We propose and characterize solid-state photonic structures where light experiences an artificial gauge field. A non-trivial phase for photons tunneling between adjacent sites of a coupled cavity array can be obtained by inserting optically active materials in the structure or by inducing a suitable coupling of the propagation and polarization degrees of freedom. We also discuss the feasibility of observing strong gauge field effects in the optical spectra of realistic systems, including the Hofstadter butterfly spectrum.

We report a theoretical study of the collective optical response of a two-dimensional array of nonlinear cavities in the impenetrable photon regime under a strong artificial magnetic field. Taking advantage of the nonequilibrium nature of the photon gas, we propose an experimentally viable all-optical scheme to generate and detect strongly correlated photon states which are optical analogs of the Laughlin states of fractional quantum Hall physics.

We consider a gas of non-interacting spinless fermions in a rotating optical lattice and calculate the density profile of the gas in an external confinement potential. The density profile exhibits distinct plateaus, which correspond to gaps in the single particle spectrum known as the Hofstadter butterfly. The plateaus result from insulating behavior whenever the Fermi energy lies within a gap. We discuss the necessary conditions to realize the Hofstadter insulator in a cold atom setup and show how the quantized Hall conductance can be measured from density profiles using the Středa formula.Recently, some fundamental models of many-particle quantum systems have been experimentally realized using trapped ultra-cold fermions. Some of these experiments, such as transport in optical lattices [1], has demonstrated well known effects with improved precision, while others, such as spin imbalanced superfluidity [2,3], have provided access to previously unexplored regimes. With constantly improving experimental control over ultra-cold systems, it is expected that many other fundamental ideas can be tested in laboratory for the first time.A basic problem in quantum mechanics is the dynamics of a charged particle moving in a periodic potential under a magnetic field. The single particle spectrum depends sensitively on the ratio of the flux through a unit cell of the lattice to flux quantum. For a tight binding lattice, a single band splits into narrow magnetic bands, forming a self-similar energy spectrum known as the Hofstadter butterfly [4]. The gaps in the Hofstadter spectrum form continuous regions for a finite range of flux. For a system of non-interacting fermions, it was shown by Thouless et. al. that whenever the Fermi energy lies in one of these gaps, the Hall conductance of the system is quantized [5]. This quantization is topological in nature, and the quantized Hall conductance is determined uniquely by the magnetic translation symmetry [6]. This Hofstadter insulating phase is a topological insulator that can be characterized by the first Chern number.Despite its mathematical elegance, the Hofstadter insulator can hardly be achieved in solid state systems because the magnetic field needs to be thousands of Tesla in order to create a magnetic flux which can be comparable to one flux quantum per unit cell [9]. While in some experiments super-lattice structures have been used to study the splitting of Landau levels under a periodic potential, the tight-binding regime (strong magnetic field limit) has never been experimentally realized [10]. The main purpose of this Letter is to propose an alternative way to achieve and to experimentally study this topological insulator by using ultra-cold Fermi gases in a rotating optical lattice. We discuss (i) the conditions to realize the Hofstadter insulator in rotating optical lattices, and (ii) the manifestation of this insulator in real space density profile and the method to detect the Hall conductance in a cold atom setup.The Hamiltonian for a particle in a rotating latti...

We consider the Bose-Hubbard model in a two dimensional rotating optical lattice and investigate the consequences of the effective magnetic field created by rotation. Using a Gutzwiller type variational wavefunction, we find an analytical expression for the Mott insulator(MI)-Superfluid(SF) transition boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The dependence of phase boundary on the effective magnetic field is complex, reflecting the self-similar properties of the single particle energy spectrum. Finally, we argue that fractional quantum Hall phases exist close to the MI-SF transition boundaries, including MI states with particle densities greater than one.

We theoretically investigate a driven-dissipative model of strongly interacting photons in a nonlinear optical cavity in the presence of a synthetic magnetic field. We show the possibility of using a frequency-dependent incoherent pump to create a strongly-correlated ν = 1/2 bosonic Laughlin state of light: thanks to the incompressibility of the Laughlin state, fluctuations in the total particle number and excitation of edge modes can be tamed by imposing a suitable external potential profile for photons. We further propose angular momentum-selective spectroscopy of the emitted light as a tool to obtain unambiguous signatures of the microscopic physics of the quantum Hall liquid of light.