Density-Matrix approach to a Strongly Coupled Two-Component Bose-Einstein Condensate

TL;DR

This paper derives analytical equations describing the slow dynamics of a strongly coupled two-component Bose-Einstein condensate, capturing phenomena like Rabi oscillation collapse and revival, and proposes a method to create stable vortices.

Contribution

It introduces a density-matrix approach that analytically models the slow dynamics of a strongly coupled two-component BEC, including collapse and revival phenomena.

Findings

Derived rate equations for slow dynamics including collapse and revival

Captured dependence on detuning and trap displacement

Proposed a method to create stable vortices

Abstract

The time evolution equations for average values of population and relative phase of a strongly coupled two component BEC is derived analytically. The two components are two hyper-fine states coupled by an external laser that drives fast Rabi oscillations between these states. Specifically, this derivation incorporates the two-mode model proposed in [1] for the strongly coupled hyper-fine states of Rb. The fast Rabi cycle is averaged out and rate equations are derived that represents the slow dynamics of the system. These include the collapse and revival of Rabi oscillations and their subsequent dependence on detuning and trap displacement as reported in experiments of [1]. A proposal to create stable vortices is also given.