Quantum dynamics of a binary mixture of BECs in a double well potential: an Holstein-Primakoff approach

TL;DR

This paper investigates the quantum dynamics of a large-atom-number binary BEC mixture in a double well, revealing phase separation instability and tunneling behavior through a Holstein-Primakoff spin mapping.

Contribution

It introduces a Holstein-Primakoff approach to analyze the quantum dynamics of binary BECs in a double well, highlighting phase separation and tunneling regimes.

Findings

Instability towards phase separation for positive interspecies interactions.

Coherent tunneling regime for negative interspecies interactions.

Comparison with semiclassical results and experimental implications.

Abstract

We study the quantum dynamics of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto a SU(2) spin problem together with a Holstein-Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase-separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunneling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms.