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

Langer, Stephan; Schuetz, Martin J. A.; McCulloch, Ian P.; Schollwöck, Ulrich; Heidrich-Meisner, Fabian

doi:10.1103/physreva.85.043618

Cited by 37 publications

(51 citation statements)

References 48 publications

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“…It is also interesting to study the dependence of v r on initial densities n = 1. Similar to fermions, 58 we findR(t) ∝ t for all n 1 and v r (n) depends in a nonmonotonic way on the initial density. We study this dependence in more detail in Appendix B.…”

Section: Bosonssupporting

confidence: 64%

“…This is the case for the expansion of fermionic Mott insulators. 58 Indications of the absence of strictly ballistic dynamics at finite expansion times before the gas becomes infinitely dilute are therefore the following: (i) significant deviations from R(t) ∝ t, (ii) a slower expansion velocity (measured through v r and v c ), and (iii) the formation of a slowly expanding high-density core. Point (iii) is motivated by two results.…”

Section: Discussion: Diffusive Versus Ballistic Dynamics and Asymentioning

confidence: 99%

“…10. Second, analytical and numerical simulations for one-dimensional systems typically find a splitting of the cloud into left-and right-moving portions in the ballistic regime of Mott insulators, 58,67,68,72 but slowly expanding high-density cores in the diffusive case. 69,72 All these phenomena are present in the experimental data 11 for bosons in 1D at intermediate U/J in combination with the interaction quench realized in that experiment, in agreement with DMRG data for the same initial conditions.…”

Section: Discussion: Diffusive Versus Ballistic Dynamics and Asymentioning

confidence: 99%

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Sudden expansion of Mott insulators in one dimension

et al. 2013

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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.

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Section: Bosonssupporting

confidence: 64%

Section: Discussion: Diffusive Versus Ballistic Dynamics and Asymentioning

confidence: 99%

Section: Discussion: Diffusive Versus Ballistic Dynamics and Asymentioning

confidence: 99%

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Sudden expansion of Mott insulators in one dimension

et al. 2013

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“…9). Such beams have been observed, apart from the present work, theoretically and experimentally, both for bosons [7,8,40] and for fermions [40,41], and seem to be absent in the continuum case [34]. The effects of the discreteness have already been stressed by Rigol and collaborators [8], who argued that the most populated states in the diffusion process are at a well- defined value of the momentum p 0 , depending on the mean value of the energy H (with p 0 = ±π/2 when H = 0).…”

Section: Effect Of the Lattice On The Expansion Dynamicsmentioning

confidence: 76%

Bound states and expansion dynamics of interacting bosons on a one-dimensional lattice

et al. 2014

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The expansion dynamics of bosonic gases in optical lattices has recently been the focus of an incresing attention, both experimental and theoretical. We consider, by means of numerical Bethe ansatz, the expansion dynamics of initially confined wave packets of two interacting bosons on a lattice. We show that a correspondence between the asymptotic expansion velocities and the projection of the evolved wave function over the bound states of the system exists, clarifying the existing picture for such situations. Moreover, we investigate the role of the lattice in this kind of evolution.

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“…The radial expansion velocity of 1D systems was studied for the Fermi-Hubbard model [92], the Bose-Hubbard model [19,70], and the Lieb-Liniger model [93]. For Bethe-integrable 1D systems, it can be related to distributions of rapidities [94].…”

Section: B Radial Velocitymentioning

confidence: 99%

Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders

2015

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We numerically investigate the expansion of clouds of hard-core bosons in the two-dimensional square lattice using a matrix-product-state-based method. This nonequilibrium set-up is induced by quenching the trapping potential to zero and our work is specifically motivated by a recent experiment with interacting bosons in an optical lattice [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)]. As the anisotropy of the amplitudes Jx and Jy for hopping in different spatial directions is varied from the one-to the two-dimensional case, we observe a crossover from a fast ballistic expansion in the one-dimensional limit Jx Jy to much slower dynamics in the isotropic two-dimensional limit Jx = Jy. We further study the dynamics on multi-leg ladders and long cylinders. For these geometries we compare the expansion of a cloud to the melting of a domain wall, which helps us to identify several different regimes of the expansion as a function of time. By studying the dependence of expansion velocities on both the anisotropy Jy/Jx and the number of legs, we observe that the expansion on two-leg ladders, while similar to the two-dimensional case, is slower than on wider ladders. We provide a qualitative explanation for this observation based on an analysis of the rung spectrum.

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

Cited by 37 publications

References 48 publications

Sudden expansion of Mott insulators in one dimension

Sudden expansion of Mott insulators in one dimension

Bound states and expansion dynamics of interacting bosons on a one-dimensional lattice

Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders

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