Out-of-equilibrium states and quasi-many-body localization in polar lattice gases

The absence of energy dissipation leads to an intriguing out-of-equilibrium dynamics for ultracold polar gases in optical lattices, characterized by the formation of dynamically bound on-site and inter-site clusters of two or more particles, and by an effective blockade repulsion. These effects combined with the controlled preparation of initial states available in cold-gas experiments can be employed to create interesting out-of-equilibrium states. These include quasiequilibrated effectively repulsive 1D gases for attractive dipolar interactions and dynamically bound crystals. Furthermore, nonequilibrium polar lattice gases can offer a promising scenario for the study of quasi-many-body localization in the absence of quenched disorder. This fascinating out-of-equilibrium dynamics for ultracold polar gases in optical lattices may be accessible in on-going experiments.

Figure 1

(a) A dimerized lattice can be used to create a gas of singlons and dynamically bound NN dimers; (b) due to the BR a NN dimer (singlon) forms a block $D\equiv 0011$ ($S\equiv 001$); (c) effective lattice formed by the blocks D, S, and additional empty sites. This effective lattice is employed in model (2) to show the realization of quasi-MBL.

Figure 2

(a) Energy spectrum as a function of the center-of-mass quasimomentum $K$ for two particles in 40 sites for $U=0$ and $V=-100J$; density of the bound states as a function of the relative coordinate $r$ for the three bound states at $K=0$, as marked by the blue circles in panel (a), at energies $E/J\approx -5$ (b), $-13$ (c), and $-100$ (d).

Figure 3

(a) Dynamically bound crystal: density $\langle n_i\rangle$ (obtained using t-DMRG) for $U=0$ and $V=-100J$ ($r_c=2$), for 4 particles in 24 sites initially placed $r_{\mathrm{in}}=3$ sites apart. Note that since $r_{\mathrm{in}}=r_c+1$, there is still some residual dynamics. For smaller $r_{\mathrm{in}}\le r_c$ the crystal is perfectly preserved in this time scale. (b)–(c) Effective repulsive 1D gas: same parameters as in panel (a) but $r_{\mathrm{in}}=5$: (b) $g_2(t,r>0)$ at different times (in the inset we show $g_2(t,r=0)$ [42]) and (c) ${\overline{g}}_1\left(r\right)$, for $J(t_2-t_1)=5$ and different $t_2$ values. For both ${\overline{g}}_1$ and $g_2, r$ denotes the distance from an initially occupied site. Note that not only the on-site density and density fluctuations converge to quasiequilibrium, but also ${\overline{g}}_1$ and $g_2$ at longer distances. Note as well that $g_2(t,0<r\le r_c)=0$ due to BR.

Figure 4

Inhomogeneity $\mathrm{\Delta }N\left(t\right)$ as a function of $\mathrm{\Omega }t$ for $\mathrm{\Omega }/J=0.013$, for $(n_D,n_S,L)=(2,2,20)$ (dashed blue) and $(3,3,27)$ (solid red). The results are obtained by exact diagonalization averaging over 50 and 25 random initial conditions, respectively. The shaded region indicates approximately the region of fast decay due to quasiresonances. We depict for comparison the results for $(3,3,27)$ for $\mathrm{\Omega }/J=0.13$ (dotted pink). The inset shows the IPR for $(3,3,27)$ for $\mathrm{\Omega }/J=0.013$ (solid red) and $\mathrm{\Omega }/J=0.13$ (dotted pink).