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arXiv:cond-mat/0412380 · Physical Review Letters

Anomalous Quantum Reflection of Bose-Einstein Condensates from a Silicon Surface: The Role of Dynamical Excitations

R. G. Scott, A. Martin, T. M. Fromhold, F. W. Sheard

Published Aug 11, 2005• 48 citations
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Abstract

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.

DOI
10.1103/physrevlett.95.073201

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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.
Abstract We investigated the effect of the angle of incidence on the quantum reflection of Bose–Einstein condensates (BECs) from regions with rapid potential variations. The reflection process was examined for both isotropic and anisotropic 2D disk-shaped BECs. In both cases, the angle of incidence was found to play a crucial role during reflection, inducing non-uniform atom-surface interactions and thus manipulating severe disruptions on the atomic cloud in the low incident velocity regime. In this scenario, the angle of incidence minimizes or even eliminates disruptions or fragmentation of the atomic cloud, especially for incidence angles far from the normal incidence direction. Consequently, anomalous reflectivity or saturation effects, which have been challenging in previous studies, can be effectively addressed and controlled. These findings provide new insights into optimizing the quantum reflection of BECs from a solid surface, particularly regarding the enhancement of the reflection probability of BECs from a planar silicon surface, which, since their first experiments, have not been maximized due to saturation effects.
We study how interactions affect the quantum reflection of Bose-Einstein condensates. A patterned silicon surface with a square array of pillars resulted in high reflection probabilities. For incident velocities greater than 2.5 mm/s, our observations agreed with single-particle theory. At velocities below 2.5 mm/s, the measured reflection probability saturated near 60% rather than increasing towards unity as predicted by the accepted theoretical model. We extend the theory of quantum reflection to account for the mean-field interactions of a condensate which suppresses quantum reflection at low velocity. The reflected condensates show collective excitations as recently predicted.
We consider the quantum reflection of vortices in Bose-Einstein condensates incident on a solid surface. Compared with the condensate without angular momentum, the rotation of the vortex gives unique opportunities to consider the interaction process between a matter wave and a solid surface. Due to the atom-surface interaction and dynamic excitations induced by interatomic interaction, our numerical simulations show that the reflected vortex would become unstable for sufficiently low velocity and large interaction strength. The stability diagram for the reflected vortex is given, and physical mechanism for this stability diagram is discussed. It is found that the expansion ratio between the reflected and incident vortices gives the boundary between stable and unstable regions for the reflected vortex.
Recent developments in atom optics have brought Bose-Einstein condensates within 1 μm of solid surfaces where the atom-surface interactions can no longer be ignored. At longrange, the atom-surface interaction is described by the weakly attractive Casimir-Polder potential which is classically predicted to accelerate an incident atom toward the surface where it will interact strongly with the internal modes of the surface, lose energy, and land in a bound state of the surface. When the incident atom is very cold, on the order of a few nanokelvin, however, the acceleration of the atomic wavefunction is so abrupt that the atom may partially reflect from the attractive tail in a process known as quantum reflection. This work presents experimental evidence for quantum reflection from a solid surface at normal incidence. Using atoms from a 23Na BEC, cooled to a few nanokelvin in a recently demonstrated single-coil trap, controlled collisions were induced between atoms and solid silicon surface. A maximum reflection probability of ∼ 12% was observed for an incident velocity of 1 mm/s. Atoms confined against the surface at low density exhibited an enhanced lifetime due to quantum reflection. A surprising aspect of quantum reflection is that nano-structured surfaces are predicted to exhibit enhanced quantum reflection due to the reduction of the atom-surface interaction from reduced density surfaces. Using a pillared surface with an density reduced to 1% of bulk density, we observe an enhancement of the reflection probability to ∼ 60%. At velocities from 2-25 mm/s, predicted threshold dependence of the reflection probability was observed. At velocities below 2 mm/s, the reflection probability was observed to saturate. We develop a simple model which predicts the saturation as a result of mean-field interactions between atoms in the incident Bose-Einstein condensate. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacAurthur Professor of Physics Thesis Supervisor: David E. Pritchard Title: Cecil and Ida Green Professor of Physics For the parents in my life,
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.