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arXiv:quant-ph/9703055

Notes on free fall of a particle and bouncing on a reflecting surface

Tri Sulistiono

Published Apr 1, 1997• 0 citations
arXivHTMLPDF

Abstract

Considerable progress has recently been made in controling the motion of free atomic particles by means of light pressure exerted by laser radiation. The free fall of atoms and bouncing on a reflecting surface made from evanescent wave formed by internal reflection of a quasiresonant laser beam at a curved glass surface in the presence of homogeneous gravitational field has been observed. In this paper we present the energy quantization of this system by making use the asymptotic expansion method. It is shown that for large $n$ the levels go like $n^{2/3}$ which may be compared with $n^2$ for the infinite square well.

DOI
10.48550/arxiv.quant-ph/9703055

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Considerable progress has recently been made in controling the motion of free atomic particles by means of light pressure exerted by laser radiation. The free fall of atoms and bouncing on a reflecting surface made from evanescent wave formed by internal reflection of a quasiresonant laser beam at a curved glass surface in the presence of homogeneous gravitational field has been observed. In this paper we present the energy quantization of this system by making use the asymptotic expansion method. It is shown that for large nnn the levels go like n2/3n^{2/3}n2/3 which may be compared with n2n^2n2 for the infinite square well.
A curved mirror for atoms was made from an evanescent wave, formed by internal reflection of a quasiresonant laser beam at a curved glass surface. A cold cloud of cesium atoms was dropped onto the mirror and observed to rebound more than 8 times. The mirror size and reflectivity were studied, and reasonable agreement with a simple theory obtained. With 800 mW of laser power and a mirror of 1 mm diameter, we observed up to 73% of the atoms returning after each bounce, the losses being mostly during the free flight between bounces.
Summary form only given, as follows. Atomic cavities provide a convenient way to store atoms without perturbing them too much. We have recently built such a cavity for cesium atoms. A curved mirror was made for an evanescent wave, formed by internal reflection of a quasiresonant laser beam at a curved glass surface. A cold cloud of cesium atoms was dropped onto the mirror (Fig. 1a) and observed to rebound up to 10 times (Fig. 1b). The mirror size and reflectivity were studied, and reasonable agreement with a simple theory was obtained. With 800 mW of laser power and a mirror of 1 mm diameter, we observed up to 73% of the atoms returning after each bounce. We will present these experimental results, and we will also discuss some prospects to investigate the quantum nature of the atomic motion in such a cavity.
We propose a trap based on an evanescent light wave which is formed on the surface of a conical or a pyramidal cavity in a glass substrate. The far blue-detuned evanescent wave acts as a mirror for atoms, bouncing on it in the gravitational field. In addition, fast and deep Sisyphus cooling in the evanescent wave can be organized for alkali atoms. This leads to the cooling of the atoms down to the recoil-limited temperature and their collection in the field- free region near the bottom of the trap, to form an atomic gas of extremely high density.
We calculate the modes in a stable gravitational cavity where the atomic mirror at the bottom of the bounce is caused by an internally reflected intense Gaussian-mode laser beam. In contrast to Wallis, Dalibard, and Cohen-Tannoudji [Appl. Phys. B 54, 407 (1992)], who treated the bottom bouncing mechanism as due to an infinite potential, we include the effect of the exponentially decaying potential caused by the evanescent wave. Nevertheless, we find that above this evanescent wave potential the mode structure corresponds exactly to that obtained using an infinite potential. The allowed energies differ slightly due to the phase change through the evanescent wave. The broadening of the modes due to the damping effects of spontaneous emission was calculated and because of the intrinsic transverse width of the modes was found to depend strongly on energy and transverse excitation, which differs from a simple one-dimensional classical calculation. The finesse and QQQ of the cavity due to the damping effects of spontaneous emission were also calculated and in contrast to an optical Fabry-P\'erot cavity were found to depend strongly on energy.
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.
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.