The dynamics of spin waves in ultracold gases is investigated with allowance for exchange and spin-orbit interaction. The exact basis of atomic states is used taking into account all rotational quantum numbers of the atom. The dispersion relation for spin waves is obtained for fermions and bosons in the hydro-dynamic approximation.
We investigate Fermi liquid states of the ultracold magnetic dipolar Fermi gases in the simplest two-component case including both thermodynamic instabilities and collective excitations. The magnetic dipolar interaction is invariant under the simultaneous spin-orbit rotation but not under either the spin or the orbit one. Therefore, the corresponding Fermi liquid theory is intrinsically spin-orbit coupled. This is a fundamental feature of magnetic dipolar Fermi gases different from electric dipolar ones. The Landau interaction matrix is calculated and is diagonalized in terms of the spin-orbit coupled partial-wave channels of the total angular momentum J. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with J=1+ and the spin-current mode with $J={1}^{\ensuremath{-}}$, where + and $\ensuremath{-}$ represent even and odd parities, respectively. An exotic propagating collective mode is identified as spin-orbit coupled Fermi surface oscillations in which spin distribution on the Fermi surface exhibits a topologically nontrivial hedgehog configuration.
We derive an analytical expression for the scattering amplitude of two ultracold atoms of arbitrary spin and with general spin-orbit (SO) coupling, on the basis of our recent work [Phys. Rev. A 86, 053608 (2012)]. As an application, we demonstrate that SO coupling can induce scattering resonance in the case with finite scattering length. The same approach can be applied to calculate the two-body bound state of SO-coupled ultracold atoms. For the ultracold spin-1/2 Fermi gases in three- or two- dimensional systems with SO coupling, we also obtain the renormalization relation of effective contact interaction with momentum cutoff, as well as the applicability of Huang-Yang pseudopotential.
These lecture notes provide an introduction to Bose-Einstein condensates with Raman-induced spin-orbit coupling. Owing to the interplay between the peculiar single-particle dispersion, featuring a double-minimum structure, and the two-body interaction, these systems possess a complex phase diagram. Three different quantum phases can be observed, i.e., a stripe, a plane-wave, and a single-minimum phase, each characterized by different broken symmetries. The condensate dynamics is also significantly affected by the spin-orbit coupling, as revealed by the behavior of the Bogoliubov spectrum in infinite systems and the behavior of the discretized collective mode frequencies in trapped configurations, especially close to the phase transitions. In turn, the superfluid and rotational properties are also deeply modified by the coupling between the motional and spin degree of freedom. Finally, a special attention is devoted to the stripe phase and its supersolid character, which can be clearly revealed by the study of its dynamic features.
We present a theory of spin dynamics caused by spin-orbit coupling for two-dimensional gases of cold atoms and other quasiparticles with pseudospin 1/2 moving in orbital gauge fields. Our approach is based on the gauge transformation in the form of a SU(2) rotation gauging out the spin-orbit coupling. As a result, the analysis of the spin dynamics is reduced to calculation of the density-related susceptibility of the system without spin-orbit coupling at the wavevector determined by the spin-rotation length. This approach allows one to treat the spin dynamics in terms of the linear response theory for bosonic and fermionic ensembles. We study different regimes of irreversible spin relaxation and coherent spin dynamics in these systems. For bosonic gases the effects of low temperature are crucial due to accumulation of particles in the small-momentum subspace even if the Bose–Einstein condensation does not occur due to the system low dimensionality.