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

Controlling discrete and continuous symmetries in 'superradiant' phase transitions

We explore theoretically the physics of a collection of two-level systems coupled to a single-mode bosonic field in the non-standard configuration where each (artificial) atom is coupled to both field quadratures of the boson mode. We determine the rich phase diagram showing 'superradiant' phases with different symmetries. We demonstrate that it is possible to pass from a discrete, parity-like $\mathbb{Z}_2$ symmetry to a continuous U(1) symmetry even in the ultrastrong coupling regime where the rotating wave approximation for the interaction between field and two-level systems is no longer applicable. By applying this general paradigm, we propose a scheme for the experimental implementation of such continuous U(1) symmetry in circuit QED systems, with the appearance of photonic Goldstone and amplitude modes above a critical point

Comment on "Superradiant Phase Transitions and the Standard Description of Circuit QED"

A Comment on the Letter by O. Viehmann, J. von Delft, and F. Marquardt [Phys. Rev. Lett. {\bf 107}, 113602 (2011)]

Counter-polarized single-photon generation from the auxiliary cavity of a weakly nonlinear photonic molecule

We propose a scheme for the resonant generation of counter-polarized single photons in double asymmetric cavities with a small Kerr optical nonlinearity (as that created by a semiconductor quantum well) compared to the mode broadening. Due to the interplay between spatial intercavity tunneling and polarization coupling, by weakly exciting with circularly polarized light one of the cavities, we predict strong antibunching of counter-polarized light emission from the non-pumped auxiliary cavity. This scheme due to quantum interference is robust against surface scattering of pumping light, which can be suppressed both by spatial and polarization filters

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

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

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