Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1111.4214 · Physical Review A

Slow quench dynamics of Mott-insulating regions in a trapped Bose gas

Jean-Sébastien Bernier, Dario Poletti, Peter Barmettler, Guillaume Roux, Corinna Kollath

Published Mar 29, 2012• 44 citations
arXivHTMLPDF

Abstract

We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly, whereas long-range correlations require a longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy and their respective currents, the local compressibility, the local excess energy, the heat, and single-particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization-group technique and comparisons with time evolutions done within the Gutzwiller approximation are provided.

DOI
10.1103/physreva.85.033641

Related papers

Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice

Jean-Sébastien Bernier, Guillaume Roux, Corinna Kollath

We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the non-trivial scaling of the energy absorbed with the ramp time.

•Jan 1, 2011•0 citations

Mott-insulator dynamics

Emil Lundh

The hydrodynamics of a lattice Bose gas in a time-dependent external potential is studied in a mean-field approximation. The conditions under which a Mott insulating region can melt, and the local density can adjust to the new potential, are determined. In the case of a suddenly switched potential, it is found that the Mott insulator stays insulating and the density will not adjust if the switch is too abrupt. This comes about because too rapid currents result in Bloch oscillation-type current reversals. For a stirrer moved through a Mott insulating cloud, it is seen that only if the stirrer starts in a superfluid region and the velocity is comparable to the time scale set by the tunneling will the Mott insulator be affected.

arXiv:1105.1263•Physical Review A•Sep 2, 2011•5 citations

Slow Quench Dynamics of a One-Dimensional Bose Gas Confined to an Optical Lattice

Jean-Sébastien Bernier, Guillaume Roux, Corinna Kollath

We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.

arXiv:1010.5251•Physical Review Letters•May 18, 2011•54 citations

Trapped ultracold bosons in periodically modulated lattices

Jia-Wei Huo, Fu‐Chun Zhang, Wei-Qiang Chen +2 more

Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.

arXiv:1108.4574•Physical Review A•Oct 7, 2011•8 citations

Sudden expansion of Mott insulators in one dimension

Lev Vidmar, S. Langer, Ian P. McCulloch +3 more

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.

arXiv:1305.5496•Physical Review B•Dec 16, 2013•70 citations

Semiclassical quench dynamics of Bose gases in optical lattices

Kazuma Nagao, Masaya Kunimi, Yosuke Takasu +2 more

We analyze the time evolution of the Bose-Hubbard model after a sudden quantum quench to a weakly interacting regime. Specifically, motivated by a recent experiment at Kyoto University, we numerically simulate redistribution of the kinetic and on-site interaction energies at an early time, which was observed in nonequilibrium dynamics of ultracold Bose gases in a cubic optical lattice starting with a singly occupied Mott-insulator state. In order to compute the short-time dynamics corresponding to the experimental situation, we apply the truncated-Wigner approximation to the Bose-Hubbard model on a cubic lattice. We show that our semiclassical approach quantitatively reproduces the fast redistribution dynamics. We further analyze spatial spreading of density-density correlations at equal time in the Bose-Hubbard model on a square lattice with a large filling factor. When the system is initially prepared in a coherent state, we find that a propagation velocity of the correlation wave packet in the correlation function strongly depends on the final interaction strength, and it is bounded by twice the maximum group velocity of the elementary excitations. In contrast, when the system is initially in a Mott-insulator state, the propagation velocity of the wave packet is approximately independent of the final interaction strength.

arXiv:1810.04347•Physical Review A•Feb 20, 2019•21 citations
We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly, whereas long-range correlations require a longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy and their respective currents, the local compressibility, the local excess energy, the heat, and single-particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization-group technique and comparisons with time evolutions done within the Gutzwiller approximation are provided.
We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the non-trivial scaling of the energy absorbed with the ramp time.
The hydrodynamics of a lattice Bose gas in a time-dependent external potential is studied in a mean-field approximation. The conditions under which a Mott insulating region can melt, and the local density can adjust to the new potential, are determined. In the case of a suddenly switched potential, it is found that the Mott insulator stays insulating and the density will not adjust if the switch is too abrupt. This comes about because too rapid currents result in Bloch oscillation-type current reversals. For a stirrer moved through a Mott insulating cloud, it is seen that only if the stirrer starts in a superfluid region and the velocity is comparable to the time scale set by the tunneling will the Mott insulator be affected.
We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.
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.
We analyze the time evolution of the Bose-Hubbard model after a sudden quantum quench to a weakly interacting regime. Specifically, motivated by a recent experiment at Kyoto University, we numerically simulate redistribution of the kinetic and on-site interaction energies at an early time, which was observed in nonequilibrium dynamics of ultracold Bose gases in a cubic optical lattice starting with a singly occupied Mott-insulator state. In order to compute the short-time dynamics corresponding to the experimental situation, we apply the truncated-Wigner approximation to the Bose-Hubbard model on a cubic lattice. We show that our semiclassical approach quantitatively reproduces the fast redistribution dynamics. We further analyze spatial spreading of density-density correlations at equal time in the Bose-Hubbard model on a square lattice with a large filling factor. When the system is initially prepared in a coherent state, we find that a propagation velocity of the correlation wave packet in the correlation function strongly depends on the final interaction strength, and it is bounded by twice the maximum group velocity of the elementary excitations. In contrast, when the system is initially in a Mott-insulator state, the propagation velocity of the wave packet is approximately independent of the final interaction strength.