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Technical Physics

Structural factor for Bose-Einstein double-component condensate

Igor V. Kazinets, Boris G. Matisov, I. E. Mazets

Published Feb 1, 2002• 0 citations
Publisher

Abstract

The structural factors for the single-and double-component Bose-Einstein condensates of neutral atoms in a spherically symmetric harmonic trap are derived. The approach adopted in this paper is applicable in the low excitation energy limit, where the well-known Stringari dispersion relation is valid. Our expression is compared with the quasi-classical one, which is shown to overestimate the structural factor. It is argued that the second component first splits the frequency of collective condensate oscillations, which corresponds to the energy transferred by scattering, into two branches and then multiplies the single-component structural factor by some coefficient that can be greater than unity. The analysis is used to estimate the properties of an experimentally implemented double-component condensate of 87 Rb atoms.

DOI
10.1134/1.1451962

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The structural factors for the single-and double-component Bose-Einstein condensates of neutral atoms in a spherically symmetric harmonic trap are derived. The approach adopted in this paper is applicable in the low excitation energy limit, where the well-known Stringari dispersion relation is valid. Our expression is compared with the quasi-classical one, which is shown to overestimate the structural factor. It is argued that the second component first splits the frequency of collective condensate oscillations, which corresponds to the energy transferred by scattering, into two branches and then multiplies the single-component structural factor by some coefficient that can be greater than unity. The analysis is used to estimate the properties of an experimentally implemented double-component condensate of 87 Rb atoms.
The elementary excitation spectrum of a two-component Bose—Einstein condensate in different hyperfine states is obtained by Green's function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green's functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.
The linearized time-dependent coupled Gross-Pitaevskii equations describing the long-wavelength excitations of Bose-Einstein condensed binary mixtures are solved in harmonic traps for the case where only the binary phase is present. The dispersion law contains two branches whose dependence on the quantum numbers of the modes is the same as for a one-component condensate, but with different prefactors, depending on the ratios of the three sss-wave scattering lengths of the two atomic species. In the general case where the binary phase in the trap coexists with one or both one-component phases, the mode spectrum depends on the geometry of the interphase boundaries due to the boundary conditions there. Measurements of the oscillation frequencies as in recent experiments with modulated traps would yield very detailed information on this system.
Abstract We report the effects of anisotropy in the confining potential on two component Bose–Einstein condensates (TBECs) through the properties of the low energy quasiparticle excitations. Starting from generalized Gross–Pitaevskii equation, we obtain the Bogoliubov–de Gennes equation for TBECs using the Hartree–Fock–Bogoliubov theory. Based on this theory, we present the influence of radial anisotropy on TBECs in the immiscible or the phase-separated domain. In particular, the TBECs of 85 Rb– 87 Rb and 133 Cs– 87 Rb TBECs are chosen as specific examples of the two possible interface geometries, shell-structured and side by side, in the immiscible domain. We also show that the dispersion relation for the TBEC shell-structured interface has two branches, and anisotropy modifies the energy scale and structure of the two branches.
We theoretically investigate quadrupolar collective excitations in two-component Bose-Einstein condensates and their nonlinear dynamics associated with harmonic generation and mode coupling. Under the Thomas-Fermi approximation and the quadratic polynomial ansatz for density fluctuations, the linear analysis of the superfluid hydrodynamic equations predicts excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations, and those of three scissors modes. These six modes are bifurcated into in-phase and out-of-phase modes by the intercomponent interaction, yielding the nonlinear dynamics that are absent in a single-component condensate. We obtain analytically the resonance conditions for the second-harmonic generation in terms of the trap aspect ratio and the strength of intercomponent interaction. The numerical simulation of the coupled Gross-Pitaevskii equations vindicates the validity of the analytical results and reveals the dynamics of the second-harmonic generation and nonlinear mode coupling that lead to nonlinear oscillations of the condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulam problem.
The dynamics of a two-component dilute Bose-Einstein gas of atoms at zero temperature is described in the mean-field approximation by a two-component Gross-Pitaevskii equation. We solve this equation assuming a Gaussian shape for the wave function, where the free parameters of the trial wave function are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative sss-wave scattering lengths, and obtain the low-energy excitation frequencies corresponding to the collective motion of the two Bose-Einstein condensates.
The linearised time dependent coupled Gross-Pitaevskii equations describing the long wavelength excitations of Bose-condensed binary mixtures are solved, in the bulk and in harmonic traps for the case where only the binary phase is present. In the former case we obtain two zero-sound branches.In the latter case the dispersion law also contains two branches whose dependence on the quantum numbers of the modes is the same as for a one-component condensate,but with different prefactors, depending on the ratios of the three s-wave scattering lengths of the two atomic species. In the general case where the binary phase in the trap coexists with one or both one-component phases, the mode spectrum depends on the geometry of the interphase boundaries due to the boundary conditions there. Measurements of the oscillation frequencies as in recent experiments with modulated traps would yield very detailed information on this system.