Spin Diffusion in Trapped Gases: Anisotropy in Dipole and Quadrupole Modes

Abstract

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows unusual diffusion anisotropy in both dipole and quadrupole modes. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.

18 pages, 9 figures

References in corpus (14)

• Sodium Bose-Einstein Condensates in the F=2 State in a Large-volume Optical Trap
• Observation of anomalous spin-state segregation in a trapped ultra-cold vapor
• Spatial resolution of spin waves in an ultra-cold gas
• Internal state conversion in ultracold gases
• Internal waves and synchronized precession in a cold vapor
• Longitudinal spin waves in a dilute Bose gas
• Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap
• Transverse spin dynamics in a spin-polarized Fermi liquid
• Theory of transverse spin dynamics in a polarized Fermi liquid and an itinerant ferromagnet
• Large amplitude spin waves in ultra-cold gases
• Linear spin waves in a trapped Bose gas
• New Evidence for Zero-Temperature Relaxation in a Spin-Polarized Fermi Liquid
• Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium
• Anisotropic Spin Diffusion in Trapped Boltzmann Gases

Cited by in corpus (6)

• Universal Spin Transport and Quantum Bounds for Unitary Fermions
• Transverse spin diffusion in strongly interacting Fermi gases
• Dipole Oscillations in Fermionic Mixtures
• Nonlinear spin diffusion and spin rotation in a trapped Fermi gas
• Longitudinal spin diffusion in a nondegenerate trapped ${}^{87}$Rb gas
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: II. RPA response functions and collective modes