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Self-organized criticality emerges in dynamical complex systems driven out of equilibrium, and characterizes a wide range of classical phenomena in physics, geology and biology. However, for decades now, it remains a fundamental open question whether this broad property also finds a place in the quantum regime. In the talk, we shall present the first example of quantum self-organized criticality, emerging from quantum fluctuations and controlled by quantum coherence. We shall introduce a many-body quantum-coherently driven nanophotonic system where heavy photons interact in the presence of active nonlinearities. In this system, we shall show how quantum self-organized criticality emerges in an inherently new type of light localization, arising from two first-order phase transitions and being robust to dissipation, fluctuations and many-body interactions. The observed localization exhibits emergence of scale-invariant power laws and absence of finely-tuned control parameters. In analogy with the regime of quantum criticality at Tc = 0 in equilibrium static systems, we find that for our nonequilibrium dynamical system there exists a range of parameters for which the effective critical ‘temperature’ drops to zero, at which point we enter a fundamentally new regime of phase transitions – the quantum self-organized critical regime. We shall also approach the problem from a thermodynamic and information-theory perspective, deriving the multidimensional-state-vector Fokker-Planck (FP) equation for the distribution function of our problem, applying the maximum information entropy principle to make unbiased estimates on the probability distribution of microscopic states of our active nanosystem, and finally determining and analyzing the information gain and efficiency of the complex nanosystem close to its critical points.
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