Revealing the Topology of Quasicrystals with a Diffraction Experiment.

Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly observe, using an interferometric approach, all of the topological invariants of finite-length Fibonacci chains in their diffraction pattern. We also quantitatively demonstrate the stability of these topological invariants with respect to structural disorder.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Fractal energy spectrum of a polariton gas in a Fibonacci quasiperiodic potential.

We report on the study of a polariton gas confined in a quasiperiodic one-dimensional cavity, described by a Fibonacci sequence. Imaging the polariton modes both in real and reciprocal space, we observe features characteristic of their fractal energy spectrum such as the opening of minigaps obeying the gap labeling theorem and log-periodic oscillations of the integrated density of states. These observations are accurately reproduced solving an effective 1D Schrödinger equation, illustrating the potential of cavity polaritons as a quantum simulator in complex topological geometries.

Transmission of information through mesoscopic scattering systems.

The storage and transmission of information is well defined using the notions of entropy, mutual information and channel capacity as formalized by Shannon. These quantities are calculated for a quantum mesoscopic system in terms of scattering parameters. For a one-dimensional system, the mutual information is related to the thermal conductance. This relation allows to show that for an incident signal of power P, the channel capacity C has a universal upper bound given by C ≤ π√(2P/3h) independent of quantum statistics. A general framework is proposed which makes use of a natural underlying symplectic structure, to relate the entropy of a quantum mesoscopic system to the scattering matrix.

Observing a scale anomaly and a universal quantum phase transition in graphene.

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe 'Efimov physics'. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.When the continuous scale symmetry of a quantum system is broken, anomalies occur which may lead to quantum phase transitions. Here, the authors provide evidence for such a quantum phase transition in the attractive Coulomb potential of vacancies in graphene, and further envision its universality for diverse physical systems.

Photon localization and Dicke superradiance in atomic gases.

Photon propagation in a gas of N atoms is studied using an effective Hamiltonian describing photon-mediated atomic dipolar interactions. The density P(Gamma) of photon escape rates is determined from the spectrum of the NxN random matrix Gamma_{ij}=sin(x_{ij})/x_{ij}, where x_{ij} is the dimensionless random distance between any two atoms. Varying disorder and system size, a scaling behavior is observed for the escape rates. It is explained using microscopic calculations and a stochastic model which emphasizes the role of cooperative effects in photon localization and provides an interesting relation with statistical properties of "small world networks."

Intensity correlations and mesoscopic fluctuations of diffusing photons in cold atoms.

We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.

Effect of superradiance on transport of diffusing photons in cold atomic gases.

We show that in atomic gases cooperative effects like superradiance and subradiance lead to a potential between two atoms that decays like 1/r. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. The contribution of superradiant pairs to multiple scattering properties of a dilute gas, such as photon elastic mean free path and group velocity, is significantly different from that of independent atoms. We discuss the conditions under which these effects may be observed and compare our results to recent experiments on photon transport in cold atomic gases.

Nonexponential quasiparticle decay and phase relaxation in low-dimensional conductors.

We show that in low-dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one-dimensional case, both behave at small time as e(-(t/tau(in))3/2) where the inelastic time, tau(in), identical for both processes, is a power T-2/3 of the temperature. The nonexponential quasiparticle decay results from a modified derivation of the Fermi golden rule. This result implies the existence of an unusual distribution of relaxation times.