We study binary Bose-Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase diagram. We de
velop an improved effective field theory to study properties of collective modes and ground-state intercomponent entanglement. Here, we point out the importance of introducing renormalized coupling constants for coarse-grained densities. 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. By calculating the entanglement entropy, 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 studies for a quantum (spin) Hall regime. We also find that the entanglement spectrum exhibits an anomalous square-root dispersion relation, which leads to a subleading logarithmic term in the entanglement entropy. All of these are confirmed by numerical calculations based on the Bogoliubov theory with the lowest-Landau-level approximation. Finally, we investigate the effects of quantum fluctuations on the phase diagrams by calculating the correction to the ground-state energy due to zero-point fluctuations in the Bogoliubov theory. We find that the boundaries between rhombic-, square-, and rectangular-lattice phases shift appreciably with a decrease in the filling factor.
We study the entanglement entropy and spectrum between components in binary Bose-Einstein condensates in $d$ spatial dimensions. We employ effective field theory to show that the entanglement spectrum exhibits an anomalous square-root dispersion rela
tion in the presence of an intercomponent tunneling (a Rabi coupling) and a gapped dispersion relation in its absence. These spectral features are associated with the emergence of long-range interactions in terms of the superfluid velocity and the particle density in the entanglement Hamiltonian. Our results demonstrate that unusual long-range interactions can be emulated in a subsystem of multicomponent BECs that have only short-range interactions. We also find that for a finite Rabi coupling the entanglement entropy exhibits a volume-law scaling with subleading logarithmic corrections originating from the Nambu-Goldstone mode and the symmetry restoration for a finite volume.
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.
