Status of This Memo This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited.

We introduce a generic bosonic model exemplifying that (spin) Meissner currents can persist in insulating phases of matter. We consider two species of interacting bosons on a lattice. Our model exhibits separation of charge (total density) and spin (relative density): the charge sector is gapped in a bosonic Mott insulator phase with total density one, while the spin sector remains superfluid due to interspecies conversion. Coupling the spin sector to the gauge fields yields a spin Meissner effect reflecting the long-range spin superfluid coherence. We investigate the resulting phase diagram and describe other possible spin phases of matter in the Mott regime possessing chiral currents as well as a spin-density wave phase. The model presented here is realizable in Josephson junction arrays and in cold atom experiments.

We introduce generic bosonic models exemplifying that chiral Meissner currents can persist in insulating phases of matter. We first consider interacting bosons on a two-leg ladder. The total density sector can be gapped in a bosonic Mott insulator at odd-integer filling, while the relative density sector remains superfluid due to interchain hopping. Coupling the relative density to gauge fields yields a pseudospin Meissner effect. We show that the same phase arises if the bosons are replaced by spinful fermions confined in Cooper pairs, and find a dual fermionic Mott insulator with spinon currents. We prove that by tuning the mean density the Mott insulator with Meissner currents turns into a low-dimensional bosonic ν = 1 2Laughlin state for strong enough repulsive interactions across the ladder rungs. We finally discuss extensions to multileg ladders and bilayers in which spinon superfluids with Meissner currents become possible. We propose two experimental realizations, one with ultracold atoms in the setup of Atala et al., Nat. Phys. 8, 588 (2014) and another with Josephson junction arrays. We also address a Bose-Fermi mixture subject to a magnetic field in connection with the pseudo-gap phase of high-Tc cuprates.

We theoretically investigate a photonic Kagome lattice which can be realized in microwave cavity arrays using current technology. The Kagome lattice exhibits an exotic band structure with three bands one of which can be made completely flat. The presence of artificial gauge fields allows to emulate topological phases and induce chiral edge modes which can coexist inside the energy gap with the flat band that is topologically trivial. By tuning the artificial fluxes or in the presence of disorder, the flat band can also acquire a bandwidth in energy allowing the coexistence between chiral edge modes and bulk extended states; in this case the chiral modes become fragile towards scattering into the bulk. The photonic system then exhibits equivalents of both a quantum Hall effect without Landau levels, and an anomalous Hall effect characterized by a non-quantized Chern number. We discuss experimental observables such as local density of states and edge currents. We show how synthetic uniform magnetic fields can be engineered, which allows an experimental probe of Landau levels in the photonic Kagome lattice. We then draw on semiclassical Boltzmann equations for transport to devise a method to measure Berry's phases around loops in the Brillouin zone. The method is based solely on wavepacket interference and can be used to determine band Chern numbers or the photonic equivalent of the anomalous Hall response. We demonstrate the robustness of these measurements towards on-site and gauge-field disorder. We also show the stability of the anomalous quantum Hall phase for nonlinear cavities and for (artificial) atom-photon interactions.

Recent experiments in ultracold atoms and photonic analogs have reported the implementation of artificial gauge fields in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate the Haldane honeycomb lattice tight-binding model, for bosons with local interactions at the average filling of one boson per site. We analyze the ground state phase diagram and uncover three distinct phases: a uniform superfluid (SF ), a chiral superfluid (CSF ) and a plaquette Mott insulator with local current loops (PMI ). Nearest-neighbor and nextnearest neighbor currents distinguish CSF from SF, and the phase transition between them is first order. We apply bosonic dynamical mean field theory and exact diagonalization to obtain the phase diagram, complementing numerics with calculations of excitation spectra in strong and weak coupling perturbation theory. The characteristic density fluctuations, current correlation functions, and excitation spectra are measurable in ultracold atom experiments.

Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these quantities can be strongly modified with respect to their values in vacuum. Generally, this modification can be accurately captured by including only the closest resonant mode of the cavity. In the circuit quantum electrodynamics architecture, it is however found that the radiative decay rates are strongly influenced by far off-resonant modes. A multimode calculation accounting for the infinite set of cavity modes leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is. We show here that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. We then present a theoretical approach to the calculation of a finite spontaneous emission rate and the Lamb shift that is free of cutoff.Introduction. An atom-like degree of freedom coupled to continuum of electromagnetic (EM) modes spontaneously decays. When the atom is confined in a resonator, the emission rate can be modified compared with its value in free space, depending on the EM local density of states at the atomic position [1][2][3][4], which is called the Purcell effect [5]. An accompanying effect is the Lamb shift, a radiative level shift first observed in the microwave spectroscopy of the hydrogen 2 P 1/2 − 2 S 1/2 transition [6]. These quantities have been experimentally accurately characterized for superconducting Josephson junction (JJ) based qubits coupled to coplanar transmission lines [7,8] and three-dimensional resonators [9]. In the dispersive regime where a qubit with transition frequency ω j is far-detuned from the nearest resonant cavity mode (frequency ν r , loss κ r ), single mode expressions exist for the Purcell decay rate, γ P = (g/δ) 2 κ r and the Lamb shift, ∆ L = g 2 /δ. These well-known approximate estimates are often used in analyzing qubit state readout, hence we employ them to benchmark our results. Here g denotes the coupling between the qubit and the cavity mode and δ = ω j − ν r denotes their detuning [10]. However, for large couplings accessible in circuit QED, the single mode approximation is often inaccurate [7,8]. In addition, due to particular boundary conditions imposed by the capacitive coupling of a resonator to external waveguides, the qubit relaxation time is limited by the EM modes that are far-detuned from the qubit frequency [8]. Similarly the measured Lamb shift in the dispersive regime can only be accurately fit with an extended Jaynes-Cummings (JC) model including several modes and qubit levels [7]. The Purcell rate has been generalized to account for all modes

We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c = 1, which is a precursor of the two-dimensional Laughlin state at ν = 1/2. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

The measurement of quantum entanglement in many-body systems remains challenging.One experimentally relevant fact about quantum entanglement is that in systems whose degrees of freedom map to free fermions with conserved total particle number, exact relations hold relating the Full Counting Statistics associated with the bipartite charge fluctuations and the sequence of Rényi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, mediated by the Rényi entropies. In the case of the integer quantum Hall effect, we show that it is possible to reproduce the generic features of the entanglement spectrum from a measurement of the second charge cumulant only. Additionally, asking whether it is possible to extend the free fermion result to the ν = 1/3 fractional quantum Hall case, we provide numerical evidence that the answer is negative in general. We further address the problem of quantum Hall edge states described by a Luttinger liquid, and derive expressions for the spectral functions of the real space entanglement spectrum at a quantum point contact realized in a quantum Hall sample. ‡ Corresponding author karyn.lehur@cpht.polytechnique.fr. This paper is dedicated to the JSTAT special issue on Quantum Entanglement in Condensed Matter Physics. arXiv:1405.7816v3 [cond-mat.mes-hall]