Collective modes of vortex lattices in two-component Bose–Einstein condensates under synthetic gauge fields

Abstract

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.

Two-dimensional imbalanced Fermi gas in antiparallel magnetic fields

“…For related theoretical works, see Refs. [9][10][11][12][13] on 2D Bose and 3D Fermi gases as well as Refs. [14][15][16][17][18][19][20][21] in optical lattices.…”

Vortex lattices in binary Bose-Einstein condensates: Collective modes, quantum fluctuations, and intercomponent entanglement

“…As the systems in parallel and antiparallel magnetic fields are closely related with bilayer quantum Hall systems [40] and quantum spin Hall systems [41], respectively, a comparative study of these systems can make a link between the two research fields. Such studies have been conducted on collective modes of vortex lattices [42,43] and phase diagrams in a quantum (spin) Hall regime [39,44,45,46,47,48,49].…”

“…Keçeli and Oktel [42] have calculated excitation spectra in binary BECs in parallel fields by means of a hydrodynamic theory. In a previous work [43], we have conducted a comparative study of excitation modes in the parallel-and antiparallelfield cases by means of the Bogoliubov theory and an effective field theory. All the calculations in these works are based on the lowest-Landau-level (LLL) approximation.…”

“…Furthermore, for overlapping triangular lattices [Fig. 1(a)], the low-energy spectra for the two types of fields are found to be related to each other by simple rescaling [43].…”

“…We show that the low-energy excitation spectra for the two types of fields are related to each other by suitable rescaling using the renormalized constants. Namely, the rescaling relations proposed in our previous work [43] must be modified using the renormalized constants. By calculating the entanglement entropy (EE), we find that for an intercomponent repulsion (attraction), the two components are more strongly entangled in the case of parallel (antiparallel) fields, in qualitative agreement with recent exact diagonalization results for a quantum (spin) Hall regime [39,49].…”