to discuss the atomic inversion, entanglement, squeezing and correlation functions of the present system. Initially the atom is considered to be in the excited state while the other systems is in the Perelomov coherent state. Effects of the variations in the coupling parameters to the external systems are considered. They are found to be sensitive to changing entanglement, variance and entropy squeezing.
In this paper we introduce a new Hamiltonian which represents the interaction between a two-level atom and two modes of an electromagnetic field injected simultaneously within a cavity. Field–field interaction of the parametric converter type is taken into consideration. Under certain conditions the solution to the Schrödinger equation is obtained exactly. By using this solution we discuss numerically the degree of entanglement through the entropy of the field, for chosen values of the detuning and coupling parameters.
The analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric amplifier term is presented. The purity of the atomic state has been used to measure the degree of entanglement between the atom and the field. The temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case are studied. It has been shown that maximum squeezing for the variance and entropy squeezing occurs when the ratio between the amplifier coupling λ3 and the field frequency ω equals 0.26. Increasing the value of the ratio λ3/ω further leads to the vanishing of squeezing from the system. It is also noted that the existence of the coupling parameter results in the system never reaching the pure state except at the points of revival times. The Q function has been also considered to give more information in the phase space about the system. These aspects are sensitive to changes in the amplifier parameter.