Branch-entangled polariton pairs in planar microcavities and photonic wires

A scheme is proposed for the generation of branch-entangled pairs of microcavity polaritons through spontaneous inter-branch parametric scattering. Branch-entanglement is achievable when there are two twin processes, where the role of signal and idler can be exchanged between two different polariton branches. Branch-entanglement of polariton pairs can lead to the emission of frequency-entangled photon pairs out of the microcavity. In planar microcavities, the necessary phase-matching conditions are fulfilled for pumping of the upper polariton branch at an arbitrary in-plane wave-vector. The important role of nonlinear losses due to pair scattering into high-momentum exciton states is evaluated. The results show that the lack of protection of the pump polaritons in the upper branch is critical. In photonic wires, branch-entanglement of one-dimensional polaritons is achievable when the pump excites a lower polariton sub-branch at normal incidence, providing protection from the exciton reservoir.Comment: Under review at PR

Probing microcavity polariton superfluidity through resonant Rayleigh scattering

We investigate the two-dimensional motion of polaritons injected into a planar microcavity by a continuous wave optical pump in presence of a static perturbation, e.g. a point defect. By finding the stationary solutions of the nonlinear mean-field equations (away from any parametric instability), we show how the spectrum of the polariton Bogoliubov-like excitations reflects onto the shape and intensity of the resonant Rayleigh scattering emission pattern in both momentum and real space. We find a superfluid regime in the sense of the Landau criterion, in which the Rayleigh scattering ring in momentum space collapses as well as its normalized intensity. More generally, we show how collective excitation spectra having no analog in equilibrium systems can be observed by tuning the excitation angle and frequency. Predictions with realistic semiconductor microcavity parameters are given

Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies

We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a Quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a non-equilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase-coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase-coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed

Quantum fluid effects and parametric instabilities in microcavities

We present a description of the non-equilibrium properties of a microcavity polariton fluid, injected by a nearly-resonant continuous wave pump laser. In the first part, we point out the interplay between the peculiar dispersion of the Bogolubov-like polariton excitations and the onset of polariton parametric instabilities. We show how collective excitation spectra having no counterpart in equilibrium systems can be observed by tuning the excitation angle and frequency. In the second part, we explain the impact of these collective excitations on the in-plane propagation of the polariton fluid. We show that the resonant Rayleigh scattering induced by artificial or natural defects is a very sensitive tool to show fascinating effects such as polariton superfluidity or polariton Cherenkov effect. We present a comprehensive set of predicted far-field and near-field images for the resonant Rayleigh scattering emission.Comment: 25 figures, 16 pages lon

Input-output theory of cavities in the ultra-strong coupling regime: the case of a time-independent vacuum Rabi frequency

We present a full quantum theory for the dissipative dynamics of an optical cavity in the ultra-strong light-matter coupling regime, in which the vacuum Rabi frequency is comparable to the electronic transition frequency and the anti-resonant terms of the light-matter coupling play an important role. In particular, our model can be applied to the case of intersubband transitions in doped semiconductor quantum wells embedded in a microcavity. The coupling of the intracavity photonic mode and of the electronic polarization to the external, frequency-dependent, dissipation baths is taken into account by means of quantum Langevin equations in the input-output formalism. Observable spectra (reflection, absorption, transmission and electroluminescence) are calculated analytically in the case of a time-independent vacuum Rabi frequency

Superradiant phase transitions with three-level systems

We determine the phase diagram of $N$ identical three-level systems interacting with a single photonic mode in the thermodynamical limit ($N \to \infty$) by accounting for the so-called diamagnetic term and the inequalities imposed by the Thomas-Reich-Kuhn (TRK) oscillator strength sum rule. The key role of transitions between excited levels and the occurrence of first-order phase transitions is discussed. We show that, in contrast to two-level systems, in the three-level case the TRK inequalities do not always prevent a superradiant phase transition in presence of a diamagnetic term

Hydrodynamic nucleation of vortices and solitons in a resonantly excited polariton superfluid

We present a theoretical study of the hydrodynamic properties of a quantum gas of exciton-polaritons in a semiconductor microcavity under a resonant laser excitation. The effect of a spatially extended defect on the superfluid flow is investigated as a function of the flow speed. The processes that are responsible for the nucleation of vortices and solitons in the wake of the defect are characterized, as well as the regimes where the superfluid flow remains unperturbed. Specific features due to the non-equilibrium nature of the polariton fluid are put in evidence

On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices

We present a theoretical study on the robustness of multi-photon states in a frustrated lattice of coupled nonlinear optical cavities, which are described by a driven-dissipative Bose-Hubbard model. In particular, we focus here on a Lieb lattice with two elementary cells and periodic boundary conditions. Due to the geometric frustration of the lattice, the non-equilibrium steady state can exhibit dark sites with low photon density and strong correlations, ascribable to the population of multi-photon modes. We explore the sensitivity of such strong correlations on the random inhomogeneity of the lattice parameters. We show that the correlations are more sensitive to the inhomogeneity of the cavity frequencies than to the random fluctuations of the hopping strength.Comment: Accepted for publication on EPJ-Special Topics "Quantum gases and quantum coherence": 10 pages, 5 figure

Critical dynamical properties of a first-order dissipative phase transition

We theoretically investigate the critical properties of a single driven-dissipative nonlinear photon mode. In a well-defined thermodynamical limit of large excitation numbers, the exact quantum solution describes a first-order phase transition in the regime where semiclassical theory predicts optical bistability. We study the behavior of the complex spectral gap associated with the Liouvillian superoperator of the corresponding master equation. We show that in this limit the Liouvillian gap vanishes exponentially and that the bimodality of the photon Wigner function disappears. The connection between the considered thermodynamical limit of large photon numbers for the single-mode cavity and the thermodynamical limit of many cavities for a driven-dissipative Bose-Hubbard system is discussed.Comment: revised version accepted for publication in PR