Antibunching in locally driven dissipative Lieb lattices

TL;DR

This work addresses how to generate quantum correlations, specifically antibunching, in open quantum lattices by using localized driving in driven-dissipative Bose-Hubbard models arranged on Lieb geometries. It leverages the positive-P stochastic method to solve the master equation exactly for extended lattices, optimizing parameters to maximize antibunching on selected sites while maintaining measurable occupations and significant $g^{(2)}(τ)$ oscillations. The results show UPB-like interference can produce strong antibunching on target B sites in 3-site and quasi-1D Lieb lattices, with larger structures increasing the oscillation period and reducing peak antibunching drawbacks, and with background driving further enhancing observability. The findings offer a practical pathway to realize nontrivial quantum correlations in polariton micropillar experiments, even when the interaction-to-dissipation ratio is modest, and open avenues for engineering interference-based quantum states in open quantum lattices.

Abstract

In Lieb lattices, geometric frustration and destructive interference of hopping cancels the occupation of certain sites, leading to flat-band physics. Here, we show numerically how, in the driven-dissipative Bose-Hubbard (DDBH) model arranged into Lieb lattices and related geometries, specific localised driving schemes can repurpose this interference to generate enhanced antibunching via a mechanism similar to the so-called unconventional photon blockade. Stochastic simulations using the positive-P method allow us to calculate occupations and second order correlations exactly for extended lattices. We use this to optimise the parameters for the possible observation of this effect in polariton micropillar experiments. This work demonstrates the possibility of using localised driving and interference effects to generate non-trivial quantum correlations in open quantum lattice systems.

Figures (17)

• Figure 1: Diagram of a single Lieb lattice unit cell, equivalent to a 3 site 1D chain with open boundaries. Local dissipation $\gamma$ occurs equally at all sites, but a coherent drive $F$ is applied only to the $C$ site, with hopping $J$ between neighbouring sites allowing occupation to then spread to other sites in the lattice.
• Figure 2: Analytical values of optimal parameters for antibunching on central site of three site DDBH chain, calculated in the weak driving limit, across orders of magnitude in $U$. Left panel: optimal detuning $\Delta_{opt}$. Right panel: optimal hopping strength $J_{opt}$.
• Figure 3: Second order correlations $g^{(2)}_j(\tau)$ on the $B$ site using optimised parameters $\Delta = -0.28\gamma$, $U = 0.1\gamma$, $J = 2.775\gamma$, for two different values of the coherent drive $F$ applied to site $C$. Note that in both cases, $g^{(2)}_j(\tau)$ for sites $A$ and $C$ are approximately equal at all $\tau$.
• Figure 4: 5 site chain driven locally at central site. (a) Diagram of the structure, which we label using the conventions of the Lieb lattice. (b) Second order correlations $g^{(2)}_j(\tau)$ on the two $B$ sites for $\Delta = -0.2\gamma$, $U = 0.1\gamma$, $J = F = 1.5\gamma$; due to the symmetry, results are approximately equal for both $B$ sites.
• Figure 5: Diagram of locally driven quasi-1D Lieb lattice of 5 unit cells with smooth edges, i.e. there is no $A$ site on the final unit cell, with open boundary conditions. Coherent drive is applied only to site $3C$. The site $3B$, highlighted in green, achieves strong antibunching in $g^{(2)}(0)$ due to interference effects.