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Journal of Physics B Atomic Molecular and Optical Physics

Bogoliubov modes and the static structure factor for a two-species Bose–Einstein condensate

Baoqing Sun, M. S. Pindzola

Published Feb 10, 2010• 11 citations
Publisher

Abstract

Bogoliubov modes and the static structure factor for a two-species Bose–Einstein condensate were investigated within the framework of mean field approximation. We find that both quantities are strongly affected due to atomic collisions between the two species. The inter-species interaction not only changes the density distributions of the two species, but also modifies the Bogoliubov modes. As a consequence, the static structure factor exhibits a measurable difference. For a binary mixture of 87Rb and 23Na, our numerical results suggest that such an effect can be observed experimentally.

DOI
10.1088/0953-4075/43/5/055301

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Bogoliubov modes and the static structure factor for a two-species Bose–Einstein condensate were investigated within the framework of mean field approximation. We find that both quantities are strongly affected due to atomic collisions between the two species. The inter-species interaction not only changes the density distributions of the two species, but also modifies the Bogoliubov modes. As a consequence, the static structure factor exhibits a measurable difference. For a binary mixture of 87Rb and 23Na, our numerical results suggest that such an effect can be observed experimentally.
We investigate how three-body interactions affect the elementary excitations and dynamic structure factor of a Bose—Einstein condensate trapped in a one-dimensional optical lattice. To this end, we numerically solve the Gross-Pitaevskii equation and then the corresponding Bogoliubov equations. Our results show that three-body interactions can change both the Bogoliubov band structure and the dynamical structure factor dramatically, especially in the case of the two-body interaction being relatively small. Furthermore, when the optical lattice is strong enough, the analytical results, combined with the sum-rule approach, help us to understand that: the effects of three-body interactions on the static structure factor can be significantly amplified by an optical lattice. Our predictions should be observable within the current Bragg spectroscopy experiment.
Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.
Atomic interactions play an important role in the properties of ultracold atomic gases. In single-component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain semianalytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species considering the mean-field framework. We treat differently the cases in which the second species is above or below its own critical temperature and apply the obtained relations to the case of a Na 23 − K 39 bosonic mixture that can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures.
Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.
This work reports studies of a mixture of two interacting Bose condensates in a quasi-one-dimensional geometry using a finite-temperature path-integral Monte Carlo method. For weakly interacting dilute gases, the interactions between atoms are modeled by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interspecies interaction on the static properties, such as the density profile and the superfluid fraction, is discussed. Our results show that for repulsive intra- and interspecies interactions, the presence of the interspecies interactions dramatically changes the structure of both the density profile and the superfluid fraction, and two species are seen to partially separate in space, and there is a finite-size effect on the phase separation between two partially separating Bose-Einstein condensates. In general, our results agree with the theoretical predictions and experimental observations.
Spin evolution of a mixture of two species of spin-1 Bose–Einstein condensates (Rb and Na) has been investigated rigorously. The Hamiltonian under the single-mode approximation (which is the only approximation in the present theory) has been solved exactly. Both analytical expressions and numerical results on the populations of spin components are obtained. Interference between the two species is found to depend sensitively on the initial states and the inter-species interaction. A number of phenomena arising from the interference have been predicted. In particular, periodic behaviour and the alternate appearances of a zone of oscillation and a long quiet zone are found.