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 (34)

• Spinor Bose Condensates in Optical Traps
• Bose-Einstein condensation with internal degrees of freedom in alkali atom gases
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Quantum spins mixing in spinor Bose-Einstein condensates
• Twin matter waves for interferometry beyond the classical limit
• Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein Condensates
• Coherent spinor dynamics in a spin-1 Bose condensate
• Dynamics of F=2 Spinor Bose-Einstein Condensates
• Spin-Nematic Squeezed Vacuum in a Quantum Gas
• Fragmentation of Bose-Einstein Condensates
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Fragmented and Single Condensate Ground States of Spin-1 Bose Gas
• Exact Eigenstates and Magnetic Response of Spin-1 and Spin-2 Vectorial Bose-Einstein Condensates
• Atomic homodyne detection of continuous variable entangled twin-atom states
• Coherent spin mixing dynamics in a spin-1 atomic condensate
• Spinor Dynamics in an Antiferromagnetic Spin-1 Condensate
• On the single mode approximation in spinor-1 atomic condensate
• Quantum Phase Transition in an Antiferromagnetic Spinor Bose-Einstein Condensate
• Mean field ground state of a spin-1 condensate in a magnetic field
• Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate
• Spontaneous demagnetization of a dipolar spinor Bose gas at ultra-low magnetic field
• Effective field theory for S=1 quantum nematic
• Evolution of a spinor condensate: coherent dynamics, dephasing and revivals
• Long timescale dynamics of spin textures in a degenerate F=1 ${}^{87}$ Rb spinor Bose gas
• Phase diagram of spin 1 antiferromagnetic Bose-Einstein condensates
• Spin squeezing and entanglement in spinor-1 condensates
• SU(3) semiclassical representation of quantum dynamics of interacting spins
• Thermodynamics of a Bose Einstein condensate with free magnetization
• Coherent States of the SU(N) groups
• Classification of Spin-Nematic Squeezing in Spin-1 Collective Atomic Systems
• Spin fragmentation of Bose-Einstein condensates with antiferromagnetic interactions
• Quantum rotor theory of spinor condensates in tight traps
• Spin 1 microcondensate in a magnetic field: semiclassics and exact solution
• "Polar" and "antiferromagnetic" order in f=1 many-boson systems

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