Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice

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.Comment: 5 pages,3 figures. High resolution figures available upon reques

P-band in a rotating optical lattice

We investigate the effects of rotation on the excited bands of a tight binding lattice, focusing particulary on the first excited (p-) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a non-trivial splitting and magnetic fine structure of the p-band. We show that Peierls substitution can be modified to describe p-band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p-band can be investigated starting from this effective Hamiltonian.Comment: 7 pages, 4 figures, new discussion of effective Hamiltonian, references adde

Fractional quantum Hall states of photons in an array of dissipative coupled cavities

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 non-equilibrium 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.Comment: 6 pages including the Supplemental Material (accepted for publication in Phys. Rev. Lett.

Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator

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 St\v{r}eda formula.Comment: 4 pages, 4 figure

Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field

Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using gauge fields created by magnetic fields or spin orbit interactions which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created which are strong enough to realize the Harper-Hofstadter model. Despite many proposals and major experimental efforts, so far it has not been possible to prepare the ground state of this system. Here we report the observation of Bose-Einstein condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution on the wavefuction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.Comment: 6 pages, 5 figures. Supplement: 6 pages, 4 figure

Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering

Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic magnetic flux, which in combination with dissipative coupling to the mechanical bath, leads to nonreciprocal transport of photons with 35dB of isolation. Additionally, optical pumping with blue-detuned light manifests as a particle non-conserving interaction between photons and phonons, resulting in directional optical amplification of 12dB in the isolator through direction. These results indicate the feasibility of utilizing optomechanical circuits to create a more general class of nonreciprocal optical devices, and further, to enable novel topological phases for both light and sound on a microchip.Comment: 18 pages, 8 figures, 4 appendice

Out-of-equilibrium physics in driven dissipative coupled resonator arrays

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.Comment: Chapter that appeared in "Quantum Simulations with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics" edited by D.G.Angelakis, Quantum Science and Technology Series, Springer 201

Topological Photonics

Topology is revolutionizing photonics, bringing with it new theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, new optical mirrors of different wave-vector space topologies have been constructed to support new states of light propagating at their interfaces. These novel waveguides allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights the major findings in photonic crystals, coupled resonators, metamaterials and quasicrystals.Comment: progress and review of an emerging field, 12 pages, 6 figures and 1 tabl