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Physical Review A

Quantum-nondemolition determination of an atomic state via the optical Stern-Gerlach effect

S. M. Tan, Daniel F. Walls

Published Jan 1, 1993• 4 citations
Publisher

Abstract

The near-resonant interaction of an atomic beam with an optical standing-wave field can produce a deflection of the beam that depends on the initial atomic state. We investigate the extent to which the momentum transfer may be regarded as a coherent nondestructive encoding of the internal atomic state on the center-of-mass motion. Techniques developed for analyzing quantum-nondemolition measurements are used to quantify the effectiveness of this encoding. The effects of varying the detuning and the profile of the optical beam are discussed using parameter values close to those recently realized experimentally by Sleator et al. [Phys. Rev. Lett. 68, 1996 (1992)].

DOI
10.1103/physreva.47.663

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The near-resonant interaction of an atomic beam with an optical standing-wave field can produce a deflection of the beam that depends on the initial atomic state. We investigate the extent to which the momentum transfer may be regarded as a coherent nondestructive encoding of the internal atomic state on the center-of-mass motion. Techniques developed for analyzing quantum-nondemolition measurements are used to quantify the effectiveness of this encoding. The effects of varying the detuning and the profile of the optical beam are discussed using parameter values close to those recently realized experimentally by Sleator et al. [Phys. Rev. Lett. 68, 1996 (1992)].
We consider the deflection of a resonant two-level atom by a quantized electromagnetic field using the Jaynes-Cummings Hamiltonian. We show that a joint measurement of the atomic momentum and an appropriate field variable allows us to reconstruct the original photon statistics even for this demolition Hamiltonian. We demonstrate that the momentum distribution of atoms scattered at the nodes of the standing wave also follows the original photon statistics of the field. In this sense a recent experiment on the optical Stern-Gerlach effect [T. Sleator et al., Phys. Rev. Lett. 68, 1996 (1992)] measures the intensity fluctuations of the standing wave.
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.
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 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 report on criteria to detect entanglement between the light modes of two crossed optical cavities by analyzing the transverse deflection patterns of an atomic beam. The photon exchange between the modes and atoms occurs around the overlapping nodes of associated standing waves, which generates the two-dimensional (2D) version of the Optical Stern–Gerlach (OSG) effect. In this optical cross-cavity setup, we show that the discrete signatures of the field states, left in the momentum distribution of the deflected atoms, may reveal entanglement for a certain class of two-mode states. For a single photon, we present the possibility of quantifying entanglement by the rotation of the momentum distribution. For a larger number of photons, we demonstrate that quantum interference precludes the population of specific momentum states revealing maximum entanglement between the light modes.