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arXiv:cond-mat/0610053 · Physical Review A

Transmission and reflection of Bose-Einstein condensates incident on a Gaussian tunnel barrier

A. Martin, R. G. Scott, T. M. Fromhold

Published Jun 28, 2007• 19 citations
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Abstract

We investigate how Bose-Einstein condensates, whose initial state is either irrotational or contains a single vortex, scatter off a one-dimensional Gaussian tunnel barrier. We find that for low atom densities the vortex structure within the condensate is maintained during scattering, whereas at medium and high densities, multiple additional vortices can be created by the scattering process, resulting in complex dynamics and disruption of the atom cloud. This disruption originates from two different mechanisms associated, respectively, with the initial rotation of the atom cloud and the interference between the incident and reflected matter waves.

DOI
10.1103/physreva.75.065602

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We investigate how Bose-Einstein condensates, whose initial state is either irrotational or contains a single vortex, scatter off a one-dimensional Gaussian tunnel barrier. We find that for low atom densities the vortex structure within the condensate is maintained during scattering, whereas at medium and high densities, multiple additional vortices can be created by the scattering process, resulting in complex dynamics and disruption of the atom cloud. This disruption originates from two different mechanisms associated, respectively, with the initial rotation of the atom cloud and the interference between the incident and reflected matter waves.
We perform fully three-dimensional simulations, using the truncated Wigner method, to investigate the reflection of Bose-Einstein condensates from abrupt potential barriers. We show that the interatomic interactions can disrupt the internal structure of a cigar-shaped cloud with a high atom density at low approach velocities, damping the center-of-mass motion and generating vortices. Furthermore, by incorporating quantum noise we show that scattering halos form at high approach velocities, causing an associated condensate depletion. We compare our results to recent experimental observations.
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.
We present theoretical and experimental studies of the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. For low atom densities and inertial forces, the condensate performs regular Bloch oscillations, and its center-of-mass motion closely follows semiclassical single-particle trajectories, shaped by the lowest-energy band. But in other regimes, the center-of-mass motion disrupts the internal structure of the condensate by generating solitons and vortex rings, which can trigger explosive expansion of the atom cloud. We use images of the atom cloud to provide experimental evidence for this internal disruption, and find that the process occurs most readily in high-density condensates undergoing slow Bloch oscillations.
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.
The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective one-dimensional Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matter-wave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the noninteracting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.
We investigate transmission and reflection of Bose-Einstein condensate excitations in the low-energy limit across a potential barrier separating two condensates with different densities. Bogoliubov excitation in the low-energy limit has an incident angle where perfect transmission occurs. This condition corresponds to the Brewster's law for the electromagnetic wave. There also exists the total internal reflection of the Bogoliubov excitation in the low-energy limit. In the case of the normal incidence, our result in the low-energy limit is consistent with a result for weakly interacting one-dimensional Bose gases treated as Tomonaga-Luttinger liquids.