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arXiv:1710.06673 · Journal of Physics B Atomic Molecular and Optical Physics

Collective modes in multicomponent condensates with anisotropy

Sukla Pal, Arko Roy, D. Angom

Published Mar 8, 2018• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6455/aab541

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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.
Abstract We present new features of low energy Bogoliubov quasiparticle excitations of a two-component Bose–Einstein condensate (TBEC) in quasi-2D geometry at zero temperature using Hartree–Fock–Bogoliubov formalism. We, in particular, consider the TBECs of 133 Cs– 87 Rb and 85 Rb– 87 Rb, and show specific features in the low energy excitation spectrum as a function of the interaction strength. For 85 Rb– 87 Rb TBEC, the appearance of a new zero energy mode is observed. Whereas for 133 Cs– 87 Rb TBEC we report a bifurcation of the slosh mode at the point of transition from miscible to immiscible domain. The lower energy mode, after the bifurcation, goes soft and becomes a new Nambu–Goldstone mode of the system.
We explore the collective excitation of two-species Bose-Einstein condensates (TBECs) confined in quasi-two-dimensional optical lattices. For this we use a set of coupled discrete nonlinear Schr\"odinger equations to describe the system and we employ Hartree-Fock-Bogoliubov theory with the Popov approximation to analyze the quasiparticle spectra at zero temperature. The ground-state geometry, evolution of quasiparticle energies, structure of quasiparticle amplitudes, and dispersion relations are examined in detail. We observe that the TBEC acquires a side-by-side density profile when it is tuned from the miscible to the immiscible phase. In addition, the quasiparticle energies are softened as the system is tuned towards phase separation, but harden after phase separation and mode degeneracies are lifted. In terms of structure, in the miscible phase the quasiparticles have well-defined azimuthal quantum numbers, but that is not the case for the immiscible phase.
We study collective modes of vortex lattices in two-component Bose–Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. By means of the Bogoliubov theory with the lowest-Landau-level approximation, we numerically calculate the excitation spectra for a rich variety of vortex lattices that appear commonly for parallel and antiparallel synthetic fields. We find that in all of these cases there appear two distinct modes with linear and quadratic dispersion relations at low energies, which exhibit anisotropy reflecting the symmetry of each lattice structure. Remarkably, the low-energy spectra for the two types of fields are found to be related to each other by simple rescaling when vortices in different components overlap owing to an intercomponent attraction. These results are consistent with an effective field theory analysis. However, the rescaling relations break down for interlaced vortex lattices appearing with an intercomponent repulsion, indicating a nontrivial effect of an intercomponent vortex displacement beyond the effective field theory. We also find that high-energy parts of the excitation bands exhibit line or point nodes as a consequence of a fractional translation symmetry present in some of the lattice structures.
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.