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arXiv:1109.4364 · Physical Review A

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

S. Langer, Martin J. A. Schuetz, Ian P. McCulloch, Ulrich Schollwöck, Fabian Heidrich‐Meisner

Published Apr 20, 2012• 33 citations
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Abstract

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 ${V}_{\mathrm{ex}}$ from ${R}_{n}={V}_{\mathrm{ex}}t$. 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 ultracold atoms.

DOI
10.1103/physreva.85.043618

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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 Rn{R}_{n}Rn​ of the particle cloud grows linearly in time. This allow us to define the expansion velocity Vex{V}_{\mathrm{ex}}Vex​ from Rn=Vext{R}_{n}={V}_{\mathrm{ex}}tRn​=Vex​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 ultracold atoms.
We show that in the sudden expansion of a spin-balanced two-component Fermi gas in an optical lattice induced by releasing particles from a trap, over a wide parameter regime, the radius Rn of the particle cloud grows linearly in time. This allow us to define the expansion velocity Vex from Rn = Vext. 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.
The expansion of an ultracold lattice gas of fermions in a one-dimensional optical lattice after a geometric quench in which the atoms are released from a box (or parabolic) trap is studied numerically using the time-dependent density matrix renormalization group method. It is found that the momentum distributions of the two atomic species present in the simulations quickly converge toward stationary values dictated by the integrals of motion of the lattice gas at the expansion onset. An account of the central results and some of the technical details is given along with explicit examples.
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, noninteracting 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 nonequilibrium 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 noninteracting limit. These results are compared to the setup of a recent experiment [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. In the latter case, the interaction quench breaks the universal dynamics in the asymptotic regime and the expansion depends on the interaction strength. 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.
Abstract. – We discuss the effects of collisions on the expansion of an ultracold normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the temperature increase of the expanding atomic cloud. We find that for dilute gases and standard choices of the trap parameters the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution can be quite large, revealing that even at zero temperature collisions are effective in a Fermi gas. The expansion of an atomic gas following the sudden removal of the confining trap is known to provide valuable information on the state of the system and on the role of interactions [1]. In particular in the superfluid phase, where the macroscopic dynamics of the gas are governed by the equations of hydrodynamics, one expects anisotropic expansion if the gas is released from an anisotropic trap. This peculiar feature, which should be contrasted with the isotropic ballistic expansion exhibited by a non interacting gas, was first discussed in [2,3] in the case
Using the time-dependent density-matrix renormalization-group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.
We discuss the effects of collisions on the expansion of a degenerate normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the entropy increase of the expanding atomic cloud taking into account the collisional effects due to the deformation of the distribution function in momentum space. We find that in dilute gases the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution due to the entropy increase can be sizeable, revealing that even at zero temperature collisions are effective in a Fermi gas.