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Theory of strongly correlated photonic systems

Final Report Summary - CORPHO (Theory of strongly correlated photonic systems)

CORPHO was a theoretical research ERC project devoted to the physics of strongly correlated photonic systems, such as lattices of coupled optical cavities with strong quantum nonlinearities (effective photon-photon interaction). Such systems can be realized in several physical platforms, including networks of superconducting microwave resonators with Josephson junction nonlinear quantum circuits, and lattices of semiconductor microcavities. These complex open quantum systems are sparking considerable interest for the generation of exotic quantum fluids of light, the study of dissipative quantum phase transitions, the realization of photonic quantum simulators, and also for photonic quantum information.

The project had the ambitious objective to develop methods to understand the many-body physics of such open quantum systems in the presence of external driving and dissipation. CORPHO delivered on this promise by developing original techniques (corner-space renormalization method, cluster techniques, and also variational neural-network approaches for open quantum systems). The developed numerical methods, together with analytical approaches, have been successfully applied to explore the physics of 1D and 2D strongly correlated photonic systems.

The project revealed fundamental peculiar correlation properties of photonic phases realized by coherent driving of lattices with geometric frustration and flat bands. CORPHO predicted how to realize dissipatively stabilized Mott insulator phases of photons under incoherent excitation. The project uncovered fundamental properties of dissipative phase transitions, including general properties of the steady state, the determination of critical exponents via finite-size scaling and the properties of individual quantum trajectories. The project studied also dynamical properties like the behavior of the asymptotic decay rate towards the steady state, the power-law behavior of dynamical hysteresis, the role of lattice dimensionality on critical slowing down and the impact of disorder. Moreover, CORPHO also pioneered strongly correlated photonic systems in the presence of two-photon driving and dissipation, which can be realized via “reservoir engineering”. In the case of a single cavity, this kind of quadratic driving approximately confines the dynamics of the photonic state to a two-dimensional Hilbert space, creating an effective spin system that is used for the realization of photonic qubits. The methods developed in the project allowed us to study lattices of such photonic qubits, showing that they act as photonic quantum simulators of magnetic quantum critical phenomena.

Remarkably, some of the predicted phenomena have been already observed experimentally by international groups working in this emerging field, which has grown considerably during the execution of the project.