Spin 1 condensates at thermal equilibrium : a $SU(3)$ coherent state approach

Abstract

We propose a theoretical framework based on $SU(3)$ coherent states as a convenient tool to describe the collective state of a Bose-Einstein condensate of spin 1 atoms at thermal equilibrium. We work within the single-mode approximation, which assumes that all atoms condense in the same spatial mode. In this system, the magnetization $m_z$ is conserved to a very good approximation. This conservation law is included by introducing a prior distribution for $m_z$ and constructing a generalized statistical ensemble that preserves its first moments. In the limit of large particle numbers, we construct the partition function at thermal equilibrium and use it to compute various quantities of experimental interest, such as the probability distribution function and moments of the population in each Zeeman state. When $N$ is large but finite (as in typical experiments, where $N\sim 10^3-10^5$), we find that fluctuations of the collective spin can be important.

References in corpus (6)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Twin matter waves for interferometry beyond the classical limit
• Fragmentation of Bose-Einstein Condensates
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spinor Dynamics in an Antiferromagnetic Spin-1 Condensate
• Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate

Cited by in corpus (7)

• Spin nematic order in antiferromagnetic spinor condensates
• Spin squeezing in dipolar spinor condensates
• Shortcut to adiabaticity in spinor condensates
• Triplet FFLO Superconductivity in the doped Kitaev-Heisenberg Honeycomb Model
• Cooling of a Bose-Einstein Condensate by spin distillation
• Metrologically useful states of spin-1 Bose condensates with macroscopic magnetization
• Efficient two-mode interferometers with spinor Bose-Einstein condensates