Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model

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 <= 18). The first protocol involves periodic variation of the effective electric field E 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 D and the wave function overlap F at the end of a drive cycle as a function of the drive frequency omega(1), relate this effect to a generalized version of Stuckelberg interference phenomenon, and identify special frequencies for which D and 1 - F approach zero leading to near-perfect dynamic freezing phenomenon. The second protocol involves a simultaneous linear ramp of both the electric field E (with a rate omega(1)) and the boson hopping parameter J (with a rate omega(2)) starting from the ground state for a low effective electric field up to the quantum critical point. We find that both D and the residual energy Q decrease with increasing 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.