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arXiv:0709.3902 · Physical Review A

Optical Stern-Gerlach effect beyond the rotating-wave approximation

V. E. Lembessis

Published Oct 30, 2008• 9 citations
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Abstract

We show that under certain conditions, the inclusion of counter-rotating terms which are usually ignored in the interaction of a two-level atom with the electromagnetic field, leads to significant modifications of the splitting of an atomic beam in the well-known optical Stern-Gerlach effect, which now acquires a ``fine'' structure.

DOI
10.1103/physreva.78.043423

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•Oct 14, 2005•11 citations
We show that under certain conditions, the inclusion of counter-rotating terms which are usually ignored in the interaction of a two-level atom with the electromagnetic field, leads to significant modifications of the splitting of an atomic beam in the well-known optical Stern-Gerlach effect, which now acquires a ``fine'' structure.
In the optical Stern-Gerlach effect the interaction of a two-level atom with an optical-field gradient causes a state-selective deflection that leads to a splitting of the atomic trajectory. The semiclassical approach to this problem actually predicts a splitting of the atomic beam into two paths, similar to the well-known magnetic Stern-Gerlach effect for spin 1/2. Here we study a model in which the quantum nature of the field is taken into account and we show, in particular, that for an initial coherent state of the cavity light the optical Stern-Gerlach effect manifests itself as a splitting of the atomic beam into two groups containing, however, many spots. \textcopyright{} 1996 The American Physical Society.
In the optical Stern-Gerlach effect, the interaction of a traveling two-level atom with the electromagnetic field of an optical cavity causes a splitting of the atomic trajectory. One may ask if it is possible to single out particular initial configurations of the system that will lead to selective scattering, in which the atoms follow only one trajectory. We show that these configurations consist of a coherent superposition of the atomic internal states, and of a field phase state or a field coherent state, with a precise phase relation between the two subsystems: The same configurations which produce the so-called atomic coherent trapping in the Jaynes-Cummings model.
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.