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Journal of Modern Optics

Interaction of a Two-level Atom with One Mode of Anticorrelated Two-mode Field States

Christopher C. Gerry, Jerry Kiefer

Published May 1, 1991• 7 citations
Publisher

Abstract

We study the time evolution of a single two-level atom interacting with one mode of anticorrelated two-mode field states. The anticorrelated field states are SU(2) coherent states constructed from Schwinger's two-boson representation of the angular momentum algebra. We assume that only one of the modes is near resonance with the atom. Because of the anticorrelation in the initial field state, no atomic moment develops. We study the evolution of the atomic inversion and the inversion and the phase space quasi-probability SU(2) Q-function of the field.

DOI
10.1080/09500349114550921

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We study the time evolution of a single two-level atom interacting with one mode of anticorrelated two-mode field states. The anticorrelated field states are SU(2) coherent states constructed from Schwinger's two-boson representation of the angular momentum algebra. We assume that only one of the modes is near resonance with the atom. Because of the anticorrelation in the initial field state, no atomic moment develops. We study the evolution of the atomic inversion and the inversion and the phase space quasi-probability SU(2) Q-function of the field.
We study the interaction of two-level atoms with correlated two-mode states of the quantized electromagnetic field. We assume that only one of the modes is near resonance with the atomic transition so that the second mode does not interact directly with the atom. However, we find that the presence of the second field does produce a kind of nonlocal effect in that if the atom is initially in the excited or the ground state no atomic dipole moment develops. We consider two kinds of correlated field state, namely, the correlated SU(1, 1) coherent states, which are generalizations of the two-mode squeezed vacuum states, and the so-called pair coherent states. We study the atomic inversions and the evolutions of the field statistics and of the squeezing properties of the initial field.
In this paper we investigate the sensitivity of coupled atomic transitions to correlations between field modes. In particular, we show that a three-level atom interacting with a cavity field supporting two quantized modes can be highly sensitive to the nature of the correlations between the modes. Correlated two-mode states include the two-mode squeezed state, whereas the SU(2) coherent state is an example of an anticorrelated state. We study in detail the dynamics of a three-level atom in the \ensuremath{\lambda} configuration, interacting with the two modes of an SU(2) coherent state. We show that for certain choices of the atom-field coupling constants, the generalized two-photon Rabi frequency for the system becomes independent of the photon number, leading to a purely periodic behavior in time of the atomic population probabilities; for other choices of the atom-field coupling constants, we observe the usual collapse and revival of the Rabi oscillations. We study also the dynamics of the field, in particular the correlations between the modes. Finally, for comparison purposes, we present a parallel study of the case in which the field modes are initially uncorrelated.
The N-photon interaction of two two-level atoms with a single-mode quantized radiation field is studied. The general expression for the state vector of the atom–field system is presented with the probability amplitudes in analytic form. For the initial condition in which the atoms are both at their upper levels and the field is in a squeezed state, we study the time evolution of the atomic population inversions and that of the statistics of the field. We find that the ratio of the two coupling constants, the initial squeezing of the field, and N have significant effects on the features of the atoms and of the field.
The resonant interaction of two nonidentical two-level atoms with one mode of the electromagnetic field has been considered. The pure-state evolution of the atomic states for field initially in the coherent state and atoms in the ground state has been investigated. It has been shown that for intermediate values of the relative differences of two coupling constants the atoms as well as the field are returned most closely to a pure state at the revival time. The possibility of the maximally entangled states at the beginning of the collapse time has been discussed.