# Spin-1 microcondensate in a magnetic field

# Abstract

We study a spin-1 Bose-Einstein 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 separatrix in phase space or Hamiltonian monodromy corresponding to nontrivial 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.