Emergence of Glasslike Dynamics for Dissipative and Strongly Interacting Bosons

We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular, we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are due here to strong interactions. This complex two-stage dynamics reveals information on the level structure of the strongly interacting gas.

Figure 1

$1-\kappa (\tau )/\kappa (\infty )$ versus the square root of rescaled time $\tau$ for the interaction over the dissipative coupling ratio $U/\hslash \gamma =10$. Numerical results of Eq. (2) are shown for different fillings $f=0.1$, 0.5, 1, 3 in the direction of the arrow as solid lines and corresponding stretched exponential fits as dashed lines. The analytical result (6) of the diffusion equation (3) is shown as a dot-dashed (black) line.

Figure 2

Numerical evolution of the density matrix elements $\rho (n,\tau )$ [solid lines, Eq. (2)] in a semilogarithmic plot versus $n$ for large rescaled times $\tau$ between 0.1 and 50 (not equidistant) in the direction of the (red) arrow. The inset shows the same evolution at shorter times $\tau$ between 0.0002 and 0.1 (not equidistant) in the direction of the (red) arrow in a linear plot. Parameters: $f=3$ and $U/\hslash \gamma =10$. The dashed (red) lines show the (analytical) asymptotic limit.

Figure 3

Local particle fluctuations $\kappa /f^2$ versus rescaled time $\tau$ for $U/\hslash \gamma =10$. Numerical results (solid lines) for various fillings $f=3$, 5, 7, 9, 20 in the direction of the arrow are obtained solving Eq. (2). The approximate analytical solution $\kappa /f^2=[\Gamma (3/4)/\Gamma (5/4)]\sqrt{\tau }$ of the diffusion equation is represented by the dashed line.

Figure 4

(a) The dotted blue line shows the evolution of $g(x,\tau )$ versus $x$ for large rescaled times $\tau \in [28,710]$ in the direction of the red arrow. Inset: Plot of $g(x,\tau )$ versus $\eta =[x-a(\tau )]/b(\tau )$ (solid blue line) and fit with an error function (dashed red line). (b) $a(\tau )$ is plotted versus $\sqrt{\tau }$ (solid blue line) and compared to a linear fit (dashed red line). (c) $b(\tau )$ is plotted versus ${\tau }^{1/4}$ (solid blue line) and compared to a linear fit (dashed red line). Parameters: $f=0.5$ and $U/\hslash \gamma =15$.