Abstract Artificially engineered light–matter systems constitute a novel, versatile architecture for the quantum simulation of driven, dissipative phase transitions and non-equilibrium quantum many-body systems. Here, we discuss recent experimental as well as theoretical works on the simulation of geometrical frustration in interacting photonic systems out of equilibrium. In particular, we review two recent discoveries at the interface of quantum optics and condensed matter physics: (i) the experimental achievement of Bosonic condensation into a flat energy band and (ii) the theoretical prediction of crystalline phases of light in a frustrated qubit-cavity array. We show that this new line of research leads to novel and unique tools for the experimental investigation of frustrated systems and holds the potential to create new phases of light and matter with interesting spatial structure.
Abstract Artificially engineered light–matter systems constitute a novel, versatile architecture for the quantum simulation of driven, dissipative phase transitions and non-equilibrium quantum many-body systems. Here, we discuss recent experimental as well as theoretical works on the simulation of geometrical frustration in interacting photonic systems out of equilibrium. In particular, we review two recent discoveries at the interface of quantum optics and condensed matter physics: (i) the experimental achievement of Bosonic condensation into a flat energy band and (ii) the theoretical prediction of crystalline phases of light in a frustrated qubit-cavity array. We show that this new line of research leads to novel and unique tools for the experimental investigation of frustrated systems and holds the potential to create new phases of light and matter with interesting spatial structure.
In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.
We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.
We study the interplay of geometric frustration and interactions in a nonequilibrium photonic lattice system exhibiting a polariton flat band as described by a variant of the Jaynes-Cummings-Hubbard model. We show how to engineer strong photonic correlations in such a driven, dissipative system by quenching the kinetic energy through frustration. This produces an incompressible state of photons characterized by short-ranged crystalline order with period doubling. The latter manifests itself in strong spatial correlations, i.e., on-site and nearest-neighbor antibunching combined with extended density-wave oscillations at larger distances. We propose a state-of-the-art circuit QED realization of our system, which is tunable in situ.
Geometric frustration is a phenomenon where local energy constraints cannot be simultaneously satisfied because of geometric reasons. This leads to a manifold of degenerate ground states in which ordering can be highly nontrivial and exotic phases of matter could emerge. In a kagome lattice, both interaction energies of spins and kinetic energies of particles can be frustrated. In the latter case, a single-particle band structure with a flat (dispersionless) energy band results.In this dissertation, we report our experimental studies of interacting bosonic systems in kagome lattices. Such studies are performed with a quantum simulator based on ultracold atoms in optical lattices. We describe upgrades and development of the apparatus that constructs optical kagome lattices in our experiment. We briefly discuss results of an experiment studying the Bose-Hubbard model in a trimerized kagome lattice. We then report the details of an experiment investigating the interplay of kinetic frustration and interactions by probing the band structure of an optical kagome lattice with interacting ultracold bosonic atoms. Finally, we propose experimental ideas for exploring the properties of the singular band touching point in the kagome flat band.
The main scope of this thesis is the investigation of quantum properties of nonlinear, dissipative, optical and condensed matter systems. Compared with previous studies on this subjects, we reached several milestone of general interests for the theoretical and experimental community. \nThe main experimental platform we refer to in this thesis is microcavity polaritons: polaritons arise from the coupling of light with excitons in a quantum well, i.e., a 2D semiconductor material embedded in the microcavity. They have attracted the interest of the scientific community for their rich physics. Polaritons can form out-of-equilibrium Bose-Einstein condensates, they can experience superfluid phase transition and, due to their interaction via the excitonic component, they show a variety of phenomena which are typical of nonlinear physics, such as bistability and parametric scattering. \nIn particular, motivated by recent proposals about the generation of single photons from weakly nonlinear system, like the unconventional photon blockade, and by the production of squeezed states in polariton systems, we studied the possibility of obtaining antibunched light and other quantum states (like squeezed states and entangled states), when the nonlinear system shows some peculiar features: in particular we consider polariton soliton and cascade systems. \nFinally, when considering nonlinear incoherent processes, we investigate the effect of the PT-symmetry and the PT-symmetry breaking on the quantum state of the emitted light. \nHence, this research work has two main objectives: first, from the fundamental physics point of view, to understand the interplay between nonlinear phenomena and quantum optics, second to provide useful tools for future technological applications. Specifically, for the latter case, we demonstrate a theorem that links the measurement of intensity correlations with the occurrence of certain phase transitions, and we propose a setup to maximize the non-classicality of the light emitted by weakly non-linear systems via a cascade configuration. \n \n \n