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arXiv:1106.4031 · Physical Review B

Nonequilibrium dynamics of bosonic Mott insulators in an electric field

Michael Kolodrubetz, David Pekker, Bryan K. Clark, K. Sengupta

Published Mar 16, 2012• 51 citations
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Abstract

We study the nonequilibrium dynamics of one-dimensional Mott-insulating bosons in the presence of a tunable effective electric field $\mathcal{E}$ which takes the system across a quantum critical point separating a disordered and a translation symmetry broken ordered phase. We provide an exact numerical computation of the residual energy $Q$, the log fidelity $F$, the defect density $D/L$, and the order parameter correlation function for a linear-in-time variation of $\mathcal{E}$ with a rate $v$. We discuss the temporal and spatial variation of these quantities for a range of $v$ and for finite system sizes as relevant to realistic experimental setups [J. Simon et al., Nature (London) 472, 307 (2011)]. We show that in finite-sized systems $Q$, $F$, and $D$ obey Kibble-Zurek scaling, and suggest further experiments within this setup to test our theory.

DOI
10.1103/physrevb.85.100505

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We study the nonequilibrium dynamics of one-dimensional Mott-insulating bosons in the presence of a tunable effective electric field E\mathcal{E}E which takes the system across a quantum critical point separating a disordered and a translation symmetry broken ordered phase. We provide an exact numerical computation of the residual energy QQQ, the log fidelity FFF, the defect density D/LD/LD/L, and the order parameter correlation function for a linear-in-time variation of E\mathcal{E}E with a rate vvv. We discuss the temporal and spatial variation of these quantities for a range of vvv and for finite system sizes as relevant to realistic experimental setups [J. Simon et al., Nature (London) 472, 307 (2011)]. We show that in finite-sized systems QQQ, FFF, and DDD obey Kibble-Zurek scaling, and suggest further experiments within this setup to test our theory.
We study the equilibrium and nonequilibrium properties of strongly interacting bosons on a lattice in the presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose-Hubbard model and obtain the Mott insulator, Bose glass, and superfluid phases. We also study the nonequilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter, and the energy pumped into the system in this process as a function of the inverse ramp rate $\ensuremath{\tau}$. For the clean case the density of excitations goes to a constant, while the order parameter and energy relax as $1/\ensuremath{\tau}$ and $1/{\ensuremath{\tau}}^{2}$ respectively. With disorder, the excitation density decays exponentially with $\ensuremath{\tau}$, with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as $\ensuremath{\tau}$ is increased.
We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.
We study the dynamics of phase transitions in the one-dimensional Bose-Hubbard model. To drive the system from a Mott insulator to a superfluid phase, we change the tunneling frequency at a finite rate. We investigate the buildup of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.
We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.
We study the dynamics of a tilted one-dimensional Bose-Hubbard model for two distinct protocols using numerical diagonalization for a finite sized system ($N\ensuremath{\le}18$). The first protocol involves periodic variation of the effective electric field EEE seen by the bosons which takes the system twice (per drive cycle) through the intermediate quantum critical point. We show that such a drive leads to nonmonotonic variation of the excitation density DDD and the wave function overlap FFF at the end of a drive cycle as a function of the drive frequency ${\ensuremath{\omega}}_{1}$, relate this effect to a generalized version of St\"uckelberg interference phenomenon, and identify special frequencies for which DDD and $1\ensuremath{-}F$ approach zero leading to near-perfect dynamic freezing phenomenon. The second protocol involves a simultaneous linear ramp of both the electric field EEE (with a rate ${\ensuremath{\omega}}_{1}$) and the boson hopping parameter JJJ (with a rate ${\ensuremath{\omega}}_{2}$) starting from the ground state for a low effective electric field up to the quantum critical point. We find that both DDD and the residual energy QQQ decrease with increasing ${\ensuremath{\omega}}_{2}$; our results thus demonstrate a method of achieving near-adiabatic protocol in an experimentally realizable quantum critical system. We suggest experiments to test our theory.
We study the non-equilibrium dynamics of ultracold bosons in an optical lattice with a time dependent hopping amplitude J(t)=J_0 +δJ \cos(ωt) which takes the system from a superfluid phase near the Mott-superfluid transition (J= J_0+δJ) to a Mott phase (J=J_0-δJ) and back through a quantum critical point (J=J_c) and demonstrate dynamic freezing of the boson wavefunction at specific values of ω. At these values, the wavefunction overlap F (defect density P=1-F) approaches unity (zero). We provide a qualitative explanation of the freezing phenomenon, show it's robustness against quantum fluctuations and the presence of a trap, compute residual energy and superfluid order parameter for such dynamics, and suggest experiments to test our theory.