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Modern Physics Letters B

On the Enhancement of Impurity Collisions in a Bose–Einstein Condensate

Fabio Cardone A, Roberto Mignani, Walter Perconti

Published Sep 20, 2003• 0 citations
Publisher

Abstract

We present a possible explanation of the discrepancy between theory and experiment (observed by Chikkatur et al.) in the collisional density of impurities in a Bose–Einstein condensate of sodium atoms. The discrepancy is ascribed to the fact that the experiment was carried out in a situation of strong instability, where small variations of the initial number of impurities in the condensate may give rise to a large variation in the number of colliding atoms.

DOI
10.1142/s0217984903006141

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We present a possible explanation of the discrepancy between theory and experiment (observed by Chikkatur et al.) in the collisional density of impurities in a Bose–Einstein condensate of sodium atoms. The discrepancy is ascribed to the fact that the experiment was carried out in a situation of strong instability, where small variations of the initial number of impurities in the condensate may give rise to a large variation in the number of colliding atoms.
Quantum dynamics of impurities in a bath of bosons is a long-standing problem in solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms have focused on this problem, studying atomic impurities immersed in an atomic Bose–Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano−Feshbach resonance technique. Here, we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity consisting of a few 41 K atoms and a BEC of 87 Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the inter-species interaction strength (regardless of its sign), we find that the impurity, which starts from outside the BEC, simply causes the BEC cloud to oscillate back and forth, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC, and strongly changes its amplitude of oscillation. In the strong interaction regime, if the inter-species interaction is attractive, a local maximum (bright soliton) in the BEC density occurs where the impurity is trapped; if, instead, the inter-species interaction is repulsive, the impurity is not able to enter the BEC cloud and the reflection coefficient is close to one. However, if the initial displacement of the impurity is increased, the impurity is able to penetrate the cloud, leading to the appearance of a moving hole (dark soliton) in the BEC.
Impurity atoms propagating at variable velocities through a trapped Bose-Einstein condensate were produced using a stimulated Raman transition. The redistribution of momentum by collisions between the impurity atoms and the stationary condensate was observed in a time-of-flight analysis. The collisional cross section was dramatically reduced when the impurity velocity was reduced below the condensate speed of sound, in agreement with the Landau criterion for superfluidity. For large numbers of impurity atoms, we observed an enhancement of atomic collisions due to bosonic stimulation. This enhancement is analogous to optical super-radiance.
We study the interaction-induced localization —the so-called self-trapping— of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that —unlike repulsive impurities— attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value β ⋆ . Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.
We study the ground-state properties of a trapped Bose-Einstein condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions, the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized, the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This 'collapse' can possibly be investigated in bosenova-type experiments.
We study the ground-state properties of a trapped Bose-Einstein condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions, the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized, the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This ``collapse'' can possibly be investigated in bosenova-type experiments.
We study the collision of two Bose–Einstein condensates with pure dipolar interaction. A stationary pure dipolar condensate is known to be stable when the atom number is below a critical value. However, collapse can occur during the collision between two condensates due to local density fluctuations even if the total atom number is only a fraction of the critical value. Using full three-dimensional numerical simulations, we observe the collapse induced by local density fluctuations. For the purpose of future experiments, we present the time dependence of the density distribution, energy per particle and the maximal density of the condensate. We also discuss the collapse time as a function of the relative phase between the two condensates.