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arXiv:1612.08798 · Journal of Physics B Atomic Molecular and Optical Physics

Bifurcations, stability and mode evolution in segregated quasi-2D condensate mixtures

Sukla Pal, Arko Roy, D Angom

Published Aug 25, 2017• 3 citations
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Abstract

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.

DOI
10.1088/1361-6455/aa889f

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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 two-species Bose-Einstein condensates confined in quasi-two-dimensional (quasi-2D) optical lattices at finite temperatures, employing the Hartree-Fock-Bogoliubov theory with the Popov approximation. We examine the role of thermal fluctuations in the ground-state density distributions and the quasiparticle mode evolution. At zero temperature, the geometry of the ground state in the immiscible domain is side by side. Our results show that the thermal fluctuations enhance the miscibility of the condensates, and at a characteristic temperature the system becomes miscible with rotationally symmetric overlapping density profiles. This immiscible-miscible transition is accompanied by a discontinuity in the excitation spectrum, and the low-lying quasiparticle modes such as slosh mode become degenerate at the characteristic temperature.
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.
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.
We show the emergence of a third Goldstone mode in binary condensates at phase separation in quasi-one-dimensional (quasi-1D) optical lattices. We develop the coupled discrete nonlinear Schr\"odinger equations using Hartree-Fock-Bogoliubov theory with the Popov approximation in the Bose-Hubbard model to investigate the mode evolution at zero temperature, in particular, as the system is driven from the miscible to the immiscible phase. We demonstrate that the position exchange of the species in the $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{85}\mathrm{Rb}$ system is accompanied by a discontinuity in the excitation spectrum. Our results show that, in quasi-1D optical lattices, the presence of the fluctuations dramatically changes the geometry of the ground-state density profile of two-component Bose-Einstein condensates.
Abstract The ultracold atoms are an ideal platform to implement atomtronics and Josephson junctions analogous to superconducting circuits. The collective modes of a Bose gas split by a potential barrier have been known. However, the role of barriers on the collective excitation spectra of ultracold atomic mixtures has not been examined. Here, we examine the low-lying collective modes of (an)harmonically trapped quasi-one-dimensional Bose–Einstein condensates (BECs) in a Josephson barrier by employing the variational approach and Bogoliubov theory. We first show that the anharmonicity of the external potential leads to an increase in the critical barrier strength of mode softening in a single-species condensate. The Josephson barrier drives the softening of in-phase and out-of-phase dipole modes of two-species BECs, and consequently leads to two additional zero-energy Goldstone modes in the miscible phase, in agreement with the variational approach. Furthermore, the sandwich immiscible state results in an additional Goldstone mode due to the barrier, in contrast to the spatially symmetry-broken side-by-side profile. Our results unveil the distinct collective response of the Josephson barrier in binary mixtures owing to interspecies atomic correlations.