Sudden expansion of Mott insulators in one dimension

We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion: The asymptotic density dynamics is identical to that of initially localized, non-interacting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this non-equilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model: While being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the non-interacting limit. These results are compared to the set-up of a recent experiment [PRL 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways: While the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.

Long-time behavior of the momentum distribution during the sudden expansion of a spin-imbalanced Fermi gas in one dimension

We study the sudden expansion of spin-imbalanced ultracold lattice fermions with attractive interactions in one dimension after turning off the longitudinal confining potential. We show that the momentum distribution functions of majority and minority fermions approach stationary values quickly due to a quantum distillation mechanism that results in a spatial separation of pairs and majority fermions. As a consequence, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations are lost during the expansion. Furthermore, we argue that the shape of the stationary momentum distribution functions can be understood by relating them to the integrals of motion in this integrable quantum system. We discuss our results in the context of proposals to observe FFLO correlations, related to recent experiments by Liao et al., Nature 467, 567 (2010).

Non-equilibrium thermodynamics in sheared hard-sphere materials

We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume $V$ replaces the internal energy $U$ as a function of entropy $S$ in conventional statistical mechanics. In place of the effective temperature, the compactivity $X = partial V / partial S$ characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.

Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime

We show that in the sudden expansion of a spin-balanced two-component Fermi gas into an empty optical lattice induced by releasing particles from a trap, over a wide parameter regime, the radius $R_n$ of the particle cloud grows linearly in time. This allow us to define the expansion velocity $V_{ex}$ from $R_n=V_{ex}t$. The goal of this work is to clarify the dependence of the expansion velocity on the initial conditions which we establish from time-dependent density matrix renormalization group simulations, both for a box trap and a harmonic trap. As a prominent result, the presence of a Mott-insulating region leaves clear fingerprints in the expansion velocity. Our predictions can be verified in experiments with ultra-cold atoms.

A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method

Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this set-up. By computing the time-dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We discuss our findings in view of experiments on quasi-one dimensional quantum magnets and we propose that the study of the time-dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.