Spin 1 microcondensate in a magnetic field: semiclassics and exact solution

TL;DR

This paper investigates the classical and quantum properties of a spin 1 Bose microcondensate in a magnetic field, revealing integrable dynamics, phase space topology features, and quantum signatures through semiclassical and exact solutions.

Contribution

It provides a comprehensive analysis of the classical limit and exact quantum solution of a spin 1 microcondensate, highlighting phase space topology effects and their quantum signatures.

Findings

Classical limit exhibits phase space separatrix or monodromy depending on parameters.

Quantum signatures of classical phenomena are identified via semiclassical quantization.

An exact solution using Bethe ansatz is obtained for the system.

Abstract

We study a spin 1 Bose condensate small enough to be treated as a single magnetic `domain': a system that we term a microcondensate. Because all particles occupy a single spatial mode, this quantum many body system has a well defined classical limit consisting of three degrees of freedom, corresponding to the three macroscopically occupied spin states. We study both the classical limit and its quantization, finding an integrable system in both cases. Depending on the sign of the ratio of the spin interaction energy and the quadratic Zeeman energy, the classical limit displays either a separartrix in phase space, or Hamiltonian monodromy corresponding to non-trivial phase space topology. We discuss the quantum signatures of these classical phenomena using semiclassical quantization as well as an exact solution using the Bethe ansatz.