Spin relaxation in an ultracold spin-orbit-coupled40K gas

Abstract

We report the anomalous D'yakonov-Perel' spin relaxation in ultracold spin-orbit-coupled ${}^{40}$K gas when the coupling between $|9/2,9/2\ensuremath{\rangle}$ and $|9/2,7/2\ensuremath{\rangle}$ states, acting as an effective Zeeman magnetic field, is much stronger than the spin-orbit coupled field. Both the transverse and longitudinal spin relaxations are investigated with small and large spin polarizations. It is found that with small spin polarization, the transverse (longitudinal) spin relaxation is divided into four (two) regimes: the normal weak scattering regime, the anomalous D'yakonov-Perel'-like regime, the anomalous Elliott-Yafet-like regime, and the normal strong scattering regime (the anomalous Elliott-Yafet-like regime and the normal strong scattering regime). With large spin polarization, we find that the Hartree-Fock self-energy, which acts as an effective magnetic field, can markedly suppress the transverse spin relaxation in both weak and strong scattering limits. Moreover, by noting that as both the momentum relaxation time and the Hartree-Fock effective magnetic field vary with the scattering length in cold atoms, the anomalous D'yakonov-Perel'-like regime is suppressed and the transverse spin relaxation is hence divided into three regimes in the scattering length dependence: the normal weak scattering regime, the anomalous Elliott-Yafet-like regime, and the strong scattering regime. On the other hand, the longitudinal spin relaxation is again divided into the anomalous Elliott-Yafet-like and normal strong scattering regimes. Furthermore, it is found that the longitudinal spin relaxation can be either enhanced or suppressed by the Hartree-Fock effective magnetic field if the spin polarization is parallel or antiparallel to the effective Zeeman magnetic field.