Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder

Motivated by recent optical lattice experiments [J.-y. Choi et al., Science 352, 1547 (2016)], we study the dynamics of strongly interacting bosons in the presence of disorder in two dimensions. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system.

Figure 1

The site occupations for quenched dynamics at zero temperature. Columns (rows) depict results for different disorder strengths (different times). At time $t=0$ all bosons in the right half of the system are removed and the remainder evolves for $t>0$. The $t=0$ state is the ground state for a very small hopping and no disorder. For $t>0$, Gaussian disorder of strength ${\mathrm{\Delta }}_g$ is introduced and the hopping is increased. The state evolves for $t\ge 0$ with no parameter changes.

Figure 2

(a) Time evolution of the imbalance $\mathcal{I}$ for various disorder strengths at initial temperature $T=0$. Lines show simulation results while points with error bars show experimental data [28]. The vertical dashed line marks a time $t^{*}=20$ below which $\mathcal{I}$ barely changes within GMFT. The experimental results are shifted to start at $t^{*}$. From bottom to top the lines and symbols correspond to ${\mathrm{\Delta }}_g=0$, 3, 4, 8, and 13. (b) Corresponding $\mathcal{I}$ for the same parameters but at times $t=200$ and 300 against disorder strength. The experimental result after an evolution time of 187 is also plotted. The inset shows the inverse decay length [Eq. (5)] from our calculation at $t=200$ and for the experiment after an evolution time $t=187$. [(c) and (d)] The same as (a) and (b) but with an analysis window resized from $l_W=9$ [as in (a) and (b) following Ref. 28] to $l_W^{\prime }=5$, as shown in the schematic. [(e) and (f)] The same as (c) and (d) but at nonzero temperature. Here $t^{*}$ reduces to 8.

Figure 3

The solid (dashed) lines plot the normalized imbalance where the right half of the trap was initialized to a checkerboard (empty) pattern as shown in the insets. (a) The normalized imbalance against time for various disorder strengths. The pairs of (solid/dashed) lines correspond to uniform disorder ${\mathrm{\Delta }}_u=0$, 13 and 20 from bottom to top. (b) The normalized imbalance at times $t=200$ and 300 against disorder strength. The other parameters are $U=24.4$, $\mathrm{\Omega }=0.145$, and $\mu =4$.