Quantum Bose Josephson Junction with binary mixtures of BECs

TL;DR

This paper analyzes the quantum dynamics of a binary Bose-Einstein condensate mixture in a double-well potential, revealing complex oscillatory behaviors, collapse and revival phenomena, and the formation of Schrödinger cat states.

Contribution

It provides analytical solutions for energy states and explores the quantum evolution of number differences under different initial conditions in a binary BEC system.

Findings

Rich oscillatory dynamics including collapses and revivals

Irregular short-time evolution of number difference

Formation of Schrödinger cat states affecting momentum distribution

Abstract

We study the quantum behaviour of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. We focus on the small tunneling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short and the long time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunneling. In the second case the short-time scale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schroedinger cat states is considered and shown to affect the momentum distribution.