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arXiv:cond-mat/0612415 · Physical Review A

Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes

Marcos Rigol, Alejandro Muramatsu, Maxim Olshanii

Published Nov 16, 2006• 246 citations
arXivHTMLPDF

Abstract

We study the ground-state properties and nonequilibrium dynamics of hard-core bosons confined in one-dimensional lattices in the presence of an additional periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed after a sudden switch-on or switch-off of the superlattice potential, which can bring the system into insulating or superfluid phases, respectively. A collapse and revival of the zero-momentum peak can be seen in the first case. We study in detail the relaxation of these integrable systems towards equilibrium. We show how after relaxation time averages of physical observables, like the momentum distribution function, can be predicted by means of a generalization of the Gibbs distribution.

DOI
10.1103/physreva.74.053616

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We study the ground-state properties and nonequilibrium dynamics of hard-core bosons confined in one-dimensional lattices in the presence of an additional periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed after a sudden switch-on or switch-off of the superlattice potential, which can bring the system into insulating or superfluid phases, respectively. A collapse and revival of the zero-momentum peak can be seen in the first case. We study in detail the relaxation of these integrable systems towards equilibrium. We show how after relaxation time averages of physical observables, like the momentum distribution function, can be predicted by means of a generalization of the Gibbs distribution.
We study properties of the strongly repulsive Bose gas on one-dimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through Bose-Fermi mapping. We first exploit the phase transition of hard-core bosons in optical lattices from the superfluid to the Bose-glass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the one-particle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Our results indicate that the Bose-glass and superfluid phases display quite different properties and expansion dynamics.
In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].
We investigate the dynamics of the rate function and of local observables after a quench in models which exhibit phase transitions between a superfluid and an insulator in their ground states. Zeros of the return probability, corresponding to singularities of the rate functions, have been suggested to indicate the emergence of dynamical criticality and we address the question of whether such zeros can be tied to the dynamics of physically relevant observables and hence order parameters in the systems. For this we first numerically analyze the dynamics of a hard-core boson gas in a one-dimensional waveguide when a quenched lattice potential is commensurate with the particle density. Such a system can undergo a pinning transition to an insulating state and we find non-analytic behavior in the evolution of the rate function which is indicative of dynamical phase transitions. In addition, we perform simulations of the time dependence of the momentum distribution and compare the periodicity of this collapse and revival cycle to that of the non-analyticities in the rate function: the two are found to be closely related only for deep quenches. We then confirm this observation by analytic calculations on a closely related discrete model of hard-core bosons in the presence of a staggered potential and find expressions for the rate function for the quenches. By extraction of the zeros of the survival amplitude we uncover a non-equilibrium timescale for the emergence of non-analyticities and discuss its relationship with the dynamics of the experimentally relevant parity operator.
We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest- and next-nearest-neighbor sites. We obtain the ground-state phase diagram as a function of microscopic parameters using the finite-size density-matrix renormalization-group method. Depending on the sign of the next-nearest-neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI), and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the unfrustratedase), the system undergoes a transition from the SF to the SLMI at a nonzero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the frustrated case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next-nearest-neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond-order parameter. The transition from BO to SLMI appears to be first order.
We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.
We study the dynamics and the resulting state after relaxation in a quasidisordered integrable lattice system after a sudden quench. Specifically, we consider hard-core bosons in an isolated one-dimensional geometry in the presence of a quasiperiodic potential whose strength is abruptly changed to take the system out of equilibrium. In the delocalized regime, we find that the relaxation dynamics of one-body observables, such as the density, the momentum distribution function, and the occupation of the natural orbitals, follow, to a good approximation, power laws. In that regime, we also show that the observables after relaxation can be described by the generalized Gibbs ensemble, while such a description fails for the momentum distribution and the natural orbital occupations in the presence of localization. At the critical point, the relaxation dynamics is found to be slower than in the delocalized phase.