Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates

TL;DR

This paper investigates the entanglement properties of binary Bose-Einstein condensates, revealing how intercomponent tunneling influences the entanglement spectrum and entropy, and demonstrating the emulation of long-range interactions in short-range systems.

Contribution

It introduces an effective field theory analysis of entanglement in binary BECs, showing anomalous spectral dispersion and volume-law entropy scaling due to intercomponent coupling.

Findings

Entanglement spectrum shows square-root dispersion with tunneling.

Entanglement entropy scales with volume, with logarithmic corrections.

Long-range interactions can be simulated in short-range multicomponent BECs.

Abstract

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 relation 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.