Abstract:
A system of coupled photonic cavities on a two-dimensional square lattice is systematically investigated using the stochastic series expansion quantum Monte Carlo method. The ground state phase diagram contains insulating phases with integer polariton densities surrounded by a superfluid phase. The finite-size scaling of the superfluid density is used to determine the phase boundaries accurately. We find that the critical behavior is that of the generic, density-driven Mott-superfluid transition with dynamic exponent $z=2$, with no special multicritical points with $z=1$ at the tips of the insulating-phase lobes (as exist in the case of the Bose-Hubbard model). This demonstrates a limitation of the description of polaritons as structureless bosons.

Abstract:
An extreme type II superconductor with internal insulating regions, namely cavities, is studied here. We find that the cavity-bearing superconductor has lower energy than the defect-free superconductor above a critical magnetic induction $B^*$ for insulating cavities but not for metallic ones. Using a numerical approach for the Ginzburg-Landau theory we compute and compare free energy densities for several cavity radii and at least for two cavity densities, assuming a cubic lattice of spherical cavities.

Abstract:
The experimental observation of quantum phenomena in strongly correlated many particle systems is difficult because of the short length- and timescales involved. Obtaining at the same time detailed control of individual constituents appears even more challenging and thus to date inhibits employing such systems as quantum computing devices. Substantial progress to overcome these problems has been achieved with cold atoms in optical lattices, where a detailed control of collective properties is feasible but it is very difficult to address and hence control or measure individual sites. Here we show, that polaritons, combined atom and photon excitations, in an array of cavities such as a photonic crystal or coupled toroidal micro-cavities, can form a strongly interacting many body system, where individual particles can be controlled and measured. All individual building blocks of the proposed setting have already been experimentally realised, thus demonstrating the potential of this device as a quantum simulator. With the possibility to create attractive on-site potentials the scheme allows for the creation of highly entangled states and a phase with particles much more delocalised than in superfluids.

Abstract:
We develop an analytical approach for calculating the scattering and bound states of two polaritons in a one-dimensional (1D) infinite array of coupled cavities, with each cavity coupled to a two-level system (TLS). In particular, we find that in such a system a contact interaction between two polaritons is induced by the nonlinearity of the Jaynes-Cummigs Hamiltonian. Using our approach we solve the two-polariton problem with zero center-of-mass momentum, and find 1D resonances. Our results are relevant to the transport of two polaritons, and are helpful for the investigation of many-body physics in a dilute gas of polaritons in a 1D cavity array.

Abstract:
We formulate a scattering theory to study magnetic films in microwave cavities beyond the independent-spin and rotating wave approximations of the Tavis-Cummings model. We demonstrate that strong coupling can be realized not only for the ferromagnetic resonance (FMR) mode, but also for spin wave resonances (SWRs); the coupling strengths are mode dependent and decrease with increasing mode index. The strong coupling regime can be also accessed electrically by spin pumping into a metal contact.

Abstract:
Glassy behavior is a generic feature of electrons close to disorder-driven metal-insulator transitions. Deep in the insulating phase, electrons are tightly bound to impurities, and thus classical models for electron glasses have long been used. As the metallic phase is approached, quantum fluctuations become more important, as they control the electronic mobility. In this paper we review recent work that used extended dynamical mean-field approaches to discuss the influence of such quantum fluctuations on the glassy behavior of electrons, and examine how the stability of the glassy phase is affected by the Anderson and the Mott mechanisms of localization.

Abstract:
The authors show clear experimental evidence of lasing of exciton polaritons confined in L3 photonic crystal cavities. The samples are based on an InP membrane in air containing five InAsP quantum wells. Polariton lasing is observed with thresholds as low as 120 nW, below the Mott transition, while conventional photon lasing is observed for a pumping power one to three orders of magnitude higher.

Abstract:
We investigate a chain of superconducting stripline resonators, each interacting with a transmon qubit, that are capacitively coupled in a row. We show that the dynamics of this system can be described by a Bose-Hubbard Hamiltonian with attractive interactions for polaritons, superpositions of photons and qubit excitations. This setup we envisage constitutes one of the first platforms where all technological components that are needed to experimentally study chains of strongly interacting polaritons have already been realized. By driving the first stripline resonator with a microwave source and detecting the output field of the last stripline resonator one can spectroscopically probe properties of the system in the driven dissipative regime. We calculate the stationary polariton density and density-density correlations $g^{(2)}$ for the last cavity which can be measured via the output field. Our results display a transition from a coherent to a quantum field as the ratio of on site interactions to driving strength is increased.

Abstract:
Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations.

Abstract:
We propose a scheme which can realize an extended two-component Bose-Hubbard model using polaritons confined in an array of optical cavities. In addition to the density-dependent interactions, this model also contains nonlinear coupling terms between the two components of the polariton. Using a mean-field calculation, we obtain the phase diagram which shows how these terms affect the transition between the Mott insulator and the superfluid phase. In addition, we employ both a perturbation approach and an exact diagonalization method to gain more insights into the phase diagram.