The quantum-optical Josephson interferometer

The photon-blockade effect, where nonlinearities at the single-photon level alter the quantum statistics of light emitted from a cavity1, has been observed in cavity quantum electrodynamics experiments with atomic2,3 and solid-state systems4–8. Motivated by the success of single-cavity quantum electrodynamics experiments, the focus has recently shifted to the exploration of the rich physics promised by strongly correlated quantum-optical systems in multicavity and extended photonic media9–14. Even though most cavity quantum electrodynamics structures are inherently dissipative, most of the early work on strongly correlated photonic systems has assumed cavity structures where losses are essentially negligible. Here we investigate a dissipative quantum-optical system that consists of two coherently driven linear optical cavities connected through a central cavity with a single-photon nonlinearity (an optical analogue of the Josephson interferometer). The interplay of tunnelling and interactions is analysed in the steady state of the system, when a dynamical equilibrium between driving and losses is established. Strong photonic correlations can be identified through the suppression of Josephson-like oscillations of the light emitted from the central cavity as the nonlinearity is increased. In the limit of a single nonlinear cavity coupled to two linear waveguides, we show that photon-correlation measurements would provide a unique probe of the crossover to the strongly correlated regime. We investigate an optical analogue of the superconducting Josephson interferometer, which we name the quantum-optical Josephson interferometer, revealing new features due to the genuine non-equilibrium interplay of coherent tunnelling and on-site interactions. We consider two variants of the proposed device with a central nonlinear cavity coupled to two external driving lasers through either two side cavities (Fig. 1a,b) or two waveguides (Fig. 1d). The three-cavity system can be generalized to anN -cavity system with a central nonlinear one14 (Fig. 1c), and in the limiting case of very large N this reduces to the single cavity coupled to two side waveguides (Fig. 1d). In both cases, the coupling to the side cavities (or waveguides) is a consequence of photon tunnelling. We assume the central cavity to have a sizable single-photon nonlinearity, for example due to some radiation–matter interaction, be it Jaynes–Cummings-type interaction (with a single atom or quantum dot in the central cavity)15, giant Kerr nonlinearity1 or confined polariton interaction (for example with a quantum well embedded in the cavity)16. Themodel discussed here is fairly general and can be realized in a variety of quantum-optical systems. In the following we show that the light emitted from the central cavity reflects the interplay of two competing effects, tunnelling and interactions. As the relative magnitude of the interaction parameter is varied with respect to the tunnelling strength, the system shows a crossover between a coherent and a strongly correlated regime. In the coherent regime, photons are delocalized over the three cavities and the emitted light strongly depends on the phase