Abstract
We characterize photonic transport in a boundary driven array of nonlinear optical cavities. We find that the output field suddenly drops when the chain length is increased beyond a threshold. After this threshold a highly chaotic and unstable regime emerges, which marks the onset of a super-diffusive photonic transport. We show the scaling of the threshold with pump intensity and nonlinearity. Finally, we address the competition of disorder and nonlinearity presenting a diffusive-insulator phase transition.
Highlights
The mean field analysis predicts the onset of an instability beyond a threshold chain length Nt, marking a crossover between ballistic and super-diffusive photonic transport along the B-H chain
We argue here that the ballistic regime is a consequence of finite-size effects, while the transport properties in the thermodynamic limit are those corresponding to the super-diffusive regime found in the present analysis
The fact that the crossover between the two regimes as a function of N is abrupt rather than gradual, can be ascribed to the strongly nonlinear character of the system under investigation. This feature plays an important role in view of the quest for dissipative phase transitions in photonic arrays
Summary
Arrays of optical nonlinear cavities have been a field of extensive research [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] since the low temperature analogy to condensed matter was established, suggesting the possibility of simulating the Mott-Superfluid phase transition [18, 19]. An experiment was carried out [24], reporting on indications of a driven-dissipative quantum phase transition and existence of bistable phases in a boundary driven array of circuit QED resonators This pioneering work opens up the possibility to experimentally address nonequilibrium transport of interacting photons that is currently at its infancy even on theoretical grounds [25, 26]. We show that, even though small systems may appear as stable ballistic conductors, there exists a “critical” chain length Nc, beyond which the system becomes chaotic This chaotic instability marks the onset of super-diffusive transport associated to power law scaling of the currents.
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