Fluctuation driven topological transition of binary condensates in optical lattices

TL;DR

This paper investigates how quantum fluctuations induce a topological transition in binary Bose-Einstein condensates within optical lattices, revealing a third Goldstone mode and significant changes in ground state density profiles.

Contribution

It introduces a coupled DNLSE approach with HFB-Popov approximation to study fluctuation effects on phase transitions in binary condensates in optical lattices.

Findings

Emergence of a third Goldstone mode at phase separation.

Discontinuity in excitation spectrum during species swapping.

Fluctuations significantly alter ground state density profiles.

Abstract

We show the emergence of a third Goldstone mode in binary condensates at the phase-separation in quasi-1D optical lattices. We develop the coupled discrete nonlinear Schr\"odinger equations (DNLSEs) using Hartree-Fock-Bogoliubov theory with Popov approximation in the Bose-Hubbard model to investigate the mode evolution at zero temperature. In particular, as the system is driven from miscible to immiscible phase. We demonstrate that the position swapping of the species in $^{87}$Rb-$^{85}$Rb system is accompanied by a discontinuity in the excitation spectrum. Our results show that in quasi-1D optical lattices, the presence of the fluctuations dramatically change the geometry of the ground state density profile of TBEC.