Polarization and decoherence in a two-component Bose-Einstein Condensate

TL;DR

This paper theoretically explores the polarization dynamics of a two-component Bose-Einstein condensate, analyzing how nonlinear interactions and environmental decoherence influence polarization states and their geometric representation.

Contribution

It introduces quantum analogs of Stokes parameters for BECs and studies polarization oscillations and decoherence effects within this framework.

Findings

Nonlinear interactions cause periodic polarization oscillations.

Decoherence leads to depolarization of the BEC.

Special interaction conditions result in precession of the Stokes vector.

Abstract

We theoretically investigate polarization properties of a two-component Bose-Einstein condensate (BEC) and influence of decoherence induced by environment on BEC polarization through introducing four BEC Stokes operators which are quantum analog of the classical Stokes parameters for a light field. BEC polarization states can be geometrically described by a Poincar\'{e} sphere defined by expectation values of BEC Stokes operators. Without decoherence, it is shown that nonlinear inter-atomic interactions in the BEC induce periodic polarization oscillations whose periods depend on the difference between self-interaction in each component and inter-component interaction strengths. In particular, when inter-atomic nonlinear self-interaction in each BEC component equals inter-component nonlinear interaction, Stokes vector associated with Stokes operators precesses around a fixed axis in the dynamic evolution of the BEC. The value of the processing frequency is determined by the strength of the linear coupling between two components of the BEC. When decoherence is involved, we find each component of the Stokes vector decays which implies that decoherence depolarizes the BEC.