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

Abstract

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 develop 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 kindsof 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.

37 pages, 11 figures

References in corpus (13)

• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
• Artificial gauge fields with ultracold atoms
• Vortex lattices in binary Bose-Einstein condensates with dipole-dipole interactions
• Interaction driven quantum phase transition in fractional quantum spin Hall effects
• Competing Compressible and Incompressible Phases in Rotating Atomic Bose Gases at Filling Factor $\nu =2$
• Bosonic superfluid on lowest Landau level
• Dynamics of vortex matter in rotating two-species Bose-Einstein condensates
• Vortex Lattice Locking in Rotating Two-Component Bose-Einstein Condensates
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Emergent Fermi sea in a system of interacting bosons
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates