Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings.

The ability to tailor with a high accuracy the intersite connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the Su-Schrieffer-Heeger model which, in its conventional form, is limited to nearest-neighbor couplings only. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wave functions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class.

Quantum Vacuum Excitation of a Quasinormal Mode in an Analog Model of Black Hole Spacetime.

Vacuum quantum fluctuations near horizons are known to yield correlated emission by the Hawking effect. We use a driven-dissipative quantum fluid of microcavity polaritons as an analog model of a quantum field theory on a black-hole spacetime and numerically calculate correlated emission. We show that, in addition to the Hawking effect at the sonic horizon, quantum fluctuations may result in a sizable stationary excitation of a quasinormal mode of the field theory. Observable signatures of the excitation of the quasinormal mode are found in the spatial density fluctuations as well as in the spectrum of Hawking emission. This suggests an intrinsic fluctuation-driven mechanism leading to the quantum excitation of quasinormal modes on black hole spacetimes.

High-Resolution Coherent Probe Spectroscopy of a Polariton Quantum Fluid.

Characterizing elementary excitations in quantum fluids is essential to study their collective effects. We present an original angle-resolved coherent probe spectroscopy technique to study the dispersion of these excitation modes in a fluid of polaritons under resonant pumping. Thanks to the unprecedented spectral and spatial resolution, we observe directly the low-energy phononic behavior and detect the negative-energy modes, i.e., the ghost branch, of the dispersion relation. In addition, we reveal narrow spectral features precursory of dynamical instabilities due to the intrinsic out-of-equilibrium nature of the system. This technique provides the missing tool for the quantitative study of quantum hydrodynamics in polariton fluids.

Intersubband Polariton-Polariton Scattering in a Dispersive Microcavity.

The ultrafast scattering dynamics of intersubband polaritons in dispersive cavities embedding GaAs/AlGaAs quantum wells are studied directly within their band structure using a noncollinear pump-probe geometry with phase-stable midinfrared pulses. Selective excitation of the lower polariton at a frequency of ∼25 THz and at a finite in-plane momentum k_{‖} leads to the emergence of a narrowband maximum in the probe reflectivity at k_{‖}=0. A quantum mechanical model identifies the underlying microscopic process as stimulated coherent polariton-polariton scattering. These results mark an important milestone toward quantum control and bosonic lasing in custom-tailored polaritonic systems in the mid and far infrared.

Observation of Massless and Massive Collective Excitations with Faraday Patterns in a Two-Component Superfluid.

We report on the experimental measurement of the dispersion relation of the density and spin collective excitation modes in an elongated two-component superfluid of ultracold bosonic atoms. Our parametric spectroscopic technique is based on the external modulation of the transverse confinement frequency, leading to the formation of density and spin Faraday waves. We show that the application of a coherent coupling between the two components reduces the phase symmetry and gives a finite mass to the spin modes.

Kibble-Zurek Mechanism in Driven Dissipative Systems Crossing a Nonequilibrium Phase Transition.

The Kibble-Zurek mechanism constitutes one of the most fascinating and universal phenomena in the physics of critical systems. It describes the formation of domains and the spontaneous nucleation of topological defects when a system is driven across a phase transition exhibiting spontaneous symmetry breaking. While a characteristic dependence of the defect density on the speed at which the transition is crossed was observed in a vast range of equilibrium condensed matter systems, its extension to intrinsically driven dissipative systems is a matter of ongoing research. In this Letter, we numerically confirm the Kibble-Zurek mechanism in a paradigmatic family of driven dissipative quantum systems, namely exciton-polaritons in microcavities. Our findings show how the concepts of universality and critical dynamics extend to driven dissipative systems that do not conserve energy or particle number nor satisfy a detailed balance condition.

Fusion Channels of Non-Abelian Anyons from Angular-Momentum and Density-Profile Measurements.

We present a method to characterize non-Abelian anyons that is based only on static measurements and that does not rely on any form of interference. For geometries where the anyonic statistics can be revealed by rigid rotations of the anyons, we link this property to the angular momentum of the initial state. We test our method on the paradigmatic example of the Moore-Read state that is known to support excitations with non-Abelian statistics of Ising type. As an example, we reveal the presence of different fusion channels for two such excitations, a defining feature of non-Abelian anyons. This is obtained by measuring density-profile properties, like the mean square radius of the system or the depletion generated by the anyons. Our study paves the way to novel methods for characterizing non-Abelian anyons, both in the experimental and theoretical domains.

Dynamical Critical Exponents in Driven-Dissipative Quantum Systems.

We study the phase ordering of parametrically and incoherently driven microcavity polaritons after an infinitely rapid quench across the critical region. We confirm that the system, despite its driven-dissipative nature, satisfies the dynamical scaling hypothesis for both driving schemes by exhibiting self-similar patterns for the two-point correlator at late times of the phase ordering. We show that polaritons are characterized by the dynamical critical exponent z≈2 with topological defects playing a fundamental role in the dynamics, giving logarithmic corrections both to the power-law decay of the number of vortices and to the associated growth of the characteristic length scale.

Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics.

We propose a standard time-of-flight experiment as a method for observing the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. Our proposed method is validated by Monte Carlo calculations for ν=1/2 and 1/3 fractional quantum Hall liquids containing a realistic number of particles. Extensions to quantum Hall liquids of light and to non-Abelian anyons are briefly discussed.

Particle-Hole Character of the Higgs and Goldstone Modes in Strongly Interacting Lattice Bosons.

We study the low-energy excitations of the Bose-Hubbard model in the strongly interacting superfluid phase using a Gutzwiller approach. We extract the single-particle and single-hole excitation amplitudes for each mode and report emergent mode-dependent particle-hole symmetry on specific arc-shaped lines in the phase diagram connecting the well-known Lorentz-invariant limits of the Bose-Hubbard model. By tracking the in-phase particle-hole symmetric oscillations of the order parameter, we provide an answer to the long-standing question about the fate of the pure amplitude Higgs mode away from the integer-density critical point. Furthermore, we point out that out-of-phase symmetric oscillations in the gapless Goldstone mode are responsible for a full suppression of the condensate density oscillations. Possible detection protocols are also discussed.

Orbital Edge States in a Photonic Honeycomb Lattice.

We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of p-like photonic orbitals. We observe zero-energy edge states whose topological origin is similar to that of conventional edge states in graphene. Additionally, we report novel dispersive edge states in zigzag and armchair edges. The observations are reproduced by tight-binding and analytical calculations, which we extend to bearded edges. Our work shows the potentiality of coupled micropillars in elucidating some of the electronic properties of emergent two-dimensional materials with orbital bands.

Phase-Controlled Bistability of a Dark Soliton Train in a Polariton Fluid.

We use a one-dimensional polariton fluid in a semiconductor microcavity to explore the nonlinear dynamics of counterpropagating interacting Bose fluids. The intrinsically driven-dissipative nature of the polariton fluid allows us to use resonant pumping to impose a phase twist across the fluid. When the polariton-polariton interaction energy becomes comparable to the kinetic energy, linear interference fringes transform into a train of solitons. A novel type of bistable behavior controlled by the phase twist across the fluid is experimentally evidenced.

Four-Dimensional Quantum Hall Effect with Ultracold Atoms.

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semiclassical analysis, we identify the linear and nonlinear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.

Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons.

We report an experimental study of superfluid hydrodynamic effects in a one-dimensional polariton fluid flowing along a laterally patterned semiconductor microcavity and hitting a micron-sized engineered defect. At high excitation power, superfluid propagation effects are observed in the polariton dynamics; in particular, a sharp acoustic horizon is formed at the defect position, separating regions of sub- and supersonic flow. Our experimental findings are quantitatively reproduced by theoretical calculations based on a generalized Gross-Pitaevskii equation. Promising perspectives to observe Hawking radiation via photon correlation measurements are illustrated.

Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons.

Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence, we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of this structure which holds massless, massive, and infinitely massive particles opens the route towards studies of the interplay of dispersion, interactions, and frustration in a novel and controlled environment.

Oscillatory vertical coupling between a whispering-gallery resonator and a bus waveguide.

We report on a theoretical and experimental study of the optical coupling between a whispering-gallery type resonator and a waveguide lying on different planes. In contrast to the usual in-plane geometry, the present vertical one is characterized by an oscillatory behavior of the effective coupling as a function of the vertical gap. This behavior manifests itself as oscillations in both the resonance peak waveguide transmission and the mode quality factor. An analytical description based on coupled-mode theory and a two-port beam-splitter model of the waveguide-resonator vertical coupling is developed for arbitrary phase-matching conditions and is successfully used to interpret the experimental observations.

Dynamic nuclear spin polarization in the resonant laser excitation of an InGaAs quantum dot.

Resonant optical excitation of lowest-energy excitonic transitions in self-assembled quantum dots leads to nuclear spin polarization that is qualitatively different from the well-known optical orientation phenomena. By carrying out a comprehensive set of experiments, we demonstrate that nuclear spin polarization manifests itself in quantum dots subjected to finite external magnetic field as locking of the higher energy Zeeman transition to the driving laser field, as well as the avoidance of the resonance condition for the lower energy Zeeman branch. We interpret our findings on the basis of dynamic nuclear spin polarization originating from noncollinear hyperfine interaction and find excellent agreement between experiment and theory. Our results provide evidence for the significance of noncollinear hyperfine processes not only for nuclear spin diffusion and decay, but also for buildup dynamics of nuclear spin polarization in a coupled electron-nuclear spin system.

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 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.

Polariton superfluids reveal quantum hydrodynamic solitons.

A quantum fluid passing an obstacle behaves differently from a classical one. When the flow is slow enough, the quantum gas enters a superfluid regime, and neither whirlpools nor waves form around the obstacle. For higher flow velocities, it has been predicted that the perturbation induced by the defect gives rise to the turbulent emission of quantized vortices and to the nucleation of solitons. Using an interacting Bose gas of exciton-polaritons in a semiconductor microcavity, we report the transition from superfluidity to the hydrodynamic formation of oblique dark solitons and vortex streets in the wake of a potential barrier. The direct observation of these topological excitations provides key information on the mechanisms of superflow and shows the potential of polariton condensates for quantum turbulence studies.