Probing local relaxation of cold atoms in optical superlattices

Abstract

In the study of relaxation processes in coherent nonequilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity 2 provide a very fruitful test ground. We consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised by Cramer et al. ͓Phys. Rev. Lett. 101, 063001 ͑2008͔͒. We investigate the relaxation dynamics analytically in the noninteracting and hard-core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent densitymatrix renormalization ͑t-DMRG͒ approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the noninteracting and hard-core bosonic limits.

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

“…Thus, real thermalization -if it occurs at all -requires much longer times scales. This seems to be a generic feature and has been discussed for bosonic [25,[29][30][31] and fermionic systems [10, 53, 54, 61-63, 103, 104] and is sometimes called "pre-thermalization" [3,4]. This phenomenon can be visualized via the following intuitive picture: The excited state generated by the quench can be viewed as a highly coherent superposition of correlated quasi-particles.…”

“…This requires a time-dependent solution of the evolution equations (24)- (26) which crucially depends on the eigenfrequency (31). Thus, let us first discuss the general behavior of (31). In view of the definition (22), T k adopts its maximum value T k=0 = 1 at k = 0.…”

“…For small values of J/U , we can employ strong-coupling perturbation theory, i.e., an expansion in powers of J/U . It is useful to introduce the operator [30,31]…”

“…Apart from some general statements concerning the relaxation of a quantum system towards equilibrium [29][30][31], quantum quenches have been studied by using certain approximations, such as Bogoliubov-type approxi-mations or strong-coupling perturbation theory [41][42][43][44], the Gutzwiller approximation [45], or related (semi) classical methods [46][47][48], as well as (truncated) exact diagonalization [25]. However, these approximations are only reliable in certain regions of parameter space.…”

“…For bosons, many studies have been devoted to one spatial dimension by employing exact diagonalization [25][26][27][28], time-dependent density matrix renormalization group theory (t-DMRG) [25,[29][30][31][32][33][34], and Jordan-Wigner fermionization [35]. For corresponding experiments, see Refs.…”