Dissipation-induced mobility and coherence in frustrated lattices

In quantum lattice systems with geometric frustration, particles cannot move coherently due to destructive interference between tunneling processes. Here we show that purely local, Markovian dissipation can induce mobility and long-range first-order coherence in frustrated lattice systems that is entirely generated by incoherent processes. Interactions reduce the coherences and mobility but do not destroy them. These effects are observable in experimental implementations of driven-dissipative lattices with a flat band and nonuniform dissipation.

Figure 1

The lattice with tunneling rates $t$ and $t^{\prime }$ along with the labeling of the A and B sublattices and the unit cell $i$. Excitations dissipate at a rate ${\gamma }_{A\left(B\right)}$ from the individual sites of the A (B) sublattice and coherent or incoherent drives are applied with amplitude ${\mathrm{\Omega }}_{X,i}$ or intensity $P_{X,i}$ ($X=A,B$).

Figure 2

The noninteracting regime. (a) Normalized steady-state density of excitations in the Wannier basis for a coherent drive with ${\mathrm{\Omega }}_W={\gamma }_A$ at Wannier state $i=0$. (b) Normalized steady-state density for the B sublattice. (c) Normalized steady-state density for an incoherent pump with $P_{B,0}={\gamma }_A/100$ at $i=0$.

Figure 3

Decay length of the density profile $\xi$ as a function of $\kappa$ for direct coupling (dot-dashed), effective drive (dashed), and exact (solid line) calculations, where the Wannier state $W_0$ is driven coherently with ${\mathrm{\Omega }}_W={\gamma }_A$.

Figure 4

Spatial coherences in the steady state $g^{\left(1\right)}(j,l)$ for an incoherent pump at $i=0$ with $P_{B,0}={\gamma }_A/100$ and $\kappa =0.1$.

Figure 5

Diagrammatic representations of the models used to explain dissipation-induced mobility in the noninteracting regime. The central site is pumped with a drive of strength ${\mathrm{\Omega }}_{W,0}$ and there is a dissipation rate ${\gamma }_0$ for each site. (a) The single-site diffusion model assumes that only tunneling between neighboring sites is important. (b) The direct nonlocal dissipative coupling model, where the density on each site is modeled by a two-site model consisting of the relevant site and the pumped site coupled by the nonlocal dissipation term. (c) The effective drive model consists of a three-site model where the pumped site is not affected by the two remote, coupled, unpumped sites.

Figure 6

(a) Normalized steady-state density of excitations in the Wannier basis for the interacting regime and a single driven Wannier state at $i=0$, ${\mathrm{\Omega }}_{W,0}={\gamma }_A$, and $\kappa =0.2$ [cf. Fig. 2]. (b) Fraction of excitations not on the pumped site $f$ as a function of the dissipation rate asymmetry ratio $\kappa$ for an interacting system with a cross-Kerr interaction strength $U_1$.

Figure 7

Spatial coherences in the steady state $g^{\left(1\right)}(j,l)$ for a coherent drive at $i=0$ with ${\mathrm{\Omega }}_W={\gamma }_A$ and $\kappa =0.1$ in the strongly interacting regime with $U_1=100$.

Figure 8

The absolute value of the nonlocal dissipation coefficients $\left|f_j\left(a\right)\right|$ where $a={(2J/g)}^2$ is proportional to the ratio of the couplings of the A sublattice to the B and the C sublattices. For $a=2.0$, the couplings are identical to the results from the sawtooth lattice.

Figure 9

Second-order correlation function for the pumped site $\langle W_0^{†}{W}_0^{†}{W}_0{W}_0\rangle$ (on a logarithmic scale) with coherent and incoherent transfer processes set to zero. This provides an upper bound on the probability that a site is occupied by multiple excitations.