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Physical Review A

Excitation spectrum and phase separation of double Bose-Einstein condensates in optical lattices

X. P. Liu

Published Nov 16, 2007• 7 citations
Publisher

Abstract

The excitation spectrum for symmetric two-component Bose-Einstein condensate (BECs) in optical lattices is obtained, with emphasis on its quantitative dependence on intercomponent interaction parameter. The resulting two branches of the excitation spectrum have a linear spectrum asymptotically in the low momentum limit, which is expected as a behavior of superfluid. The critical superfluid velocity, depending on the intercomponent interaction parameter, is then obtained, which is quite different from the result obtained in other reference. A requirement of real excitation spectrum also results in a condition on the interaction parameters, which coincides with the phase separation condition. Hence in real spectrum excitation, it is proposed that there should be two branches of superfluid with different critical superfluid velocities, while in the complex spectrum it is predicted that there should be phase separation in the two-branch superfluid system. The excitation spectrum for an asymmetric two-component BEC system is also presented and analyzed.

DOI
10.1103/physreva.76.053615

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The excitation spectrum for symmetric two-component Bose-Einstein condensate (BECs) in optical lattices is obtained, with emphasis on its quantitative dependence on intercomponent interaction parameter. The resulting two branches of the excitation spectrum have a linear spectrum asymptotically in the low momentum limit, which is expected as a behavior of superfluid. The critical superfluid velocity, depending on the intercomponent interaction parameter, is then obtained, which is quite different from the result obtained in other reference. A requirement of real excitation spectrum also results in a condition on the interaction parameters, which coincides with the phase separation condition. Hence in real spectrum excitation, it is proposed that there should be two branches of superfluid with different critical superfluid velocities, while in the complex spectrum it is predicted that there should be phase separation in the two-branch superfluid system. The excitation spectrum for an asymmetric two-component BEC system is also presented and analyzed.
We investigate a model of a two-component Bose-Einstein condensate residing in an optical lattice. Within a Bogoliubov approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laser light wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.
We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laserlight wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.
In this paper we show that the superfluidity of cold spin-1 Bose atoms of weak interactions in an optical lattice can be realized according to the excitation energy spectrum which is derived by means of Bogliubov transformation. The characteristic of the superfluid-phase spectrum is explained explicitly in terms of the nonvanishing critical velocity, i.e., the Landau criterion. It is observed that critical velocities of superfluid are different for three spin components and, moreover, can be controlled by adjusting the lattice parameters in practical experiments to detect the superfluid phase.
The elementary excitation spectrum of a two-component Bose—Einstein condensate in different hyperfine states is obtained by Green's function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green's functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.
Abstract With the method of Green’s function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We find that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.
A weakly interacting, spin-orbit coupled, two-component, ultracold Bose gas bound to a Bravais lattice is studied. Motivated by recent experimental advances in the field of synthetically spin-orbit coupled, ultracold, neutral atomic gases showing Bose-Einstein condensation, an analytic framework with which to describe such systems in the superfluid regime is presented. This is applied to a Rashba spin-orbit-coupled Bose gas in a two-dimensional optical lattice. The exotic nature of Bose-Einstein condensation in the presence of spin-orbit coupling is an interesting study by itself. Additionally, when the optical lattice is introduced, the system provides a highly controllable experimental testing ground for numerous condensed matter physics phenomena. Five phases of the system are considered, and their excitation spectra, critical superfluid velocities and free energies are found. In obtaining the free energy, the effects of terms in the Hamiltonian that are linear in excitation operators are included, and such terms have not been studied previously in this context. Minimization of the free energy at zero temperature is used to confirm the phase diagrams reported in the literature, where it has usually been obtained by neglecting the effect of excitations. The plane and stripe wave phases in the phase diagram are bosonic analogues of Fulde-Ferrell-Larkin-Ovchinnikov states in superconductors involving nonzero condensate momenta.