Many-body out-of-equilibrium dynamics of hard-core lattice bosons with nonlocal loss

We explore the dynamics of hard-core lattice bosons in the presence of strong nonlocal particle loss. The evolution occurs on two distinct time scales, first a rapid strongly correlated decay into a highly degenerate Zeno state subspace, followed by a slow almost coherent evolution. We analytically solve the fast initial dynamics of the system, where we specifically focus on an initial Mott insulator state, and perform an analysis of the particle arrangements in the Zeno subspace. We investigate the secondary slow relaxation process that follows and find an intricate regime where the competition between dissipation and coherence results in various types of interacting particle complexes. We classify them and analyze their spectral properties in the presence and absence of nearest-neighbor interactions. Under certain circumstances the dispersion relations of the complexes feature flat bands, which are a result of an effective spin-orbit coupling.

Figure 1

(a) Evolution of the boson density $p\left(t\right)$ under the dissipative dynamics ${\mathcal{L}}_d$ from an initial Mott insulator. The stationary density is $p(t\to \infty )=e^{-2}\approx 0.14$. The inset shows a single trajectory with 40 bosons with $R=3$ and periodic boundary conditions. For this particular trajectory 16 jumps (loss processes) occur, such that the final state contains solely eight bosons. (b) Representative boson arrangements in the stationary state with $R=3$, where single free bosons and two types of particle complexes can emerge. The circles indicate sites, a filled circle indicates an occupied site, a cross indicates a site whose occupation is forbidden, as the resulting configuration would not lie in the Zeno subspace, and a box indicates the “size” of a complex. The type I complex—defined as having a size smaller than $R$—is, in this example, constituted of two bosons. These bosons are unable to tunnel away from each other without running into a forbidden site which leads to an effective binding. The type II complex has a spatial extent that is larger than $R$. It is qualitatively different to type I in the sense that the removal of one boson (in the center) destroys the binding for the remaining ones. (c) Probability distributions for single bosons, type I and type II complexes in the stationary state that is reached from a Mott insulator for the cases of $R=3,12$. The relative abundances of the species change once $R$ becomes comparable to the mean interparticle distance $e^2$ in the stationary state.

Figure 2

(a) Dispersion relations (solid curves) for type I complexes of two bosons with $R=3$ and $R=4$. Both cases show a crossing at $q_K=\pi$, and when $R=4$ a flat band occurs. In the presence of nearest neighbor interactions (here $V=J$) the degeneracy is lifted and the flat bands are distorted (dashed curves). The sketches above the panels show a particular internal state of the respective complex. (b) Evolution of the boson density of a type I complex formed by two bosons in the state $|F_j^{\left(\mathrm{I}\right)}\rangle$ with $R=4$ (see sketch above the panel) and $\gamma =100J$ on a lattice of 10 sites simulated with the full master equation.

Figure 3

(a) Evolution of boson density for a type II complex in the immobile state $|F_3^{\left(\mathrm{II}\right)}\rangle$, with $R=3$ and $\gamma =100J$. (b) Dispersion relation for a type II complex consisting of four bosons with $R=4$.

Figure 4

(a) Evolution of the boson density for a single boson impinging an immobile type II complex ($R=2$). The single boson is in the wave packet state $|G\rangle$ with initial central quasimomentum of $q_0=\pi /2$ and width $\sigma =2$. The two-particle loss rate is $\gamma =100J$. The single boson is reflected elastically off the type II complex due to the presence of an effective next nearest neighbor exclusion interaction. (b) We show three examples of two type I complexes, in different internal states, interacting with one another. We see that the distance of the interaction depends on the internal state of the complexes.