Collective excitations of trapped binary mixtures of Bose-condensed gases

TL;DR

This paper analyzes the collective excitations in trapped binary Bose-condensed gases using coupled Gross-Pitaevskii equations, revealing multiple excitation branches and the influence of interphase boundary geometry on mode spectra.

Contribution

It provides a detailed theoretical analysis of excitation spectra in binary Bose condensates, including effects of trapping geometry and phase coexistence, extending previous single-component studies.

Findings

Identified two zero-sound branches in bulk excitations.

Derived dispersion relations with mode dependence on scattering length ratios.

Showed boundary conditions influence mode spectrum in mixed phases.

Abstract

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.