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Preface; Contents; Introduction; 1 Strongly Correlated Polaritons in Nonlinear Cavity Arrays; 1.1 Introduction; 1.2 Modelling of Nonlinear Cavity-Arrays; 1.2.1 Effective Photon-Photon Interaction in Nonlinear Cavities; 1.2.2 Photon-Mediated Coupling Between Nonlinear Cavities; 1.2.3 Photon-Induced Losses and Decoherence; 1.3 Equilibrium Phase Diagram of Cavity-Array Models; 1.3.1 The Mott-Insulator
Superfluid Quantum Phase Transition; 1.3.2 Vanishing Photon Hopping Amplitude; 1.3.3 Finite Photon Hopping Amplitude; 1.4 Nonequilibrium Dynamics of Cavity-Array Models.
1.4.1 Nonequilibrium Signatures of the Equilibrium Phase Diagram1.4.2 Liouvillian Engineering and Driven-Dissipative Dynamics; References; 2 Phase Diagram and Excitations of the Jaynes-Cummings-Hubbard Model; 2.1 Introduction; 2.2 Degenerate Perturbation Theory; 2.3 Greens Function Approach; 2.4 Slave-Boson Approach; 2.4.1 Slave-Boson Formulation; 2.4.2 Gutzwiller Ansatz; 2.4.3 Quadratic Fluctuations; 2.5 Critical Exponents; 2.6 Relation to the Dicke Model; References; 3 Out-of-Equilibrium Physics in Driven Dissipative Photonic Resonator Arrays; 3.1 Introduction; 3.2 Modelling CRAs.
3.3 Computing the Properties of CRAs3.4 Non-equilibrium Many-Body Phases of Photons in CRAs; 3.4.1 Jaynes-Cummings Versus Kerr-Nonlinear Resonator; 3.4.2 Photon Super-Bunching; 3.4.3 Localisation-Delocalisation Transition of Photons; 3.4.4 Fermionisation of Hardcore Photons; 3.4.5 Polariton Crystallisation; 3.4.6 Phases in 2D Arrays; 3.4.7 Quantum Hall Physics with Light; 3.4.8 Other Works; 3.5 Summary and Outlook; References; 4 Topological Physics with Photons; 4.1 Introduction; 4.2 Gauge Field and Topological Features in Noninteracting Photonic System.
4.2.1 Magneto-Optic Effects and MW Experiment4.2.2 Synthetic Gauge Field in Coupled Resonators ; 4.2.3 Other Approaches: Helical Waveguides, Polarization Scheme, Modulation; 4.3 Interacting Photons and Many-Body Regime ; 4.3.1 Strong Kerr Nonlinearity and Laughlin State of Light; 4.3.2 Three-Body Interaction and Pfaffian States of Light; 4.4 Outlook; References; 5 Exciton-Polariton Quantum Simulators; 5.1 Introduction; 5.1.1 Digital and Analog Quantum Simulators; 5.1.2 Photonic Analog Quantum Simulators; 5.2 Hardware of Exciton-Polariton Quantum Simulators.
5.2.1 Particle:Exciton-Polariton Condensates5.2.2 Lattice: Photonic and Excitonic Lattices; 5.2.3 Probes: Photoluminescence; 5.3 Software of Exciton-Polariton Analog Quantum Simulators; 5.3.1 Single-Particle Physics; 5.3.2 Many-Particle Physics; 5.4 Exciton-Polaritons in Two-Dimensional Lattices; 5.4.1 Experiment; 5.4.2 Bosonic Orbital Order; 5.4.3 Degenerate High-Orbital Condensates; 5.5 Outlook; References; 6 Strongly Correlated Photons in Nonlinear Nanophotonic Platforms; 6.1 Introduction; 6.2 Nanophotonic Platforms: Light Propagation and Confinement.
Superfluid Quantum Phase Transition; 1.3.2 Vanishing Photon Hopping Amplitude; 1.3.3 Finite Photon Hopping Amplitude; 1.4 Nonequilibrium Dynamics of Cavity-Array Models.
1.4.1 Nonequilibrium Signatures of the Equilibrium Phase Diagram1.4.2 Liouvillian Engineering and Driven-Dissipative Dynamics; References; 2 Phase Diagram and Excitations of the Jaynes-Cummings-Hubbard Model; 2.1 Introduction; 2.2 Degenerate Perturbation Theory; 2.3 Greens Function Approach; 2.4 Slave-Boson Approach; 2.4.1 Slave-Boson Formulation; 2.4.2 Gutzwiller Ansatz; 2.4.3 Quadratic Fluctuations; 2.5 Critical Exponents; 2.6 Relation to the Dicke Model; References; 3 Out-of-Equilibrium Physics in Driven Dissipative Photonic Resonator Arrays; 3.1 Introduction; 3.2 Modelling CRAs.
3.3 Computing the Properties of CRAs3.4 Non-equilibrium Many-Body Phases of Photons in CRAs; 3.4.1 Jaynes-Cummings Versus Kerr-Nonlinear Resonator; 3.4.2 Photon Super-Bunching; 3.4.3 Localisation-Delocalisation Transition of Photons; 3.4.4 Fermionisation of Hardcore Photons; 3.4.5 Polariton Crystallisation; 3.4.6 Phases in 2D Arrays; 3.4.7 Quantum Hall Physics with Light; 3.4.8 Other Works; 3.5 Summary and Outlook; References; 4 Topological Physics with Photons; 4.1 Introduction; 4.2 Gauge Field and Topological Features in Noninteracting Photonic System.
4.2.1 Magneto-Optic Effects and MW Experiment4.2.2 Synthetic Gauge Field in Coupled Resonators ; 4.2.3 Other Approaches: Helical Waveguides, Polarization Scheme, Modulation; 4.3 Interacting Photons and Many-Body Regime ; 4.3.1 Strong Kerr Nonlinearity and Laughlin State of Light; 4.3.2 Three-Body Interaction and Pfaffian States of Light; 4.4 Outlook; References; 5 Exciton-Polariton Quantum Simulators; 5.1 Introduction; 5.1.1 Digital and Analog Quantum Simulators; 5.1.2 Photonic Analog Quantum Simulators; 5.2 Hardware of Exciton-Polariton Quantum Simulators.
5.2.1 Particle:Exciton-Polariton Condensates5.2.2 Lattice: Photonic and Excitonic Lattices; 5.2.3 Probes: Photoluminescence; 5.3 Software of Exciton-Polariton Analog Quantum Simulators; 5.3.1 Single-Particle Physics; 5.3.2 Many-Particle Physics; 5.4 Exciton-Polaritons in Two-Dimensional Lattices; 5.4.1 Experiment; 5.4.2 Bosonic Orbital Order; 5.4.3 Degenerate High-Orbital Condensates; 5.5 Outlook; References; 6 Strongly Correlated Photons in Nonlinear Nanophotonic Platforms; 6.1 Introduction; 6.2 Nanophotonic Platforms: Light Propagation and Confinement.