Slow Quench Dynamics of a One-Dimensional Bose Gas Confined to an Optical Lattice

We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.

Figure 1

$U_i=2J$ and $U_f=3J$ at $n=1$. (a) Scaling of the heat put into the homogeneous system vs $1/\tau$ showing a nontrivial exponent in the near-adiabatic regime. Inset: Collapse of data for different $\delta U$ (ED). (b) Comparison to perturbation theory (${\tau }_c\simeq 3.47\hslash /J$). Inset: $\mathcal{B}(\omega )$ for $U=2J$ (ED).

Figure 2

Observables for a quench from $U_i=2J$ to $U_f=4J$ (ED). (a) Occupation probability $P_n$ and compressibility $\kappa$ vs ramp time $\tau$ in the homogeneous system. (b) Perturbation theory of Eq. (2) gives a quantitative prediction for $L=11$. The $L=16$ data give an idea of finite-size effects.

Figure 3

Local observables at the center of the homogeneous and trapped ($V=0.006J$) systems vs $\tau$ (DMRG calculations). The gray area shows the time scales over which the responses are identical. (a) Slow change from $U_i=2J$ to $U_f=4J$. (b) $U_i=4J$ to $U_f=6J$.

Figure 4

Slow quenches with $\tau =20\hslash /J$, $L=64$, and $V=0.006\mathrm{J}$. (a) $U=(2\to 4)J$, (b) $U=(4\to 6)J$. Contour plots: Density $n$ (up) and compressibility $\kappa$ (down) as a function of position and time. Graphs: $n$ (up) and $\kappa$ (down) vs position for various times $t$ (full lines). Circles and squares stand for ground-state predictions with corresponding $U(t)$.