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Physical Review A

Low-lying excitations of double Bose-Einstein condensates

Brett D. Esry, Chris H. Greene

Published Feb 1, 1998• 66 citations
Publisher

Abstract

We present the excitation spectrum of a double Bose-Einstein condensate for the JILA time orbiting potential trap including the effects of gravity. We consider two cases: (i) fixed scattering lengths and equal numbers of each atomic species as a function of the number of atoms and (ii) fixed intraspecies scattering lengths and a fixed, equal number of atoms in each state as a function of interspecies scattering length. The spectra reveal the rich dynamics of the system and in particular show simultaneous collective excitations of both condensates.

DOI
10.1103/physreva.57.1265

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We present the excitation spectrum of a double Bose-Einstein condensate for the JILA time orbiting potential trap including the effects of gravity. We consider two cases: (i) fixed scattering lengths and equal numbers of each atomic species as a function of the number of atoms and (ii) fixed intraspecies scattering lengths and a fixed, equal number of atoms in each state as a function of interspecies scattering length. The spectra reveal the rich dynamics of the system and in particular show simultaneous collective excitations of both condensates.
We present a new theoretical treatment of the collective excitation spectrum of a two-species Bose-Einstein condensate confined in a magnetic trap. We show that the interspecies interaction significantly modifies the excitation spectrum and gives rise to a rich set of new phenomena. We identify a novel metastable state of the double condensate and show that under external perturbation there can be a macroscopic quantum transition between this metastable state and the true ground state of the double condensate system.
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We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large particle numbers, and agree exactly with the Stringari results in the strong interaction limit. Excellent agreement is obtained with the recent JILA experiment and predictions for the negative scattering length case are also made.
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.
We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs, stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark, and dark-dark solitons with our analytical prediction and with that of Painlev\'e analysis of the dynamical equation. We demonstrate that tuning the interspecies scattering length away from the predicted value (keeping the intraspecies coupling fixed) breaks the stability of the soliton pairs.
The phase separation and collective excitations of two-component Bose-Einstein condensates in traps are studied. Using the variational method, we show that the separated state is favorable in the case where the interspecies interaction is strongly repulsive and the number of atoms is large enough. This phase separation condition is explained in terms of the softening of a dipole mode collective excitation. Other low-lying excitation modes and their softenings which lead to the instability of the mixed state are also studied by use of the sum-rule approach.