Stability of nonstationary states of spin-1 Bose-Einstein condensates

TL;DR

This paper analyzes the stability of nonstationary states in spin-1 Bose-Einstein condensates, revealing how magnetic fields influence instabilities and providing bounds for stable condensate sizes.

Contribution

It introduces a Bogoliubov analysis framework for nonstationary states and derives conditions for stability and validity of approximations in spinor condensates.

Findings

Magnetic fields induce instabilities in $^{23}$Na condensates.

Instability wavelengths can be tuned by magnetic field strength.

An analytical bound for stable condensate size is established.

Abstract

The stability of nonstationary states of homogeneous spin-1 Bose-Einstein condensates is studied by performing Bogoliubov analysis in a frame of reference where the state is stationary. In particular, the effect of an external magnetic field is examined. It is found that a nonzero magnetic field introduces instability in a $^{23}$Na condensate. The wavelengths of this instability can be controlled by tuning the strength of the magnetic field. In a $^{87}$Rb condensate this instability is present already at zero magnetic field. Furthermore, an analytical bound for the size of a stable condensate is found, and a condition for the validity of the single-mode approximation is presented. Realization of the system in a toroidal trap is discussed and the full time development is simulated.