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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Excited atomic wavepackets after a non-adiabatic reflection on a laser mirror

Luis Santos, L. Roso

Published Jun 1, 1998• 0 citations
Publisher

Abstract

The reflection of an atomic wavepacket on a laser mirror under non-adiabatic conditions has been analysed numerically. In particular, we have proved that for realistic laser profiles it is possible to obtain an excited atomic wavepacket which is stopped in the direction perpendicular to the laser mirror. The possibility of completely stopping a reflected excited wavepacket is also discussed.

DOI
10.1088/1355-5111/10/3/013

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The reflection of an atomic wavepacket on a laser mirror under non-adiabatic conditions has been analysed numerically. In particular, we have proved that for realistic laser profiles it is possible to obtain an excited atomic wavepacket which is stopped in the direction perpendicular to the laser mirror. The possibility of completely stopping a reflected excited wavepacket is also discussed.
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We study the reflection of narrow (in space) quantum wavepackets from nonabsorptive mirrors (totally or partially reflecting). If the initial mean value of the momentum component perpendicular to the mirror surface is less than the momentum uncertainty, then the mean value of this component gradually increases with time at the expense of shrinking the packet in the momentum space. As a consequence, very slow particles moving initially in the direction parallel to the mirror surface will be deflected to appreciable angles, even when they pass at macroscopical distances from the mirror. We give analytical expressions describing the asymptotical behaviour of wavefunctions and density matrices in the coordinate and momentum representations for arbitrary narrow initial packets. We show that the asymptotical mean values and variances do not depend on the phases of the complex reflection and transmission coefficients. Moreover, they are insensitive to the concrete form of the reflective potential in the case of totally reflecting mirrors. For partially reflecting mirrors we introduce the concept of conditional wavefunctions and mean values. The dependences of the asymptotical values of different quantities characterizing the packet (e.g. the `momentum transformation coefficient' and the `invariant uncertainty product') on the parameters of the reflecting potential (the height and width or characteristic length of the transition region) are analysed in the examples of the potentials of Epstein's type and their limit cases (the ideal reflecting wall and the delta potential). A possibility for the verification of the effect of quantum deflection in experiments with ultracold atoms is briefly discussed.
The propagation of a two-level atomic wave packet across a laser beam is considered. For small incident kinetic energies of the atom, the wave nature of the center-of-mass motion becomes apparent, giving reflections and refractions in the case of a square profile of the laser beam. When the incident momentum is low enough, we show that one of the dressed states cannot propagate inside the laser beam, giving rise to an evanescent atomic wave packet. Also a stopped excited component is found when the incident momentum equals in modulus---not in direction---the one-photon recoil. \textcopyright{} 1996 The American Physical Society.
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.
We propose a laser arrangement that can allow a multipeaked laser profile with periodicity of the order of the laser wavelength. We analyse the reflection properties of atoms dropped onto this periodical laser. This periodicity produces bands in the reflection spectrum of the atoms. We have studied the case of repulsive and attractive laser potential. In particular we prove the feasibility of constructing an atom mirror with an attractive potential, i.e. a potential without turning points. We include in our calculations the gravitational effects. The spontaneous emission is also analysed as a lossy mechanism, and we have proved that for sufficiently large detuning the bands remain.
We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.