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

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.

16 pages and as many figures

References in corpus (7)

• Spinor Dynamics in an Antiferromagnetic Spin-1 Condensate
• Quantum quenches in a spinor condensate
• Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate
• Quantum quenches from integrability: the fermionic pairing model
• Antiferromagnetic Spinor Condensates are Quantum Rotors
• Quantum corrections to the semiclassical collective dynamics in the Tavis-Cummings model
• Quantum rotor theory of spinor condensates in tight traps

Cited by in corpus (10)

• Non-equilibrium dynamics of an unstable quantum pendulum
• Dynamics in spinor condensates controlled by a microwave dressing field
• Dynamic stabilization of a quantum many-body spin system
• Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions
• From many-body oscillations to thermalization in an isolated spinor gas
• Spin fragmentation of Bose-Einstein condensates with antiferromagnetic interactions
• Phase-space mixing in dynamically unstable, integrable few-mode quantum systems
• Monodromy and chaos for condensed bosons in optical lattices
• Spin 1 condensates at thermal equilibrium : a $SU(3)$ coherent state approach
• Observation of ergodicity breaking and quantum many-body scars in spinor gases