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 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 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 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 topological transformation of quasi-2D Bose-Einstein condensates of dilute atomic gases, and changes in the collective modes as the confining potential is modified from rotationally symmetric multiply connected to multiply connected with broken rotational symmetry and ultimately to a simply connected geometry. In particular, we show that the condensate density, and the non-condensate density arising from the quantum fluctuations, follow the transition in the geometry of the confining potential. The non-condensate density arising from the thermal fluctuations, in contrast, remain multiply connected when the thermal energy exceeds the maximum value in the basin of the confining potential. Otherwise, both the condensate and non-condensate densities become simply connected. The topology of the non-condensate densities is determined by the thermal energy, the repulsive interaction energy between atoms, and the trapping potential energy. In particular, the origin of the difference lies in the structure of the low-energy collective modes, which we examine using the Hartree-Fock-Bogoliubov formalism. We then use the Hartree-Fock-Bogoliubov theory with the Popov approximation to investigate the density and the momentum distribution associated with the thermal fluctuations.
Abstract We explore the topological transformation of quasi-2D Bose–Einstein condensates of dilute atomic gases, and changes in the collective modes as the confining potential is modified from rotationally symmetric multiply connected to multiply connected with broken rotational symmetry and ultimately to a simply connected geometry. In particular, we show that the condensate density, and the non-condensate density arising from the quantum fluctuations, follow the transition in the geometry of the confining potential. The non-condensate density arising from the thermal fluctuations, in contrast, remain multiply connected when the thermal energy exceeds the maximum value in the basin of the confining potential. Otherwise, both the condensate and non-condensate densities become simply connected. The topology of the non-condensate densities is determined by the thermal energy, the repulsive interaction energy between atoms, and the trapping potential energy. In particular, the origin of the difference lies in the structure of the low-energy collective modes, which we examine using the Hartree–Fock–Bogoliubov formalism. We then use the Hartree–Fock–Bogoliubov theory with the Popov approximation to investigate the density and the momentum distribution associated with the thermal fluctuations.
Abstract We present a systematic investigation of symmetries and ground state phase transitions in two-dimensional Bose–Einstein condensates with rotational and spin–orbit couplings confined within one-dimensional optical lattices. For lattice phases φ = π 2 , the vortex arrangement exhibits mirror symmetry about the y-axis, and the density distribution in momentum space maintains mirror symmetry about the k x -axis. For φ = 0, in contrast, the system exhibits spontaneous symmetry breaking, leading to ground state degeneracy. The optical lattice divides the condensate into distinct units. With a fixed spin–orbit coupling strength, the two-component condensates in different units successively undergo immiscible to miscible transitions as the rotational angular frequency increases. For φ = 0, in particular, the unit of condensate located in the center of the external potential consistently remains in the phase separation.