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arXiv:1403.3068 · Physical Review A

Dispersion relation and excitation character of a two-component Bose-Einstein condensate

Christopher Ticknor

Published May 5, 2014• 26 citations
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Abstract

We present a study for the dispersion relation and character of the excitations of a single- and two-component Bose-Einstein condensate (BEC). We study the single-component dispersion for a finite BEC system and look at examples of quasiparticles to understand and characterize the dispersion relation. Next we present the dispersion relation for a two-component BEC in both the miscible and immiscible parameter regimes. Then we present examples of the quasiparticles for both regimes.

DOI
10.1103/physreva.89.053601

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We present a study for the dispersion relation and character of the excitations of a single- and two-component Bose-Einstein condensate (BEC). We study the single-component dispersion for a finite BEC system and look at examples of quasiparticles to understand and characterize the dispersion relation. Next we present the dispersion relation for a two-component BEC in both the miscible and immiscible parameter regimes. Then we present examples of the quasiparticles for both regimes.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.
We study the dispersion relation of Kelvin waves propagating along single- and half-quantum vortices in miscible two-component Bose-Einstein condensates based on the analysis of the Bogoliubov--de Gennes equation. With the help of the interpolating formula connecting the dispersion relations in low- and high-wave-number regimes, we reveal the nontrivial dependence of the dispersion relation on the intercomponent interaction through the change in the vortex-core size of the vortical component. We also find the splitting of the Kelvin wave dispersion into gapless and gapped branches when both components have overlapping single-quantized vortices.
We present an analytical study for density profiles of two-component Bose–Einstein condensates (BECs) in an isotropic trap within the miscible regime. The analytical equations for the density profiles and the conditions for three different density configurations are presented, which allow us to explore the density profile diagrams of general two-component BECs depending on broad ranges of experimental parameters. Furthermore, we show that the obtained explicit expressions of the density profiles can also be applied to study the collective modes of the two-component BECs, and the frequencies of the two-component BECs clearly characterize the density configurations.
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.
Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition to the breaking of two U(1) symmetries in the presence of two complex order parameters. We clarify the properties of the low-energy excitations and identify that there exist two Nambu-Goldstone modes: an in-phase phonon with a linear dispersion and a ripplon with a fractional dispersion. The signature of the characteristic dispersion can be verified in segregated condensates in a harmonic potential.