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Quasi-analytical theory for the anomalous quantum reflection of Bose-Einstein condensates

Alexander Jurisch, Jan Michael Rost

Published Apr 2, 2008• 0 citations
OpenAlex

Abstract

We develop a quasi-analytical theory for the quantum reflection amplitude of Bose-Einstein condensates. We derive and calculate the decay-width of a Bose-Einstein condensate. A general relation between the time-dependent decay-law of the system and its quantum reflection amplitude allows us to explain the quantum reflection anomaly of Bose-Einstein condensates present in BEC-surface systems as a direct consequence of the repulsive particle interaction.

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We develop a quasi-analytical theory for the quantum reflection amplitude of Bose-Einstein condensates. We derive and calculate the decay-width of a Bose-Einstein condensate. A general relation between the time-dependent decay-law of the system and its quantum reflection amplitude allows us to explain the quantum reflection anomaly of Bose-Einstein condensates present in BEC-surface systems as a direct consequence of the repulsive particle interaction.
We investigate the effect of interatomic interactions on the quantum-mechanical reflection of Bose-Einstein condensates from regions of rapid potential variation. The reflection process depends critically on the density and incident velocity of the condensate. For low densities and high velocities, the atom cloud has almost the same form before and after reflection. Conversely, at high densities and low velocities, the reflection process generates solitons and vortex rings that fragment the condensate. We show that this fragmentation can explain the anomalously low reflection probabilities recently measured for low-velocity condensates incident on a silicon surface.
We study the dynamic behavior of a Bose-Einstein condensate (BEC) containing a dark soliton separately reflected from potential drops and potential barriers. It is shown that for a rapidly varying potential and in a certain regime of incident velocity, the quantum reflection probability displays the cosine of the deflection angle between the incident soliton and the reflected soliton, i.e., R(θ)∼cos⁡2θR(θ) \sim \cos 2θR(θ)∼cos2θ. For a potential drop, R(θ)R(θ)R(θ) is susceptible to the widths of potential drop up to the length of the dark soliton and the difference of the reflection rates between the orientation angle of the soliton θ=0θ=0θ=0 and θ=π/2θ=π/2θ=π/2, δRsδR_sδRs​, displays oscillating exponential decay with increasing potential widths. However, for a barrier potential, R(θ)R(θ)R(θ) is insensitive for the potential width less than the decay length of the matter wave and δRsδR_sδRs​ presents an exponential trend. This discrepancy of the reflectances in two systems is arisen from the different behaviors of matter waves in the region of potential variation.
We study dynamical behaviors of a Bose–Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R s ∼ cos [λ(θ – π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitiv width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.