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Physical Review A

Influences of ac Stark shifts on coherent population trapping in the atom-field coupling system via Raman two-photon processes

Gao‐xiang Li, Jin-sheng Peng

Published Jul 1, 1995• 52 citations
Publisher

Abstract

By means of adiabatically eliminating the upper level or levels of a \ensuremath{\Lambda}-configuration atom coupling to a two-mode quantized field, we have studied the influences of ac Stark shifts on the atomic coherent population trapping in two important atom-field coupling systems via nondegenerate Raman two-photon processes. The states of the field that trap the atom in its two nondegenerate lower levels are obtained, and the important roles of ac Stark shifts and properties of the atomic upper level or levels in the states of the trapping field in two Raman-coupling systems are also analyzed.

DOI
10.1103/physreva.52.465

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By means of adiabatically eliminating the upper level or levels of a \ensuremath{\Lambda}-configuration atom coupling to a two-mode quantized field, we have studied the influences of ac Stark shifts on the atomic coherent population trapping in two important atom-field coupling systems via nondegenerate Raman two-photon processes. The states of the field that trap the atom in its two nondegenerate lower levels are obtained, and the important roles of ac Stark shifts and properties of the atomic upper level or levels in the states of the trapping field in two Raman-coupling systems are also analyzed.
We have measured the ac Stark effect in a two-zone stimulated Raman interaction in a sodium atomic beam. In addition, we have derived simple theoretical expressions for the ac Stark shift, based on a closed three-level system, in the Λ configuration, and have achieved qualitative agreement with the data. In particular, the magnitude and sense of the ac Stark shifts are found to depend on laser intensities as well as on the initial populations of the two low-lying levels of the Λ configuration. Specifically, the observed ac Stark shifts are smaller for larger laser intensities and also for smaller initial population differences between the two low-lying levels. The ac Stark effect must be considered for many potential applications of the Raman effect, such as a Raman clock. In this connection, we have identified conditions for the reduction of the ac Stark shift in our sodium Raman clock.
We have studied the atomic coherent population trapping in the system of a two-mode quantized field interacting with a Λ-configuration multilevel atom with one lower discrete state and two sets of quasicontinuum states, or a set of quasicontinuum states and a set of true continuum states. The influence of the atom's initial preparation and the properties of the atomic upper levels on whether or not atomic coherent population trapping occurs, and the states of the field which trap the atom are analyzed.
The cavity field spectrum of an atom interacting with two-mode field through non-degenerate Raman coupling with the presence of AC-Stark shift in an ideal cavity is investigated. The results for the atom in the low-level state and the initial fields in pure number states, coherent states, and squeezed vacuum states are calculated. When the initial fields are in number states, the three-peak structure of each model cavity field spectra appear for weak fields, and two-peak or single-peak structure appear for strong fields. When both field modes are in a superposition of number states initially, the cavity field spectra are generally of two-peak structure. With the increase of γ=g2/g1,one peak rises and the other peak reduces.
We investigate the population trapping in a Raman-coupled three-level system interacting with a pump mode and a Stokes mode in a quantized cavity. We show that with an initial atom-field decoupled state and the atomic state prepared in a coherent superposition of two nondegenerate ground states, population trapping occurs when the phase of the atomic dipole is equal to the phase difference of the two modes and the two-mode field state satisfies a specific photon distribution. In the limit of large total photon number, under some specific conditions, the corresponding two-mode trapping state can be identified as a phase difference state. We have studied the variance of superposition mode quadrature and its evolution, statistical properties, and the phase-space properties of the two-mode trapping field state. It has been observed that although under different conditions the two-mode field exhibits both sub- and super-Poissonian statistics, no squeezing is observed in any case.