Below a critical temperature, a sufficiently high density of bosons undergoes Bose-Einstein condensation (BEC). Under this condition, the particles collapse into a macroscopic condensate with a common phase, showing collective quantum behaviour like superfluidity, quantised vortices, interferences, etc. Up to recently, BEC was only observed for diluted atomic gases at μK temperatures. Following the recent observations of non-equilibrium BEC in semiconductor microcavities at temperatures of ~10 K, using momentum-1 and real-space 2 trapping, the quest is now towards the observation of the superfluid motion of a polariton BEC. For the same reasons that polaritons benefit from unusually favourable features for condensation, such as very high critical temperatures, it is expected that their superfluid properties would likewise manifest with altogether different magnitudes, such as very high critical velocities. Since they have shown many deviations in their Bose-condensed phase from the cold atoms paradigm, it is not clear a priori to which extent their superfluid properties would coincide or depart from those observed with atoms, among which quantised vortices 6 , frictionless motion 7 , linear dispersion for the elementary excitations 8 , or more recently Čerenkov emission of a condensate flowing at supersonic velocities 9 , are among the clearest signatures of quantum fluid propagation.Microcavity polaritons are two-dimensional bosons of mixed electronic and photonic nature, formed by the strong coupling of excitons-confined in semiconductor quantum wells-with photons trapped in a micron scale resonant cavity. First observed in 1992 10 , these particles have been profusely studied in the last fifteen years due to their unique features. Thanks to their photon fraction, polaritons can easily be excited by an external laser source and detected by light emission in the direction perpendicular to the cavity plane. However, as opposed to photons, they experience strong interparticle interactions owing to their partially electronic fraction. Due to the deep polariton dispersion, the effective mass of these particles is 10 4 -10 5 smaller than the free electron mass, resulting in a very low density of states. This allows for a high state 3 occupancy even at relatively low excitation intensities. However, polaritons live only a few 10 -12 s in a cavity before escaping and therefore thermal equilibrium is never achieved. In this respect, a macroscopically degenerate state of polaritons departs strongly from an atomic Bose-condensed phase. The experimental observations of spectral and momentum narrowing, spatial coherence and long range order-which have been used as evidence for polariton Bose-Einstein condensation-are also present in a pure photonic laser 11 . The recent observation of long range spatial coherence 12 , vortices 4 and the loss of coherence with increasing density in the condensed phase 13,14 , are in accordance with macroscopic phenomena proper of interacting, coherent bosons 15 . But a direct manifestation ...

We discuss the luminescence spectra of coupled light-matter systems realized with semiconductor heterostructures in microcavities in the presence of a continuous, incoherent pumping, when the matter field is Fermionic. The linear regime-which has been the main topic of investigation both experimentally and theoretically-converges to the case of coupling to a Bosonic material field, and has been amply discussed in the first part of this work. We address here the nonlinear regime, and argue that, counter to intuition, it is better observed at low pumping intensities. We support our discussion with particular cases representative of, and beyond, the experimental state of the art. We explore the transition from the quantum to the classical regime, by decomposing the total spectrum into individual transitions between the dressed states of the light-matter coupling Hamiltonian, reducing the problem to the positions and broadenings of all possible transitions. As the system crosses to the classical limit, rich multiplet structures mapping the quantized energy levels melt and turn to cavity lasing and to an incoherent Mollow triplet in the direct exciton emission for very good structure. Less ideal figures of merit can still betray the quantum regime, with a proper balance of cavity versus electronic pumping.

We show that strong-coupling (SC) of light and matter as it is realized with quantum dots (QDs) in microcavities differs substantially from the paradigm of atoms in optical cavities. The type of pumping used in semiconductors yields new criteria to achieve SC, with situations where the pump hinders, or on the contrary, favours it. We analyze one of the seminal experimental observation of SC of a QD in a pillar microcavity [Reithmaier et al., Nature (2004)] as an illustration of our main statements.

Controlling the ouput of a light emitter is one of the basic tasks of photonics, with landmarks such as the laser and single-photon sources. The development of quantum applications makes it increasingly important to diversify the available quantum sources. Here, we propose a cavity QED scheme to realize emitters that release their energy in groups, or “bundles” of N photons, for integer N. Close to 100% of two-photon emission and 90% of three-photon emission is shown to be within reach of state of the art samples. The emission can be tuned with system parameters so that the device behaves as a laser or as a N-photon gun. The theoretical formalism to characterize such emitters is developed, with the bundle statistics arising as an extension of the fundamental correlation functions of quantum optics. These emitters will be useful for quantum information processing and for medical applications.

We apply our recently developed theory of frequency-filtered and timeresolved N -photon correlations [1] to study the two-photon spectra of a variety of systems of increasing complexity: single mode emitters with two limiting statistics (one harmonic oscillator or a two-level system) and the various combinations that arise from their coupling. We consider both the linear and nonlinear regimes under incoherent excitation. We find that even the simplest systems display a rich dynamics of emission, not accessible by simple single photon spectroscopy. In the strong coupling regime, novel two-photon emission processes involving virtual states are revealed. Furthermore, two general results are unraveled by two-photon correlations with narrow linewidth detectors: i) filtering induced bunching and ii) breakdown of the semi-classical theory. We show how to overcome this shortcoming in a fully-quantized picture.