Interaction-Induced Impeding of Decoherence and Anomalous Diffusion

We study how the interplay of dissipation and interactions affects the dynamics of a bosonic many-body quantum system. In the presence of both dissipation and strongly repulsive interactions, observables such as the coherence and the density fluctuations display three dynamical regimes: an initial exponential variation followed by a power-law regime, and finally a slow exponential convergence to their asymptotic values. These very long-time scales arise as dissipation forces the population of states disfavored by interactions. The long-time, strong coupling dynamics are understood by performing a mapping onto a classical diffusion process displaying non-Brownian behavior. While both dissipation and strong interactions tend to suppress coherence when acting separately, we find that strong interaction impedes the decoherence process generated by the dissipation.

Figure 1

(a),(b) Density fluctuations (a) and rescaled coherence (b) versus rescaled time $\tau$. A data collapse is observed for large interaction strength $U$ and atom number $N$, independently of the other system parameters. The analytical results are taken from Eqs. (6, 7). The inset of (a) shows the real parts of the smallest ${\lambda }_{\alpha }$ versus $N$ and a fit $\propto 1/N^2$. (c),(d) Coherence decay at short (c) and long (d) times ($N=60$, $U/J=20$, and $\hslash \gamma /J=1$) with exponential fit (continuous green line). $L=2$.

Figure 2

Diagonal terms of the density matrix ${\rho }_{n,n}$ versus rescaled time $\tau$ in log-log form: the exact solutions of Eq. (1) for $n=41(\mathrm{\text{top}})\dots 80(\mathrm{\text{bottom}})$ are represented by blue continuous lines; the element $n=40$ (thick red line) is proportional to the probability of finding a balanced configuration $P_b$; the corresponding diffusion density $p(x=n/N,\tau )$ Eq. (5) up to $n/N=60$ are shown in dashed green lines. Inset: 3D plot of the evolution. Parameters: $U/J=20$, $\hslash \gamma /J=1$, $N=80$, and $L=2$.

Figure 3

Coherence divided by number of atoms versus time for different interactions and for $N=60$, $\hslash \gamma /J=1$, and $L=2$. Inset: zoom on the short times.