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arXiv:1408.4463 · Physical Review B

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

Uma Divakaran, K. Sengupta

Published Nov 19, 2014• 38 citations
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Abstract

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 $E$ 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 ${\ensuremath{\omega}}_{1}$, relate this effect to a generalized version of St\"uckelberg interference phenomenon, and identify special frequencies for which $D$ 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 $E$ (with a rate ${\ensuremath{\omega}}_{1}$) and the boson hopping parameter $J$ (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 $D$ and the residual energy $Q$ 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.

DOI
10.1103/physrevb.90.184303

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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≤18N\ensuremath{\le}18N\ensuremath≤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 \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​, relate this effect to a generalized version of St"uckelberg interference phenomenon, and identify special frequencies for which DDD and 1\ensuremath−F1\ensuremath{-}F1\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 \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​) and the boson hopping parameter JJJ (with a rate \ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​) 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 \ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​; 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.
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