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Physical Review A

Atomic deflection in the transition between diffractive and diffusive regimes: A numerical simulation

S. M. Tan, Daniel F. Walls

Published Sep 1, 1991• 17 citations
Publisher

Abstract

The transition between diffractive and diffusive regimes in the deflection of atoms by a standing-wave light field has recently been observed experimentally by Gould et al, [Phys. Rev. A 43, 585 (1991)]. We describe and present the results of a numerical simulation which allows these results to be understood in terms of the theory developed by Tanguy, Reynaud, and Cohen-Tannoudji [J. Phys. B 17, 4623 (1984)].

DOI
10.1103/physreva.44.r2779

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The transition between diffractive and diffusive regimes in the deflection of atoms by a standing-wave light field has recently been observed experimentally by Gould et al, [Phys. Rev. A 43, 585 (1991)]. We describe and present the results of a numerical simulation which allows these results to be understood in terms of the theory developed by Tanguy, Reynaud, and Cohen-Tannoudji [J. Phys. B 17, 4623 (1984)].
We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.
We have observed momentum transfer from a standing-wave light field to an atomic beam. The atomic beam is split symmetrically into two peaks whose separation increases with field strength. The short interaction time ensures that this deflection is due to induced forces; these are described using a semiclassical dressed-atom treatment, which gives good agreement with the data. In addition to the splitting, we have observed diffraction of the atomic beam due to the exchange of even numbers of photons with the field.
Momentum transfer to atoms by a standing light wave is measured in the presence of spontaneous decay. As the number of spontaneous decays is increased, the well-known Kapitza-Dirac diffractive structure observed in the absence of spontaneous decay evolves into a smooth diffusive pattern. Theoretical treatments based on a diffusive model adequately describe the rms momentum transfers and the envelopes of the momentum distributions. However, we observe significant persistence of diffractive structure at our long interaction times and find that details of the deflection profiles are accurately predicted only when several spontaneous decays occur during the interaction.
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.
The exchange of momentum between atoms and photons in a deflection experiment is usually described by different formalisms depending on whether the interaction time T is shown or long compared with the radiative lifetime tau R . The authors present a new approach to this problem leading to a single theoretical expression valid in both limits and therefore allowing the transition between them to be studied. They interpret in this way the resonant Kapitza-Dirac effect and the optical Stern and Gerlach effect appearing in the short-time limit (T<< tau R ) as well as the deflection profiles usually deduced from a Fokker-Planck equation in the long-time limit (T>> tau R ). The transition between these two regimes is interpreted in terms of momentum transfer due to absorption and stimulated emission of laser photons, convoluted by the distribution of recoil due to spontaneously emitted photons.