Probing quantum chaos in many-body quantum systems by the induced dissipation

We theoretically analyze the depletion dynamics of an ensemble of cold atoms in a quasi-one-dimensional optical lattice where atoms in one of the lattice sites are subject to decay. Unlike the previous studies of this problem in Labouvie et al., Phys. Rev. Lett. 116, 235302 (2016), we focus on the case where the system is brought to the chaotic regime, which crucially modifies the depletion dynamics as compared to the regular case. It is shown that depletion of the affected site results in gradual depletion of the neighboring sites according to the $t^{1/3}$ scaling law. We also show that by measuring occupations of the lattice sites one can extract important information on chaotic dynamics of the original conservative system.

Figure 1

The classical Bose-Hubbard model. Upper panel: Relative volume of the energy shell as the function of the shell energy $E$ where energy is measured in units of $J$. Lower panel: Lyapunov exponent $\lambda$ of 1000 trajectories with the initial conditions uniformly distributed over the whole phase space. Vertical lines mark energies of the periodic trajectories (9). Parameters are $L=6$ and $g/J=4$.

Figure 2

Occupations of the lattice sites in the course of time where time is measured in units of the tunneling period. Upper panels: Occupations of the lattice sites with $l=L/2,...,L/2+4$ (from bottom to top) as functions of time in the linear and logarithmic scales. Lower-left panel: Occupation dynamics as a color map (dark blue $=0$, bright yellow $=1$). Lower-right panel: Total number of the depleted particles normalized to $\overline{n}$ for different positions of the weak link; see text. Parameters are $L=20$ (periodic boundary conditions), $g/J=4$, and $\gamma =0.1$. Average over 1000 trajectories.