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arXiv:1412.0405 · Physical Review A

Fluctuation-driven topological transition of binary condensates in optical lattices

Kuldeep Suthar, Arko Roy, D. Angom

Published Apr 13, 2015• 25 citations
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Abstract

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.

DOI
10.1103/physreva.91.043615

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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 87Rb\ensuremath-85Rb^{87}\mathrm{Rb}\text{\ensuremath{-}}^{85}\mathrm{Rb}87Rb\ensuremath-85Rb 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.
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.
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 show that the third Goldstone mode, which emerges in binary condensates at phase separation, persists to higher interspecies interaction for density profiles where one component is surrounded on both sides by the other component. This is not the case with symmetry-broken density profiles where one species is entirely to the left and the other is entirely to the right. We, then, use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution at $T\ensuremath{\ne}0$ and demonstrate the existence of mode bifurcation near the critical temperature. The Kohn mode, however, exhibits deviation from the natural frequency at finite temperatures after the phase separation. This is due to the exclusion of the noncondensate atoms in the dynamics.
We show that the presence of a soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficiently enough to induce dynamical instability of the system. We also predict that for two-species condensates, two Goldstone modes emerge in the excitation spectrum at phase separation. Of these, one is due to the presence of the soliton. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution, and demonstrate that when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also report a soliton-induced change in the topology of the density profiles of the two-species condensates at phase separation.
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 study the miscible-immiscible quantum phase transition in a linearly coupled binary Bose-Hubbard model in one dimension that can describe the low-energy properties of a two-component Bose-Einstein condensate in optical lattices. With the quantum many-body ground state obtained from the density matrix renormalization group algorithm, we calculate the characteristic physical quantities of the phase transition controlled by the linear coupling between the two components. Furthermore we calculate the Binder cumulant to determine the critical point and construct the phase diagram. The strong-coupling expansion shows that in the Mott insulator regime the model Hamiltonian can be mapped to a spin-1/21/21/2 XXZ\mathit{XXZ}XXZ model with a transverse magnetic field.