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Physical Review A

Numerical modeling of evanescent-wave atom optics

Craig M. Savage, Dan Gordon, Timothy C. Ralph

Published Dec 1, 1995• 11 citations
Publisher

Abstract

We numerically solve the time-dependent Schr\"odinger equation for a two-level atom interacting with an evanescent light field. The atom may be reflected or diffracted. Using the experimental parameter values we quantitatively model the evanescent field dopplerons (velocity-tuned resonances) observed by Stenlake et al. [Phys. Rev. A 49, 16 (1994)]. Besides successfully modeling the experiment, our approach provides complementary insights to the usual solution of the time-independent Schr\"odinger equation. We neglect spontaneous emission.

DOI
10.1103/physreva.52.4741

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We numerically solve the time-dependent Schr"odinger equation for a two-level atom interacting with an evanescent light field. The atom may be reflected or diffracted. Using the experimental parameter values we quantitatively model the evanescent field dopplerons (velocity-tuned resonances) observed by Stenlake et al. [Phys. Rev. A 49, 16 (1994)]. Besides successfully modeling the experiment, our approach provides complementary insights to the usual solution of the time-independent Schr"odinger equation. We neglect spontaneous emission.
Usually the reflection of two level atoms by a detuning evanescent laser wave was studied in past few years. In previous paper we have presented an exact solution for this model based on the matrix Laplace transformation technique, and proceeded the numerical calculations for a given set of parameters. However in the special case of resonance interaction considered in this paper, the solution for Schrödinger wave equation and reflectivity calculation can be greatly simplified; besides, the resonant solution provides a check to the numerical data based on the general solution of the previous paper.
We study theoretically the diffraction of atoms by a standing-wave light field. Conceptually the text is divided into two parts. In the first part we deal with the coherent interaction only. We use a band theoretical approach to describe the laser-atom interaction, and to characterize two-beam resonances (Dopplerons and Bragg resonances). These two-beam resonances are major candidates to develop effective atom beam splitters. We study the interaction with classical light fields as well as with quantum fields. In the second part we take incoherent processes, i.e. spontaneous emission, into account and present a numerical scheme for the solution of the generalized optical Bloch equations. This scheme is based on the split-operator technique, and we use it to study numerically the influence of spontaneous emission on the diffraction process. We compare our results with recent experimental data, and investigate the impact of spontaneous emission on the performance of two-beam resonances.
We describe a numerical method for solving the problem of the interaction of a monoenergetic atomic beam represented by a plane wave with a classical light field at glancing incidence. In the approximation where spontaneous emission is simply treated as a loss, this leads to a vector Schr\"odinger equation which is solved using a matrix technique. This allows the analysis of arbitrary optical intensity profiles rather than the rectangular profile previously considered by Zhang and Walls [Phys. Rev. Lett. 68, 3287 (1992)]. Selected numerical results show that the method describes a variety of phenomena including state-selective reflection and velocity-tuned (doppleron) resonances.
We analyze the condition of observation of Doppler-tuned multiphotonic (``doppleron'') resonances in an atom reflection by a standing evanescent wave. A theoretical model based on Ehrenfest's theorem for external atomic motion is proposed. The light forces exerted by the stationary evanescent wave are calculated either with a perturbation approach, or with a continuous-fraction method. The appearance of the multiphotonic lines in the specularly reflected atomic beam is clearly shown. These predictions are in good agreement with previous and present experimental results, which are discussed.
Multi-photon Doppleron resonances are investigated for the diffraction of atoms by a classical standing-wave optical field in the regime where energy conservation limits the diffraction orders. In this regime, atomic recoil is incorporated into the description, and consideration of the dynamical shift of the resonance condition from the purely kinematic results becomes critical to observing the desired diffraction of the atomic wave function. Special attention is given to the development of a technique for evaluating the resonances which constitutes a significant simplification of the usual degenerate perturbation theory approach for a quantum-mechanical Hamiltonian. Also developed is a specialized off-resonant atom-field interaction which is shown to be maximally efficient at producing high-order diffraction of the atomic wave function. Suggestions for its implementation are given.