Out-of-Equilibrium Phase Transitions in Nonlinear Optical Systems

Abstract : In this thesis we theoretically study driven-dissipative nonlinear systems, whosedynamics is capture by a Lindblad master equation. In particular, we investigate theemergence of criticality in out-of-equilibrium dissipative systems. We present a generaland model-independent spectral theory relating first- and second-order dissipative phasetransitions to the spectral properties of the Liouvillian superoperator. In the critical region,we determine the general form of the steady-state density matrix and of the Liouvillianeigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We discuss the relevanceof individual quantum trajectories to unveil phase transitions. After these general results,we analyse the inset of criticality in several models. First, a nonlinear Kerr resonator in thepresence of both coherent (one-photon) and parametric (two-photon) driving and dissipation.We then explore the dynamical properties of the coherently-driven Bose-Hubbard and of thedissipative XYZ Heisenberg model presenting a first-order and a second-order dissipativephase transition, respectively. Finally, we investigate the physics of photonic Schrödingercat states in driven-dissipative resonators subject to engineered two-photon processes andone-photon losses. We propose and study a feedback protocol to generate a pure cat-likesteady state
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Fabrizio Minganti. Out-of-Equilibrium Phase Transitions in Nonlinear Optical Systems. Physics [physics]. Université Sorbonne Paris Cité, 2018. English. ⟨NNT : 2018USPCC004⟩. ⟨tel-02003919⟩

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