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arXiv:cond-mat/9810269

Impurity Expulsion From a Bose-Einstein Condensate

Siu A. Chin, Harald Forbert

Published Oct 21, 1998• 0 citations
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Abstract

When a sizable, hard-sphere-like impurity is placed in a trapped Bose-Einstein condensate, it will create a hole in the condensate wave function. Since it costs more energy to drill a hole at the wave function's maximum (near the trap center) than at its minimum (near the trap edge), the impurity will be expelled from the condensate. This suggests that C-60 molecules freely falling through a condensate of atomic hydrogen may be deflected by a radial acceleration comparable to g. The scattered fullerenes would then form a characteristic banded density pattern outside of the trap. The detection of these deflected molecules can be used to identify the onset of Bose-Einstein condensation.

DOI
10.48550/arxiv.cond-mat/9810269

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When a sizable, hard-sphere-like impurity is placed in a trapped Bose-Einstein condensate, it will create a hole in the condensate wave function. Since it costs more energy to drill a hole at the wave function's maximum (near the trap center) than at its minimum (near the trap edge), the impurity will be expelled from the condensate. This suggests that C-60 molecules freely falling through a condensate of atomic hydrogen may be deflected by a radial acceleration comparable to g. The scattered fullerenes would then form a characteristic banded density pattern outside of the trap. The detection of these deflected molecules can be used to identify the onset of Bose-Einstein condensation.
We estimate the changes in the condensate ground state energy induced by one or more "sizable" impurities. By "sizable", we mean an impurity whose size is within a few orders of magnitude of the trap size and not necessarily atomic in scale. A sizable impurity will "drill" a hole in the condensate wave function and alter the condensate energy. The question is whether this microscopic change can be detected macroscopically because of the Bose-Einstein condensation effect. We discuss the effect of impurity expulsion, condensate interactions, and the induced interaction between two impurities.
Motivated by recent experiments, we investigate a single 133Cs{}^{133}\text{Cs}133Cs impurity in the center of a trapped 87Rb{}^{87}\text{Rb}87Rb Bose-Einstein condensate (BEC). Within a zero-temperature mean-field description we provide a one-dimensional physical intuitive model which involves two coupled differential equations for the condensate and the impurity wave function, which we solve numerically. With this we determine within the equilibrium phase diagram spanned by the intra- and interspecies coupling strength whether the impurity is localized at the trap center or expelled to the condensate border. In the former case we find that the impurity induces a bump or dip on the condensate for an attractive or a repulsive Rb-Cs interaction strength, respectively. Conversely, the condensate environment leads to an effective mass of the impurity which increases quadratically for small interspecies interaction strength. Afterwards, we investigate how the impurity imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the impurity-induced bump in the condensate wave function starts decaying marginally, whereas the dip decays with a characteristic time scale which decreases with increasing repulsive impurity-BEC interaction strength. Second, once the attractive or repulsive interspecies coupling constant is switched off, we find that white-shock waves or bisolitons emerge which both oscillate within the harmonic confinement with a characteristic frequency.
We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for a<0a<0a<0 and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If a>0a>0a>0, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.
We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic 6Li atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into 6Li2 molecules. Below 600 nK, a Bose-Einstein condensate of up to 900 000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.
Several properties of trapped hard-sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single-particle Gaussian and a hard-sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard-sphere radius and the number of particles. Special attention is given to diagonalizing the one-body density matrix and obtaining the corresponding single-particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single-particle orbital with the highest occupation. The effect of interaction on other quantities such as the ground-state energy, the mean radial displacement, and the momentum distribution is calculated as well. Results are compared with mean-field theory in the dilute limit.