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Physical Review A

Quantum fine structure of the optical Stern-Gerlach effect

Alessandro Vaglica

Published Oct 1, 1996• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.3195

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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.
We report the observation of the splitting of an atomic beam by the optical Stern-Gerlach effect. A beam of metastable He atoms interacts with a nearly or exactly resonant laser field with a well-defined intensity gradient perpendicular to the atomic beam. The coherent splitting of the atomic beam is produced in the case of exact resonance. For the nonresonant case, a deflection of the atomic beam is observed. We have studied the splitting and deflection of the atomic beam as a function of laser detuning from resonance. Our results are in good agreement with theoretical predictions.
Two recent experiments demonstrating novel atomic lenses—one using a free standing Fresnel zone plate and the other using an optical standing wave with large (40 μm) period—will be discussed. In addition, an experiment demonstrating the splitting of an atomic beam by the optical Stern–Gerlach effect will be described. In this effect, a beam of (two-level) atoms is coherently split into two paths by an exactly resonant optical field gradient, each path containing atoms in one of the two dressed states. The field gradient was derived from a large period standing wave, produced by bouncing a laser beam from a glass surface at grazing incidence. The experiments were carried out with metastable He atoms interacting through the 23S1to 23P2 transition with an optical field at 1.083 μm. The interaction times were significantly less than the 23P natural lifetime of 100 ns, so spontaneous emission played no role during the interaction.
We report a different type of optical Stern-Gerlach effect, where a magnetic-field gradient is replaced with a light-intensity gradient and a paramagnetic atom is deflected according to its magnetic quantum number. The laser light is detuned between the D1D1D1 and D2D2D2 frequencies, with the size of the detuning from the D2D2D2 resonance being twice that from the D1D1D1 resonance, and it is circularly polarized to produce an ac Stark shift that takes the form of a pure Zeeman shift. Slow rubidium atoms are extracted from a magneto-optical trap and then spin polarized. The atoms traversing the laser-intensity gradient on one side of the Gaussian beam profile show deflections that depend on the atomic spin state and the laser polarization. When the laser-beam axis is aligned with the slit that defines the atomic beam, we observe focusing and defocusing of the atomic beam.
We consider the deflection of a three-level atom of Λ-type interacting with a light field of two coherent laser beams. We employ the dressed state formalism, which is suitable for large Rabi frequencies and/or large detunings. A full study of the interaction and relaxation processes is performed. We show that a beam of atoms is split into three beams once it crosses the light field. This is a three-state version of the well-known optical Stern–Gerlach effect, which has been theoretically studied and experimentally demonstrated for two-level atoms. Under coherent population trapping conditions, the splitting of the beam becomes twofold. This gives us, in principle, the opportunity of a mechanical demonstration of the coherent population trapping effect.