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arXiv:1512.04868 · Physical Review A

Probing photon correlations in the dark sites of geometrically frustrated cavity lattices

Wim Casteels, R. Rota, Florent Storme, Cristiano Ciuti

Published Apr 19, 2016• 31 citations
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Abstract

We explore theoretically the driven-dissipative physics of geometrically frustrated lattices of cavity resonators with relatively weak nonlinearities, i.e., a photon-photon interaction smaller than the loss rate. In such systems, photon modes with zero probability at dark sites are present at the single-particle level due to interference effects. In particular, we study the behavior of a cell with three coupled resonators as well as extended Lieb lattices in one and two dimensions. By considering a partial pumping scheme, with the driving field not applied to the dark sites, we predict that even in the presence of relatively weak photon-photon interactions the nominally dark sites achieve a finite photonic population with strong correlations. We show that this is a consequence of biphoton and multiphoton states that in the absence of frustration would not be visible in the observables.

DOI
10.1103/physreva.93.043833

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We explore theoretically the driven-dissipative physics of geometrically frustrated lattices of cavity resonators with relatively weak nonlinearities, i.e., a photon-photon interaction smaller than the loss rate. In such systems, photon modes with zero probability at dark sites are present at the single-particle level due to interference effects. In particular, we study the behavior of a cell with three coupled resonators as well as extended Lieb lattices in one and two dimensions. By considering a partial pumping scheme, with the driving field not applied to the dark sites, we predict that even in the presence of relatively weak photon-photon interactions the nominally dark sites achieve a finite photonic population with strong correlations. We show that this is a consequence of biphoton and multiphoton states that in the absence of frustration would not be visible in the observables.
We demonstrate how pump engineering drives the emergence of frustration-induced quasi-long-range order in a low-dimensional photonic cavity array. We consider a Lieb chain of nonlinear cavities as described by the Bose-Hubbard model and featuring a photonic flatband in the single-particle spectrum. Incoherent pumping of the Lieb lattice leads to a photonic density wave which manifests an algebraic decay of correlations with twice the period of the lattice unit cell. This work opens up other directions for the emergence of strongly correlated phases in quantum optical frustrated systems through pump design.
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In a recent work [Liew and Savona, Phys. Rev. Lett. 104, 183601 (2010)] it was numerically shown that a resonantly driven photonic ``molecule'' consisting of two coupled cavities can exhibit strong photon antibunching with a surprisingly weak Kerr nonlinearity. Here, we analytically identify the subtle quantum interference effect that is responsible for the predicted efficient photon blockade effect. We then extend the theory to the experimentally relevant Jaynes-Cummings system consisting of a single quantum emitter in a coupled-cavity structure and predict the strong antibunching even for single-atom cooperativity on the order of or smaller than unity. The potential of this quantum interference effect in the realization of strongly correlated photonic systems with only weak material nonlinearities is assessed by comparing on-site and inter-site correlations in a ring of three coupled photonic molecules.
We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the nonlinearity is much smaller than the losses, contrary to common expectations. Quantum correlations in this case arise from the interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize, in particular, two systems: a linear chain of three coupled cavities and an array of eight coupled cavities. We demonstrate the existence of a parameter range where the system emits photons with continuous-variable bipartite and quadripartite entanglement, in the case of the first and the second system, respectively. This entanglement is shown to survive realistic rates of pure dephasing and opens up a new perspective for the realization of quantum simulators or entangled photon sources without the challenging requirement of strong optical nonlinearities.
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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. Specifically, producing antibunching in the dark sites of the flat band system rather than the usual and less useful bunching.