The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We investigate the formation of magnetic domains at finite temperature and magnetic field in two dimensions in an optical trap. We study the general ground state phase diagram of a spin-1 system and focus on a phase that has a magnetic Ising order parameter and numerically determine the nature of the finite-temperature superfluid and magnetic phase transitions. We then study three different dynamical models: model A, which has no conserved quantities, model F, which has a conserved second-sound mode, and the Gross-Pitaevskii (GP) equation, which has a conserved density and magnetization. We find the dynamic critical exponent to be the same for models A and F $(z=2)$ but different for GP $(z\ensuremath{\approx}3)$. Externally imposed magnetization conservation in models A and F yields the value $z\ensuremath{\approx}3$, which demonstrates that the only conserved density relevant to domain formation is the magnetization density.The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We investigate the formation of magnetic domains at finite temperature and magnetic field in two dimensions in an optical trap. We study the general ground state phase diagram of a spin-1 system and focus on a phase that has a magnetic Ising order parameter and numerically determine the nature of the finite-temperature superfluid and magnetic phase transitions. We then study three different dynamical models: model A, which has no conserved quantities, model F, which has a conserved second-sound mode, and the Gross-Pitaevskii (GP) equation, which has a conserved density and magnetization. We find the dynamic critical exponent to be the same for models A and F $(z=2)$ but different for GP $(z\ensuremath{\approx}3)$. Externally imposed magnetization conservation in models A and F yields the value $z\ensuremath{\approx}3$, which demonstrates that the only conserved density relevant to domain formation is the magnetization density.

arXiv:0704.3440Physical Review BSep 25, 200736 citations

Kinetic Theory of a Spin-1/2 Bose-Condensed Gas

Tetsuro Nikuni, JAMES E. JUN. WILLIAMS

We derive a kinetic theory for a spin-1/2 Bose-condensed gas of two-level atoms at finite temperatures. The condensate dynamics is described by a generalized Gross-Pitaevskii equation for the two-component spinor order parameter, which includes the interaction with the uncondensed fraction. The noncondensate atoms are described by a quantum kinetic equation, which is a generalization of the spin kinetic equation for spin-polarized quantum gases to include couplings to the condensate degree of freedom. The kinetic equation is used to derive hydrodynamic equations for the noncondensate spin density. The condensate and noncondensate spins are coupled directly through the exchange mean field. Collisions between the condensate and noncondensate atoms give rise to an additional contribution to the spin diffusion relaxation rate. In addition, they give rise to mutual relaxation of the condensate and noncondensate due to lack of local equilibrium between the two components.We derive a kinetic theory for a spin-1/2 Bose-condensed gas of two-level atoms at finite temperatures. The condensate dynamics is described by a generalized Gross-Pitaevskii equation for the two-component spinor order parameter, which includes the interaction with the uncondensed fraction. The noncondensate atoms are described by a quantum kinetic equation, which is a generalization of the spin kinetic equation for spin-polarized quantum gases to include couplings to the condensate degree of freedom. The kinetic equation is used to derive hydrodynamic equations for the noncondensate spin density. The condensate and noncondensate spins are coupled directly through the exchange mean field. Collisions between the condensate and noncondensate atoms give rise to an additional contribution to the spin diffusion relaxation rate. In addition, they give rise to mutual relaxation of the condensate and noncondensate due to lack of local equilibrium between the two components.

arXiv:cond-mat/0304095Apr 4, 20031 citation

Phase ordering dynamics in spin-1 ferromagnetic condensates

L. A. Williamson, P. B. Blakie

Bulletin of the American Physical SocietyMay 25, 20160 citations

Phase Space Dynamics in an Antiferromagnetic Spinor Condensate

Yingmei Liu, E. Gómez, Stephen Maxwell +3 more

Bulletin of the American Physical SocietyMay 22, 20090 citations

The

s=1

spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We investigate the formation of magnetic domains at finite temperature and magnetic field in two dimensions in an optical trap. We study the general ground state phase diagram of a spin-1 system and focus on a phase that has a magnetic Ising order parameter and numerically determine the nature of the finite-temperature superfluid and magnetic phase transitions. We then study three different dynamical models: model A, which has no conserved quantities, model F, which has a conserved second-sound mode, and the Gross-Pitaevskii (GP) equation, which has a conserved density and magnetization. We find the dynamic critical exponent to be the same for models A and F

(z=2)

but different for GP $(z\ensuremath{\approx}3)$. Externally imposed magnetization conservation in models A and F yields the value $z\ensuremath{\approx}3$, which demonstrates that the only conserved density relevant to domain formation is the magnetization density.