Dynamics of Interacting Fermions in Spin-Dependent Potentials

Abstract

Recent experiments with dilute trapped Fermi gases observed that weak interactions can drastically modify spin transport dynamics and give rise to robust collective effects including global demagnetization, macroscopic spin waves, spin segregation, and spin self-rephasing. In this work we develop a framework for studying the dynamics of weakly interacting fermionic gases following a spin-dependent change of the trapping potential which illuminates the interplay between spin, motion, Fermi statistics, and interactions. The key idea is the projection of the state of the system onto a set of lattice spin models defined on the single-particle mode space. Collective phenomena, including the global spreading of quantum correlations in real space, arise as a consequence of the long-ranged character of the spin model couplings. This approach achieves good agreement with prior measurements and suggests a number of directions for future experiments.The interplay between spin and motional degrees of freedom in interacting electron systems has been a longstanding research topic in condensed matter physics. Interactions can modify the behavior of individual electrons and give rise to emergent collective phenomena such as superconductivity and colossal magnetoresistance [1]. Theoretical understanding of non-equilibrium dynamics in interacting fermionic matter is limited, however, and many open questions remain. Ultracold atomic Fermi gases, with precisely controllable parameters, offer an outstanding opportunity to investigate the emergence of collective behavior in out-of-equilibrium settings.Progress in this direction has been made in recent experiments with ultracold spin-1/2 fermionic vapors, where initially spin-polarized gases were subjected to a spin-dependent trapping potential ( Fig. 1) implemented by a magnetic field gradient [2-4], or a spin-dependent harmonic trapping frequency [5-8] -equivalent to a spatially-varying gradient. Even in the weakly interacting regime, drastic modifications of the single-particle dynamics were reported. Moreover, despite the local character of the interactions, collective phenomena were observed, including demagnetization and transverse spinwaves in the former, and a time-dependent separation (segregation) of the spin densities and spin self-rephasing in the latter. Although mean-field and kinetic theory formulations have explained some of these phenomena [8][9][10][11][12][13][14][15][16][17][18], a theory capable of describing all the time scales and the interplay between spin, motion, and interactions has not been developed.In this work, we develop a framework that accounts for the coupling of spin and motion in weakly interacting Fermi gases. We qualitatively reproduce and explain all phenomena of the aforementioned experiments and obtain quantitative agreement with the results of Ref. [7]. In this formulation the state of the system is represented as a superposition of spin configurations which live on lattices whose sites correspond to modes of the underlying single-particle sy...

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

“…(1) and C (2) S appear over regular time intervals for later times. Our results for this interaction interval are compliant with the spin-dynamics analysed in [28,45] and we shall refer to this regime as the weak-g demagnetization regime. Indeed within this regime each of the particles precesses with a different Larmor frequency leading to the loss of the polarization magnitude P (1) S after a few precession cycles.…”

“…This outcome cannot be retrieved within the HF description and exposes the crucial role of correlations in the magnetic properties of spin-1/2 fermions even away from the strongly interacting regime. We show that the decay of the polarization and the emerging correlated spin-order can be understood by generalizing the spin-chain model of [28]. The coupling of the initial state to lower spin-S values is found to cause the dephasing of the collective Larmor precession of the spins.…”

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

“…This would allow one to address many observables and use the fact that DMRG is accurate and can be scaled to larger system sizes for spin models than typical exact diagonalization routines which are exponentially slow for longer spin chains. More generally, one may also consider an approach where one expands the Hamiltonian in a basis set [78]. In an occupation number basis one may then by appropriate truncation produce lattice models that can be solved using a DMRG routine.…”

Crossover from collisionless to collisional spin dynamics of polarized fermions

“…In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two regimes have been studied experimentally and theoretically in cold atoms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], liquid helium [16][17][18][19], and solid state systems [20][21][22].…”

“…At lower temperatures one would need to include the Hartree-Fock mean-field terms which drive the Leggett-Rice effect [3], and demagnetization [8]. Our linearization of the collision integral will break down at large λ, where the dynamics create spin configuration which are far from equilibrium.…”