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Laser Physics

Signatures of Bose-Einstein condensation in very low energy atomic scattering from trapped gases

A. Wynveen, J. W. Halleý

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

We report wave packet analysis of scattering of identical particles from for a Bose condensed dilute gas trapped in a spherical square well of finite depth, using solutions to the Bogoliubov equations which we previously reported. Simulations show clearly that exchange effects lead to significant amplitudes for passage of the particle through the condensate, a transparency effect, accounting for the extremely small cross sections previously calculated. The interactions are treated in the scattering length approximation. The states exhibiting enhanced transparency appear to arise from a kind of self stabilizing Ramsauer-Townsend effect. We also observe anomalously large scattering of the identical particles from the condensate for a few other combinations of coupling strength and k vector. We show that these scattering states associated with large cross section are resonance states in which there is a large enhancement of the amplitude of the scattering state in the region of the condensate, corresponding to a state which is nearly bound. We also exhibit simulations of the scattering density at large k, where we previously consistently observed that exchange reduced the cross section. The simulations show enhanced transparency.

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We report wave packet analysis of scattering of identical particles from for a Bose condensed dilute gas trapped in a spherical square well of finite depth, using solutions to the Bogoliubov equations which we previously reported. Simulations show clearly that exchange effects lead to significant amplitudes for passage of the particle through the condensate, a transparency effect, accounting for the extremely small cross sections previously calculated. The interactions are treated in the scattering length approximation. The states exhibiting enhanced transparency appear to arise from a kind of self stabilizing Ramsauer-Townsend effect. We also observe anomalously large scattering of the identical particles from the condensate for a few other combinations of coupling strength and k vector. We show that these scattering states associated with large cross section are resonance states in which there is a large enhancement of the amplitude of the scattering state in the region of the condensate, corresponding to a state which is nearly bound. We also exhibit simulations of the scattering density at large k, where we previously consistently observed that exchange reduced the cross section. The simulations show enhanced transparency.
We calculate the scattering states and cross sections for a Bose-Einstein condensed dilute gas trapped in a spherical square well of finite depth. The interactions are treated in the scattering length approximation. We solve the Gross-Pitaevskii equation and the Bogoliubov equations for bound and scattering states. The results show that there are transparency effects reminiscent of those conjectured to occur for strongly coupled systems. When incident particle wavelengths $\ensuremath{\lambda}$ are comparable to the well size a, exchange induced transparency enhancement is dramatic only for particular combinations of well depth, interaction strength, and particle number. For particles with large momenta $(a/\ensuremath{\lambda}\ensuremath{\gg}1),$ however, exchange with the condensate results in enhanced transmission for all coupling strengths. We calculated the rate of decay of the scattering states to leading order in anharmonic corrections to the Bogoliubov approximation and found the corresponding inelastic cross sections to be extremely small.
We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.
Summary form only given. In a Bose-Einstein condensate, due to the very low temperature, the s-wave scattering length can be used as a measure for the strength of the atom-atom interaction. Under typical experimental conditions, this interaction is weak and hence can be treated in terms of a mean field. However, when scattering length is large or the density is high, the mean field approximation breaks down. In this collisional (hydrodynamic) regime, effects of the interactions such as quantum depletion or shifts in the frequencies of the elementary excitations become large. It is therefore of great interest to study condensates close to or in the collisional regime. It has been demonstrated in recent experiments that the scattering length and thus the interactions among the atoms can be tuned by means of a Feshbach resonance (Inouye et al, 1998; Courteille et al., 1998; Vuleti et al., 1999; Cornish et al., 2000). In the vicinity of Feshbach resonances, however, the increase of the cross-section for elastic collisions is accompanied by a dramatic increase of particle losses. In this paper we report on the observation of anomalous losses from a /sup 87/Rb condensate with a high column density in the absence of an inelastic scattering resonance.
The occurrence of a molecular Bose-Einstein condensate is studied for an atomic system near a zero energy resonance of the binary scattering process, with a large and positive scattering length. The interaction potential is modeled by a pseudo-potential having one bound state. Using a variational Gaussian ansatz for the NNN-body density operator, we discuss the thermodynamic properties at low temperature and the relative stability of the system towards the formation of an atomic Bose-Einstein condensate. We also derive an approximate Gross-Pitaevskii equation for the molecular condensate leading to the prediction of a Bogoliubov spectrum.
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the sss-wave scattering length. Adopting this relation, we are then able to regularize the zero-point energy of the spherical Bose gas and to obtain its equation of state, which includes the corrections due to the finite radius of the sphere and coincides with the flat-case result in the infinite-radius limit. We also provide a microscopic derivation of the superfluid density of the system, reproducing a result postulated in a previous work. Our results are relevant for modeling the ongoing microgravity experiments with two-dimensional bubble-trapped Bose-Einstein condensates.
We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density E of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda* that determines the low-energy observables in the three-body sector. The second-order correction to E has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative a, we calculate the coefficient of the three-body mean-field term in E in terms of a and Lambda*. It can be very large if there is an Efimov state near threshold.