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Physical Review A

Quantum-trajectory analysis of an optical Stern-Gerlach experiment

Young-Tak Chough, Kyungwon An

Published Jun 24, 2004• 4 citations
Publisher

Abstract

We present a Monte Carlo simulation of a typical cavity-QED experiment on the optical Stern-Gerlach effect in terms of the quantum trajectory method. We show that the phenomenon of wave packet splitting may be experimentally observed even in a moderate coupling regime where the atomic and cavity damping rates are comparable to the atom-field coupling strength.

DOI
10.1103/physreva.69.063817

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We present a Monte Carlo simulation of a typical cavity-QED experiment on the optical Stern-Gerlach effect in terms of the quantum trajectory method. We show that the phenomenon of wave packet splitting may be experimentally observed even in a moderate coupling regime where the atomic and cavity damping rates are comparable to the atom-field coupling strength.
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.
In the optical Stern-Gerlach effect the two branches in which the incoming atomic packet splits up can display interference pattern outside the cavity when a field measurement is made which erases the which-way information on the quantum paths the system can follow. On the contrary, the mere possibility to acquire this information causes a decoherence effect which cancels out the interference pattern. A phase-space analysis is also carried out to investigate on the negativity of the Wigner function and on the connection between its covariance matrix and the distinguishability of the quantum paths.
We investigate the single-atom detection system using an optical standing-wave cavity, from the viewpoint of the quantized center-of-mass motion of the atomic wave packet. We show that since the atom-field coupling strength depends upon the overlap integral of the atomic wave packet and the field mode function, the effect of the wave-packet spreading via the momentum exchange process brings about a significant effect in the detection efficiency. We find that, as a result, the detection efficiency is not sensitive to the individual atomic trajectory for reasonably slow atoms. We also address an interesting phenomenon of the atomic wave-packet splitting occurring when an atom passes through a node of the cavity field.
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.