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-Ricetype 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.

Spin Dynamics of a Trapped Spin-1 Bose Gas above the Bose-Einstein Transition Temperature

“…where the total effective potential U is defined in Eqs. ( 26), (32), and (33), and explicit expression for the collision integral is given in Eq.(A20). The above kinetic equation is one of the main results in this paper.…”

“…Even though the JILA experiments were done in relatively high-temperature regime T ∼ 2T BEC , where the quantum degeneracy has little effect on the thermodynamic properties, this spin-1/2 system exhibited collective spin dynamics due to the exchange effect, such as spin segregation [25,26,27,28], and spin-wave oscillations [24,29]. There have been many theoretical studies discussing collective spin oscillations in the spin-1/2 system [26,27,28,29,30,31,32,33,34], which showed very good agreement with the experiments [25,35,36].…”

Transverse spin diffusion in strongly interacting Fermi gases

“…Experiments in dilute solutions of 3 He in liquid 4 He can be understood essentially within kinetic theory and the Born approximation for weakly interacting quasiparticles. Kinetic equations for transverse spin transport were derived by Landau and Silin [5] and applied to degenerate and/or polarized gases [1,[6][7][8][9][10][11][12][13][14]. Transverse diffusion is influenced by the spin-rotation effect by which the spin current precesses around the molecular field of a polarized gas [1]; a similar effect of identical particle spin rotation occurs when two scattering spins rotate around the common axis given by the sum of the two spins [6].…”

Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. II. RPA response functions and collective modes

“…In ultracold gases, spin waves have been observed, even spatially resolved 17,18 , and were described by longitudinal spin waves 19 . The spin diffusion in trapped Bose gases shows an anisotropy in modes 20 and the collisionless damping has been seen to deviate for quadrupole modes from experiments 21 indicating the role of collisional correlations. The spin-wave damping has been measured in a polarized Fermi-liquidlike 3 He- 4 He mixture even at zero temperature 22 and as an 'identical spin-rotation effect' 23 .…”