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arXiv:quant-ph/0507276 · Physical Review A

Diffraction of a Bose-Einstein condensate in the time domain

Yves Colombe, B. Mercier, Hélène Perrin, V. Lorent

Published Dec 5, 2005• 35 citations
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Abstract

We have observed the diffraction of a Bose-Einstein condensate of rubidium atoms on a vibrating mirror potential. The matter wave packet bounces back at normal incidence on a blue-detuned evanescent light field after a $3.6\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ free fall. The mirror vibrates at a frequency of $500\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ with an amplitude of $3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The atomic carrier and side bands are directly imaged during their ballistic expansion. The locations and the relative weights of the diffracted atomic wave packets are in very good agreement with the theoretical prediction of Henkel et al. [J. Phys. II 4, 1877 (1994)].

DOI
10.1103/physreva.72.061601

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We have observed the diffraction of a Bose-Einstein condensate of rubidium atoms on a vibrating mirror potential. The matter wave packet bounces back at normal incidence on a blue-detuned evanescent light field after a 3.6mm3.6\phantom{\rule{0.3em}{0ex}}\mathrm{mm}3.6mm free fall. The mirror vibrates at a frequency of 500kHz500\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}500kHz with an amplitude of 3nm3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}3nm. The atomic carrier and side bands are directly imaged during their ballistic expansion. The locations and the relative weights of the diffracted atomic wave packets are in very good agreement with the theoretical prediction of Henkel et al. [J. Phys. II 4, 1877 (1994)].
We study the dynamics of the matter-wave soliton interacting with a vibrating mirror created by an evanescent light and provide a quantum scattering picture for the time-domain diffraction of the matter-wave soliton. Under Kramers-Henneberger (KH) transformation, i.e., in a vibrating coordinate, the vibration of the mirror can be cast to an effective gauge field. We then can exploit the Dyson series and the quantum scattering theory to investigate the dynamics of the soliton that moves in the effective gauge field and is reflected by a static mirror. Our analytical theory can quantitatively deduce the locations and the relative weights of the scattered wave packets, which is consistent with our numerical simulations of directly solving a nonlinear Schr\"odinger equation. In particular, for a two-frequency vibrating case, our theory predicts some interesting multipeak sideband structures in the diffracted matter-wave distributions, which can be resorted to the resonance of two frequencies. Underlying mechanisms and possible applications are discussed.
Cesium atoms prepared in a state of well-defined total energy have been reflected from a vibrating mirror, causing the matter waves to be phase modulated. The mirror is an evanescent light wave whose intensity is modulated in time at a frequency $\ensuremath{\nu}$ in the range 0 to 2 MHz; the atoms are reflected at normal incidence. The resulting beam consists of a ``carrier'' plus various sidebands corresponding to de Broglie waves propagating at different velocities. The precision and flexibility of this technique make it a promising tool in atom optics.
We investigate the evolution of Bose-Einstein condensates falling under gravity and bouncing off a mirror formed by a far-detuned sheet of light. After reflection, the atomic density profile develops splitting and interference structures which depend on the drop height, on the strength of the light sheet, as well as on the initial mean field energy and size of the condensate. We compare experimental results with simulations of the Gross-Pitaevski equation. A comparison with the behavior of bouncing thermal clouds allows us to identify quantum features specific for condensates.