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Acta Physica Sinica (Overseas Edition)

Interaction of a Λ-type three-level atom with a two-mode field and a two-mode Raman-coupled model

Zhang Zhi-ming, Lin-sheng He, Zhou Shi-kang

Published Feb 1, 1999• 1 citation
Publisher

Abstract

The Hamiltonian is derived for the interaction of a Λ-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Λ-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.

DOI
10.1088/1004-423x/8/2/007

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The Hamiltonian is derived for the interaction of a Λ-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Λ-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.
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.
A system comprising of Lambda-type three-level atoms and the two-mode cavity field is considered in this paper. Under the adiabatical approximation and the large detuning condition, the effective Hamiltonian of the system in the interaction picture can be given out. If the two identical three-level atoms pass through the cavity in turn, the entangled state atoms can be generated. When the interaction time is taken to an appropriate value, the maximally entangled states are created. At the same time, the dynamic behaviors of the system are studied in detail.
Interaction of a V-type three-level atom with two mode fields is studied in detail. Under large-detuning condition, the ground state can be adiabatically eliminated, i.e., this model may be converted into a non-degenerate Raman coupled model which an effective two-level atom interacts with two mode cavity fields. We derive the modified effective Hamiltonian and their wave functions of both non-degenerate Raman coupled and a degenerate Raman coupled model respectively. Based on state-selective measurements on V-type three-level atoms crossing the cavity, We present a new scheme of generation of Schrdinger cat states which are made up of superposition of the coherent states with controllable weighting factors and phases, through Raman interaction of degenerate V-type three atoms with one cavity field.
We describe the dynamics of an exactly solvable Raman coupled model interacting with two modes of a quantized cavity electromagnetic field. The model consists of a three-level atom in the \ensuremath{\Lambda} configuration whose excited state is considered to be far off resonance and is adiabatically eliminated. The effective Hamiltonian for this system contains products of the transition operators between the two ground-state levels and a field annihilation operator from one mode and a creation operator from the other. This Hamiltonian provides an example of a zero-photon process. We study the atomic inversion and investigate the production of nonclassical effects such as antibunched light, violations of the Cauchy-Schwartz inequality, and squeezing.
In this paper we investigate the properties of a four-level atomic system interacting with two modes of the electromagnetic field in a cavity. By linearization of the Hamiltonian we show that the corresponding mathematical model is exactly solvable. To obtain simpler effective Hamiltonians the method of multiple scales is applied. It is shown that under some special values of the detunings and coupling constants, exactly predictable collapses and revivals in the atomic populations appear. Also, due to the specific interactions of the atom with the cavity modes and the ensuing measurement of energy or angular momentum and energy, two-mode Schr\"odinger-cat states arise in the cavity. Finally, the stabilization and trapping properties of the system are demonstrated in a lossy cavity within the Wigner-Weisskopf approximation. The existence of stationary states is shown and it is also shown that interference effects can cause cancellation of one line in both transmitted light and spontaneous emission spectra.