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Physical Review A

Mean field for a dilute Bose gas in the light field of an evanescent wave

Hartmut Wallis

Published Sep 1, 1997• 16 citations
Publisher

Abstract

The mean field for atoms undergoing ground-state collisions in a gravito-optical trap is determined in a fully self-consistent way. The atoms are confined by gravity and one atomic mirror formed by an evanescent laser wave. The vertical density distribution of the trapped Bose gas at zero temperature and the refractive modification of the electromagnetic field are obtained iteratively. In the regime of nearly total internal reflection, the sensitive variation of the evanescent wave with the index of the gas leads to large dipole-dipole shifts. In the limit of a steep evanescent wave and large detuning, ground-state interactions dominate.

DOI
10.1103/physreva.56.2060

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The mean field for atoms undergoing ground-state collisions in a gravito-optical trap is determined in a fully self-consistent way. The atoms are confined by gravity and one atomic mirror formed by an evanescent laser wave. The vertical density distribution of the trapped Bose gas at zero temperature and the refractive modification of the electromagnetic field are obtained iteratively. In the regime of nearly total internal reflection, the sensitive variation of the evanescent wave with the index of the gas leads to large dipole-dipole shifts. In the limit of a steep evanescent wave and large detuning, ground-state interactions dominate.
Abstract We study both static and dynamic properties of a weakly interacting Bose–Einstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross–Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas–Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.
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 report on the creation of a two-dimensional Bose-Einstein condensate of cesium atoms in a gravito-optical surface trap. The condensate is produced a few microm above a dielectric surface on an evanescent-wave atom mirror. After evaporative cooling by all-optical means, expansion measurements for the tightly confined vertical motion show energies well below the vibrational energy quantum. The presence of a condensate is observed in two independent ways by a magnetically induced collapse at negative scattering length and by measurements of the horizontal expansion.
The effect of the dipole-dipole interaction on the far-off-resonance optical dipole trapping scheme is calculated by a mean-field approach. The trapping laser field polarizes the atoms and the accompanying dipole-dipole energy shift deepens the attractive potential minimum in a pancake-shaped cloud. At high density the thermal motion cannot stabilize the gas against self-contraction and an instability occurs. We calculate the boundary of the stable and unstable equilibrium regions on a two-dimensional phase diagram of the atom number and the ratio of the trap depth to the temperature. We discuss the limitations imposed by the dipole-dipole instability on the parameters needed to reach Bose-Einstein condensation in an optical dipole trap.
Summary form only given. The gravito-optical surface trap (GOST) confines cesium atoms by a blue-detuned repulsive evanescent wave (EW) in combination with gravity. Horizontal confinement is provided by the conservative optical dipole potential of a hollow, cylindrical laser beam, far blue-detuned from resonance. For preparing a very cold and dense cesium gas in the GOST, we use evanescent wave 'Sisyphus' cooling, which is based on inelastic reflections of the atoms from the EW. Using this method we have obtained a temperature of 3 /spl mu/K, which corresponds to an average distance of the atoms from the surface of 19 /spl mu/m. As a very important feature for attaining very high densities, EW cooling allows one to keep the atoms predominantly in the absolute ground state, thus avoiding trap loss by light assisted collisions.
An alternative technique is proposed to create microscopic atom traps loaded with atoms from a gravito-optical surface trap (GOT), which is composed of an evanescent-wave mirror and a vertically aligned hollow laser beam. Our trap design is based on the use of current-carrying transparent conductors and transparent permanent magnets fabricated on the surface of a glass prism in the form of an internal structure of a refractive-index-matched thin dielectric film. The conductors can be fabricated of indium tin oxide (ITO) and the magnets of yttrium iron garnet (YIG). Different kinds of traps may be envisaged: i) spin-independent electro-optical ii) magneto-optical for either high- or low-field seeking atoms, and iii) purely magnetic for atoms in the low-field seeking states. In case iii), the magnetic-field minimum is located far enough from the film surface to make the contribution of the optical field negligible.