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

We study the dynamics of tilted one-dimensional Bose-Hubbard model for two distinct protocols using numerical diagonalization for finite sized system ($N\le 18$). 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 non-monotonic variations of the excitation density $D$ and the wavefunction 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 St\"uckelberg 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 ramp of both the electric field $E$ (with a rate $\omega_1$) and the boson hopping parameter $J$ (with a rate $\omega_2$) 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.