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Physical Review A

Reflection and diffraction of atomic de Broglie waves by an evanescent laser wave

Rainer A. Deutschmann, Wolfgang A. Ertmer, Hartmut Wallis

Published Mar 1, 1993• 54 citations
Publisher

Abstract

The diffraction theory of a reflection grating for atoms based on a standing light wave is developed in a particular dressed-state approximation. The basis states take into account internal and external atomic degrees of freedom simultaneously and correspond to diffraction orders in the asymptotic region. In this basis the atom is described as an effective multilevel system. In an adiabatic approximation for the motion perpendicular to the grating, these levels serve as position-dependent potentials. An incoming de Broglie wave is coupled to higher diffraction orders by nonadiabatic transitions near avoided crossings of the potentials. Numerical results confirm the qualitative predictions following from the physical picture of the diffraction process and lead to an improved description of experiments.

DOI
10.1103/physreva.47.2169

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The diffraction theory of a reflection grating for atoms based on a standing light wave is developed in a particular dressed-state approximation. The basis states take into account internal and external atomic degrees of freedom simultaneously and correspond to diffraction orders in the asymptotic region. In this basis the atom is described as an effective multilevel system. In an adiabatic approximation for the motion perpendicular to the grating, these levels serve as position-dependent potentials. An incoming de Broglie wave is coupled to higher diffraction orders by nonadiabatic transitions near avoided crossings of the potentials. Numerical results confirm the qualitative predictions following from the physical picture of the diffraction process and lead to an improved description of experiments.
We present two results in an investigation of reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both results use the bare-state rather than dressed-state picture. One is based on the Born series, whereas the other is based on the Laplace transformation of the coupled differential equations. The two solutions yield the same theoretical expressions for reflected and diffracted atomic waves in the whole space, including the interaction and the asymptotic regions.
Realization of the analogues of optical components for the manipulation of atomic de Broglie waves has recently become possible through the use of laser-based techniques. The strong fields generated by laser light have already been used to reflect atoms using travelling evanescent waves, and to diffract atomic beams through small angles using transmission gratings formed by a standing laser light wave in vacuo. Present experiments aim to combine these techniques to produce a reflection diffraction grating formed by a standing evanescent laser-light field, and to exploit the larger diffraction angles made possible theoretically by such a scheme.
The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore, we give the limiting cases of the amplitudes in the uniform semiclassical limit, which is valid in all regions including near the classical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel functions. We find our uniform semiclassical limit to be closer to the exact result over the full range of parameter values than the previously reported calculations.
In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.
In order to diffract atoms from an evanescent light reflection grating the Rabi frequency must be greater than the Doppler shift associated with the atomic velocity. For thermal atoms this cannot be achieved using dye lasers. Rather than slow the atoms we have produced a moving light grating and observe resonances in the reflectivity of the grating for certain grating velocities. The position of these resonances fulfils the Doppleron condition Δ’=nΔD’, which is consistent with a dressed state model for diffraction from such a grating.
Abstract. — We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed. 1. Introduction. The diffraction of atomic de Broglie waves by standing wave light fields [1-4] or mechanical microstructures [5] has recently received considerable interest because of its potential application as an atomic beam splitter, one of the key components for the development of atom optics and interferometry