Interaction-Tuned Dynamical Transitions in a Rashba Spin-Orbit-Coupled Fermi Gas

Abstract

We consider the time evolution of the magnetization in a Rashba spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting non-linear system of equations gives rise to three distinct dynamical regimes with qualitatively different asymptotic behaviors of the magnetization at long times. The distinct regimes and the transitions between them are controlled by the interaction strength: for weakly interacting fermions, the magnetization decays to zero. For intermediate interactions, it displays undamped oscillations about zero and for strong interactions, a partially magnetized state is dynamically stabilized. The dynamics we find is a spin analog of interaction induced self-trapping in double-well Bose Einstein condensates. The predicted phenomena can be realized in trapped Fermi gases with synthetic spin-orbit interactions.The physics of spin-orbit coupling is responsible for a wide range of physical phenomena such as atomic spectra, the spin Hall effect and topological insulators [1][2][3]. More recently, the creation of artificial gauge fields [4,5] and spin-orbit coupling [6] in ultra-cold Bose and Fermi systems [7][8][9] has brought spin-orbit-coupled systems to the forefront of research in atomic, molecular, and optical physics. Furthermore, cold atoms bring to bear new tools for studying correlated systems. One such tool is the ability to dynamically tune the single-particle and many body energy scales [10]. By varying system parameters adiabatically or diabatically, experimentalists can probe interacting states both in and out of equilibrium. Such studies have not only provided access to thermodynamic quantities, but have also yielded insights into how correlations develop and spread across a system following a parameter quench, how long-range order is established, and the mechanisms underlying thermalization in isolated interacting systems [11][12][13][14][15]. Here we ask: what is the interplay between spin-orbit coupling and interactions in a gas which is driven out-of-equilibrium?We study spin dynamics occurring in a weakly interacting, uniform spin-orbit coupled Fermi gas, which is initially spin polarized. We assume that the momentum distribution in the initial state is the classical Maxwell distribution. Interplay between classical motion in the thermal gas, quantum spin degrees of freedom subject to spin-orbit coupling (SOC) and interactions gives rise to interesting dynamical regimes, which are the focus of this work. Our main results are summarized in Fig. 1: we find that there are three possible distinct steady states which can be labelled as: unpolarized state, oscillating magnetization state, and partially polarized state. Different steady states correspond to different values of the ratio of the interaction strength to the SOC strength (denoted as λ), and we find clear transitions between different regimes as we change this λ. FIG. 1:(color online) Schematic plot s...

Probing ferromagnetic order in few-fermion correlated spin-flip dynamics

“…This might establish a link to relevant condensed matter systems where such demagnetization mechanisms are well-studied [59][60][61]. Such dynamics have recently been examined in the case of thermal Fermi gases in the collisionless regime [62][63][64].…”

Spin diffusion in ultracold spin-orbit-coupledK40gas

“…For the Bose system, the spin dynamics of the Bose-Einstein condensation has attracted much attention. [1][2][3][4][5][6][7][8] For the Fermi cold atoms, the systems without [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and with [26][27][28][29][30][31][32] spin-orbit coupling (SOC) are extensively investigated. In the absence of the SOC, many interesting phenomena, such as the Leggett-Rice effect in unitary gas [17][18][19][20][21] and anomalous spin segregation in extremely weak scattering limit, [22][23][24][25] have enriched the understanding of the spin dynamics of Fermions.…”

“…With the synthetic SOC experimentally realized by laser control technique in cold atoms, 7,8,26,27 the spin relaxation for the Fermi cold atoms with SOC has been studied both experimentally [26][27][28] and theoretically. [29][30][31][32] This is partly motivated by the wellcontrolled laser technique, which provides more freedom for the cold atoms than the conventional solids. On one hand, rich regimes can be realized by tuning the SOC strength; on the other hand, not only the interatom interaction can be tuned by the Feshbach resonance, 33 but also the atom-disorder interaction can be introduced and controlled by the speckle laser technique.…”

“…In above equation, k = (k x , k y , k z ) denotes the centerof-mass momentum of the atom; Ω acts as an effective Zeeman field along the x-direction; δ is the Raman detuning, which is set to be zero in our work; Ω z (k) = αk x represents the k-dependent effective magnetic field along the ẑ-direction, which is perpendicular to the Zeeman field, with |α| being the strength of the spin-orbit coupled field. With this specific effective magnetic field Ω(k) by setting δ = 0, it has been revealed that both the conventional 29,30,32 and anomalous 31,38,39 D'yakonov-Perel' (DP) 40 spin relaxations can be realized with |Ω z (k)| Ω and |Ω z (k)| ≪ Ω, respectively. For the conventional situation, in the strong (weak) scattering limit when |Ω(k)| τ * k ≪ 1 ( |Ω(k)| τ * k 1), the spin relaxation time (SRT) τ s is inversely proportional (proportional) to the momentum scattering time τ * k .…”

Topological superfluids with time-reversal symmetry from $s$-wave interaction in a bilayer system

“…We found that the topological phase can be realized in a narrow parameter regime even at finite temperature though the Zeeman field is (much) larger than the pairing strength [32,33], so the induced p-wave pairing provides a new mechanism to go beyond the Chandrasekhar-Clogston limit [43,44]. The recent interests in this system also include the topological inhomogeneous superfluids [37][38][39], the quench dynamics of the topological superfluids [40,41] and the topological superradiant state [42]. Thus the exploring of these exotic phases in this model is still an important topic in modern research.…”