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Physica Scripta

Interaction of aΛ-type three-level atom with a single-mode field without rotating wave approximation: perturbation theory approach

M Rastegarzadeh, Mohammad Kazem Tavassoly

Published Jan 28, 2015• 19 citations
Publisher

Abstract

In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ -type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the 'constant detuning' with the 'intensity-dependent detuning' in the first order, and the 'constant atom–field coupling' with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.

DOI
10.1088/0031-8949/90/2/025103

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Acta Physica Sinica•Jan 1, 1998•0 citations
In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ -type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the 'constant detuning' with the 'intensity-dependent detuning' in the first order, and the 'constant atom–field coupling' with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.
Recalling that the rotating wave approximation (RWA) is only valid in the weak coupling regimes, the purpose of this paper is to study the Hamiltonian dynamics describing the full quantum mechanical approach of the interaction between various configurations of three-level atoms Lambda, V and ladder distinctly with a two-mode radiation field, while the RWA is not considered; the counter-rotating terms (CRTs) are taken into account. Generally, the presence of CRTs in the Hamiltonian prevents one to achieve an analytical solution. Moreover, as we will show in the present work, using the perturbation theory, analytical solvable Hamiltonians can be successfully obtained. According to our calculations, the contribution of CRTs within the ordinary Hamiltonian is equivalent to the replacement of the constant detuning with a specific intensity dependent detuning in the first order, and the constant atom field coupling with a particular intensity dependent (f deformed) coupling in the second order of the associated perturbation parameter. Moreover, noticing that according to the initial expression of the Hamiltonian, each mode of the field interacts only with a specific pair of the allowed transitions of each type of the three-level atom, it is surprisingly observed that via applying the mentioned approach, the obtained intensity dependent coupling functions depend on both modes of the field, f(na,nb). In this way, it is seen that the CRTs are removed with the price of arriving at some intermixed intensity dependent atom field coupling functions of the two modes of the field. In this way, the obtained final Hamiltonians are analytically solvable. At last, by determining the time evolution of the atom field wave function, we study the effects of CRTs on a few nonclassical properties of the state of the system, including the atomic population inversion and photon statistics.
One of the simplest models involving the atom-field interaction is the coupling of a single two-level atom with single-mode optical field. Under the rotating wave approximation, this problem is reduced to a form that can be solved exactly. But the approximation is only valid when the two levels are resonant or nearly resonant with the applied electromagnetic radiation. Here we present an analytical solution without the rotating wave approximation and applicable to general atom-field interaction far away from the resonance. We find that there exists remarkable influence of the initial phase of optical field on the Rabi oscillations and Rabi splitting, and this issue cannot be explored in the context of the rotating wave approximation. Due to the retention of the counter-rotating terms, higher-order harmonic appears during the Rabi splitting. The analytical solution suggests a way to regulate and control the quantum dynamics of a two-level atom and allows for exploring more essential features of the atom-field interaction.
In this paper, we study the interaction between a three-level atom and a quantized single-mode field with 'intensity-dependent coupling' in a 'Kerr medium'. The three-level atom is considered to be in a Λ-type configuration. Under particular initial conditions, which may be prepared for the atom and the field, the dynamical state vector of the entire system will be explicitly obtained, for the arbitrary nonlinearity function f(n) associated with any physical system. Then, after evaluating the variation of the field entropy against time, we will investigate the quantum statistics as well as some of the nonclassical properties of the introduced state. During our calculations we investigate the effects of intensity-dependent coupling, Kerr medium and detuning parameters on the depth and domain of the nonclassicality features of the atom–field state vector. Finally, we compare our obtained results with those of V -type three-level atoms.
We study the interaction between a moving three-level lambda rubidium atom and a single mode cavity field in the presence of Kerr-like medium. We derive the basic equations of motion for atomic system and show that it is exactly solvable in the rotating wave approximation (RWA). The momentum increment, the momentum diffusion and the Mandel Q parameter of this system are studied. We investigate numerically the influence of Kerr-Like medium on the evolution of the previous statistical properties in the exact resonate and nonresonate case where the atom is initially prepared in a momentum eigenstate and the field in the squeezed state. It is found that the Kerr medium has an important effect on their evolution. Finally, conclusion and discussion are given.
It is shown that a three-level atom in the \ensuremath{\Lambda} configuration with arbitrary detunings can be exactly reduced to a two-level system with an effective Raman coupling, which depends nonlinearly on the intensity of the two radiation fields. This is done by exactly evaluating the unitary transformation introduced by Alexanian and Bose [Phys. Rev. A 52, 2218 (1995)] for a three-level atom coupled to two modes of the radiation field. We obtain an exact transformed Hamiltonian in which one of the three levels is decoupled for all values of the detunings. In particular, our result is then valid for any ratios of the coupling constants to detunings, even for zero detuning, in contrast to earlier work which requires that these ratios be small. We find the the eigenvalues of the exact transformed Hamiltonian and study its population dynamics. \textcopyright{} 1996 The American Physical Society.
The dynamics of a cascade three-level atom interacting with the single mode coherent state under the Counter-Rotating-Wave approximation (C-RWA) is investigated.The properties of the mean-photon number (N(t)) and the degree of second-order coherence (g2(t)) are analyzed in this model.The little indentation which represents the quantum noise of the system appears in the evolution curves of the mean-photon number and the degree of second-order coherence under the C-RWA.The quantum noise which is caused by the virtual photon field gradually becomes weak when ω increases.The quantum noise increases when increases.The anti-bunching effect of the system under the C-RWA is stronger than the one under the RWA.Besides,the relation of N(t) and g2(t) with the atom-field coupling constant λ is revealed in our results.