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Register a new userCollective excitations in one-dimensional ultracold Fermi gases: a comparative study
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Time-dependent density-functional theory (TDDFT) is a powerful tool to study the non-equilibrium dynamics of inhomogeneous interacting many-body systems. Here we show that the simple adiabatic local-spin-density approximation for the time-dependent exchange-correlation potential is surprisingly accurate in describing collective density and spin dynamics in strongly correlated one-dimensional ultracold Fermi gases. Our conclusions are based on extensive comparisons between our TDDFT results and accurate results based on the adaptive time-dependent density-matrix renormalization-group method.
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We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $omega_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value $omega_2=2omega_0$ to the quasi-ordered, super-strongly interacting value $omega_2=sqrt{5}omega_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.
We measure collective excitations of a harmonically trapped two-dimensional (2D) SU($N$) Fermi gas of $^{173}$Yb confined to a stack of layers formed by a one-dimensional optical lattice. Quadrupole and breathing modes are excited and monitored in the collisionless regime $lvertln(k_F a_{2D})rvertgg 1$ with tunable spin. We observe that the quadrupole mode frequency decreases with increasing number of spin components due to the amplification of the interaction effect by $N$ in agreement with a theoretical prediction based on 2D kinetic equations. The breathing mode frequency, however, is measured to be twice the dipole oscillation frequency regardless of $N$. We also follow the evolution of collective excitations in the dimensional crossover from two to three dimensions and characterize the damping rate of quadrupole and breathing modes for tunable SU($N$) fermions, both of which reveal the enhanced inter-particle collisions for larger spin. Our result paves the way to investigate the collective property of 2D SU($N$) Fermi liquid with enlarged spin.
Motivated by the large interest in the non-equilibrium dynamics of low-dimensional quantum many-body systems, we present a fully-microscopic theoretical and numerical study of the charge and spin dynamics in a one-dimensional ultracold Fermi gas following a quench. Our approach, which is based on time-dependent current-density-functional theory, is applicable well beyond the linear-response regime and produces both spin-charge separation and spin-drag-induced broadening of the spin packets.
Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed spin drag relaxation time $tau_{rm sd}$. In this paper we present both numerical and analytical calculations of $tau_{rm sd}$ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for $tau_{rm sd}$, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in 1D inhomogeneous systems of interacting fermions.
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or - potentially - to exotic forms of superfluidity such as FFLO-state, Sarma state or breached pair state. We consider ultracold Fermi gases with polarization, i.e. spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the BCS-superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.
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