Strong correlations in lossy one-dimensional quantum gases: From the quantum Zeno effect to the generalized Gibbs ensemble

We consider strong two-body losses in bosonic gases trapped in one-dimensional optical lattices. We exploit the separation of timescales typical of a system in the many-body quantum Zeno regime to establish a connection with the theory of the time-dependent generalized Gibbs ensemble. Our main result is a simple set of rate equations that capture the simultaneous action of coherent evolution and two-body losses. This treatment gives an accurate description of the dynamics of a gas prepared in a Mott insulating state and shows that its long-time behavior deviates significantly from mean-field analyses. The possibility of observing our predictions in an experiment with ${}^{174}\mathrm{Yb}$ in a metastable state is also discussed.

Figure 1

Time evolution of the number of atoms according to the rate equations (5) for the initial state ${\rho }_0$ (dashed red line). We take $U/J=20$ and $U/\left(\hslash {\gamma }_{2\mathrm{B}}\right)=1.33$ as in ${}^{174}\mathrm{Yb}$. Our result is benchmarked with simulations based on quantum trajectories for $L=10$, 12, and 14 (each point is averaged over ${10}^4$ trajectories and the associated statistical error bars are shown only for some points to increase readability). The dot-dashed black line represents the mean-field solution $N\left(t\right)/L$ in Eq. (3). The inset highlights the different long-time decay as $t^{-1}$ for the mean-field solution and as $t^{-1/2}$ for the rate equation.

Figure 2

Fermionic (left) and bosonic (right) quasimomentum distributions. Dashed lines are the predictions using the rate equation. Data from quantum-trajectory simulations for $L=14$ (symbols) are presented for two times.

Figure 3

Decay of atom number for lattice Tonks-Girardeau gases with density $\overline{n}\le 1$. The various curves are calculated according to the rate equations (5) for different initial conditions. The initial state is taken to be a lattice Tonks-Girardeau gas with $n_k(t=0)$ given by the Fermi-Dirac distribution at zero temperature with mean density $\overline{n}$.