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arXiv:cond-mat/0603463 · Physical Review Letters

Low Velocity Quantum Reflection of Bose-Einstein Condensates

Thomas A. Pasquini, Michele Saba, Gyu-Boong Jo, Yong-il Shin, Wolfgang Ketterle, David E. Pritchard, Tim A. Savas, Norbert Mulders

Published Aug 30, 2006• 172 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.97.093201

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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 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.
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 observed quantum reflection of ultracold atoms from the attractive potential of a solid surface. Extremely dilute Bose-Einstein condensates of 23Na, with peak density 10(11)-10(12) atoms/cm(3), confined in a weak gravitomagnetic trap were normally incident on a silicon surface. Reflection probabilities of up to 20% were observed for incident velocities of 1-8 mm/s. The velocity dependence agrees qualitatively with the prediction for quantum reflection from the attractive Casimir-Polder potential. Atoms confined in a harmonic trap divided in half by a solid surface exhibited extended lifetime due to quantum reflection from the surface, implying a reflection probability above 50%.
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.
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 construct an invisible quantum barrier which represents the phenomenon of quantum reflection using available data on atom-wall and Bose-Einstein-condensate--wall reflection. We use the Abel equation to invert the data. The resulting invisible quantum barrier is double valued in both axes. We study this invisible barrier in the case of atom and Bose-Einstein condensate (BEC) reflection from a solid silicon surface. A time-dependent, one-spatial-dimension Gross-Pitaevskii equation is solved for the BEC case. We found that the BEC behaves very similarly to the single atom except for size effects, which manifest themselves in a maximum in the reflectivity at small distances from the wall. The effect of the atom-atom interaction on the BEC reflection and correspondingly on the invisible barrier is found to be appreciable at low velocities and comparable to the finite-size effect. The trapping of an ultracold atom or BEC between two walls is discussed.