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Physical Review A

Phase sensitivity in atom-field interaction via coherent superposition

Khalid Zaheer, Muhammad Suhail Zubairy

Published Feb 1, 1989• 108 citations
Publisher

Abstract

Considering a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a coherent state of the field, we show that the dynamics of the atom as well as the spectrum of the field are sensitive to the relative phase between the atomic dipole and the cavity field. It is shown that, for a certain choice of this phase, ``coherent trapping'' occurs in two-level atoms. In the case of spectra, for the same choice of the phase, instead of a three-peaked symmetric spectrum, we have an asymmetric two-peaked spectrum.

DOI
10.1103/physreva.39.2000

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Considering a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a coherent state of the field, we show that the dynamics of the atom as well as the spectrum of the field are sensitive to the relative phase between the atomic dipole and the cavity field. It is shown that, for a certain choice of this phase, ``coherent trapping'' occurs in two-level atoms. In the case of spectra, for the same choice of the phase, instead of a three-peaked symmetric spectrum, we have an asymmetric two-peaked spectrum.
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An expression for the population inversion in the Jaynes-Cummings model and the most general initial state of the atom-field system is presented. States that maintain the same level of population inversion when the atom and the field are initially decoupled are found. When the atom is prepared in a coherent superposition of its states and the field is in an eigenstate of the Susskind-Glogower phase operator, for a certain choice of the relative phase between the atomic dipole and the field, coherent trapping occurs. The evolution of the squeezing of the field for these states is given, and the dependence on the phase and on the mean photon number of the field is studied.
Atomic-dipole squeezing in the presence of the Stark shift in two-photon Jaynes-Cummings model for an atom initially prepared in a coherent superposition of states, interacting with the coherent- or squeezed-vacuum-state field, is studied. Closed expressions for dispersive and absorptive components of the dipole for the coherent-field input under the large-n\ifmmode\bar\else\textasciimacron\fi{} approximation are derived. It is shown that atomic-dipole squeezing is sensitive to both the phase of the initial field and the relative phase between the two atomic levels. Our results show that, for certain choices of these phases, permanent dipole squeezing can be obtained.
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.