Physics – Condensed Matter – Quantum Gases
Scientific paper
2011-01-05
Physics
Condensed Matter
Quantum Gases
16 pages and as many figures
Scientific paper
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.
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