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Journal of Physics Condensed Matter

Excitations and phase segregation in a two-component Bose-Einstein condensate with an arbitrary interaction

A. S. Alexandrov, V. V. Kabanov

Published Apr 26, 2002• 28 citations
Publisher

Abstract

Bogoliubov-de Gennes equations and the excitation spectrum of a two-component Bose-Einstein condensate (BEC) are derived with an arbitrary interaction between bosons, including long-range and short-range forces. Spectra of optical and acoustic plasmons (APs) are obtained. For the Coulomb interaction the AP has a quadratic long-wavelength dispersion in contrast with the linear dispersion in the normal-state two-component plasma. The nonconverting BEC mixture segregates into two phases for some two-body interactions. Gross-Pitaevskii equations are solved for the phase-segregated BEC. A possibility of boundary-surface and other localized excitations is studied.

DOI
10.1088/0953-8984/14/18/101

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Bogoliubov-de Gennes equations and the excitation spectrum of a two-component Bose-Einstein condensate (BEC) are derived with an arbitrary interaction between bosons, including long-range and short-range forces. Spectra of optical and acoustic plasmons (APs) are obtained. For the Coulomb interaction the AP has a quadratic long-wavelength dispersion in contrast with the linear dispersion in the normal-state two-component plasma. The nonconverting BEC mixture segregates into two phases for some two-body interactions. Gross-Pitaevskii equations are solved for the phase-segregated BEC. A possibility of boundary-surface and other localized excitations is studied.
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Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. In the second type of waves the two components have a counter-phase local motion. In the case of different values of inter- and intra-component interaction constants, the long wave-length behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion the first mode is described by the well-known Korteweg-de Vries (KdV) equation. We show that in the same limit the second mode can be described by the Gardner (modified KdV) equation, if the intra-component interaction constants have close enough values. This leads to a rich phenomenology of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which does not exist in the KdV description.
Abstract Our investigation focuses on the condensate density, excited and condensed fractions of bosons in a mixture of two-component segregated weakly interacting Bose–Einstein condensates (BECs) at zero temperature based on the Gross–Pitaevskii (GP) and Cornwall-Jackiw-Tomboulis (CJT) theories. We find that the repulsive interaction among interspecies of bosons is the origin of the local behavior and the decline of quantum fluctuation. These features are disparate to the single BEC or miscible BECs. The numerical evaluation of the condensed fraction is provided to support the experimental observation.
The paper considers a model for Bose gases in the so-called 'high-temperature range' below the temperature Tc, where Bose-Einstein condensation sets in.The model is of non-linear two-component type, consisting of a kinetic equation with periodic boundary conditions for the distribution function of a gas of excitations interacting with a Bose condensate, which is described by a Gross-Pitaevskii equation. Results on well-posedness and long time behaviour are proved in a H1-setting close to equilibrium.