Cavity quantum electrodynamics (QED) studies the interaction between a quantum emitter and a single radiation-field mode. When an atom is strongly coupled to a cavity mode, it is possible to realize important quantum information processing tasks, such as controlled coherent coupling and entanglement of distinguishable quantum systems. Realizing these tasks in the solid state is clearly desirable, and coupling semiconductor self-assembled quantum dots to monolithic optical cavities is a promising route to this end. However, validating the efficacy of quantum dots in quantum information applications requires confirmation of the quantum nature of the quantum-dot-cavity system in the strong-coupling regime. Here we find such confirmation by observing quantum correlations in photoluminescence from a photonic crystal nanocavity interacting with one, and only one, quantum dot located precisely at the cavity electric field maximum. When off-resonance, photon emission from the cavity mode and quantum-dot excitons is anticorrelated at the level of single quanta, proving that the mode is driven solely by the quantum dot despite an energy mismatch between cavity and excitons. When tuned to resonance, the exciton and cavity enter the strong-coupling regime of cavity QED and the quantum-dot exciton lifetime reduces by a factor of 145. The generated photon stream becomes antibunched, proving that the strongly coupled exciton/photon system is in the quantum regime. Our observations unequivocally show that quantum information tasks are achievable in solid-state cavity QED.

THEORY OF OPTOMECHANICAL EIT, EIA AND PARAMETRIC AMPLIFICATIONHere we provide a theoretical treatment of some of the main aspects of EIT [1][2][3][4], EIA [5] and parametric amplification [6][7][8] in optomechanical systems. Modeling the optomechanical system with the Hamiltonianit is possible to linearize the operation of the system, under the influence of a control laser at ω c , about a particular steady-state given by intracavity photon amplitude α 0 and a static phonon shift β 0 . The interaction of the mechanics and pump photons at ω c with secondary "probe" photons at ω s = ω c ± ∆ with two-photon detuning ∆ can then be modeled by making the substitutionŝAssuming that the pump is much larger than the probe, |α 0 | |α ± |, the pump amplitude is left unaffected and the equations for each sideband amplitude α ± are found to beWe have defined ∆ OC = ω o − ω c as the pump detuning from the optical cavity (including the static optomechanical shift, ω o ), and β + = β * − . In these situations it is typical to define G = gα 0 , as the effective optomechanical coupling rate between a sideband and the mechanical subsystem, mediated by the pump. Red-detuned pump: Electromagnetically Induced TransparencyWith the pump detuned from the cavity by a two-photon detuning ∆, the spectral selectivity of the optical cavity causes the sideband populations to be skewed in a drastic fashion. It is then an acceptable approximation to neglect one of these sidebands, depending on whether the pump is on the red or blue side of the cavity. When the pump resides on the red side (∆ OC > 0), the α + is reduced and can be neglected. This is the rotating wave approximation (RWA) and is valid so long as ∆ κ. Then Eqs. (S3-S4) may be solved for the reflection and transmission coefficients r(ω s ) and t(ω s ) of the side-coupled cavity system. We find that These equations are plotted in Figs. S1 and S2.

An outstanding goal in quantum optics is the realization of fast optical non-linearities at the single-photon level. Such non-linearities would allow for the realization of optical devices with new functionalities such as a single-photon switch/transistor or a controlled-phase gate, which could form the basis of future quantum optical technologies. While non-linear optics effects at the single-emitter level have been demonstrated in different systems, including atoms coupled to Fabry-Perot or toroidal micro-cavities, super-conducting qubits in strip-line resonators or quantum dots (QDs) in nano-cavities, none of these experiments so far has demonstrated single-photon switching on ultrafast timescales. Here, we demonstrate that in a strongly coupled QD-cavity system the presence of a single photon on one of the fundamental polariton transitions can turn on light scattering on a transition from the first to the second Jaynes-Cummings manifold with a switching time of 20 ps. As an additional device application, we use this non-linearity to implement a single-photon pulse-correlator. Our QD-cavity system could form the building-block of future high-bandwidth photonic networks operating in the quantum regime

The oscillator susceptibility χ(ω) given in the main text follows from the differential equation of the harmonic oscillator:Transforming to Fourier space, this readsWith F appl (ω)/m = a appl , this yields the accelerometer responseThis function has the following properties:For the device studied here with ω m = 2π × 27.5 kHz, this gives an acceleration sensitivity of χ(0) = 329 pm/g with g = 9.81 m/s 2 . II. TRANSMISSION FUNCTION OF SIDE-COUPLED OPEN CAVITYIn order to calculate the intensity transmission profile T (ω) of a photonic-crystal resonator side-coupled by a fiber-taper waveguide, we start from the equation of motion ofâ, the annihilation operator of the cavity field:Here, ∆ = ω l − ω c is the laser-cavity detuning, κ e is the total taper-cavity coupling rate, κ = κ i + κ e is the total cavity decay rate, with κ i the intrinsic cavity damping rate, andâ in is the taper input field, which together with the output fieldâ out obeys the boundary conditionâThe last two terms on the right-hand-side of eq. (S7) represent the vacuum inputs due to coupling with the intrinsic (loss) bath of the cavity and the backward fiber taper waveguide mode, respectively (these input terms are ignored going forward as they are in the vacuum state and do not modify the classical field equations). In steady state, where dâ dt ≡ 0, the intracavity field operator isâ

Optical non-linearities at the single-photon level are key ingredients for future photonic quantum technologies [1]. Prime candidates for the realization of strong photon-photon interactions necessary for implementing quantum information processing tasks [2] as well as for studying strongly correlated photons [3,4] in an integrated photonic device setting are quantum dots embedded in photonic crystal nanocavities. Here, we report strong quantum correlations between photons on picosecond timescales. We observe (a) photon antibunching upon resonant excitation of the lowest-energy polariton state, proving that the first cavity photon blocks the subsequent injection events, and (b) photon bunching when the laser field is in two-photon resonance with the polariton eigenstates of the second Jaynes-Cummings manifold, demonstrating that two photons at this color are more likely to be injected into the cavity jointly, than they would otherwise. Together, these results demonstrate unprecedented strong single-photon non-linearities, paving the way for realizing a single-photon transistor [5] or a quantum optical Josephson interferometer [6].Cavity quantum electrodynamics (cQED) studies the quantum limit of light-matter interaction where a single two-level quantum emitter is coupled to a single cavity mode [2]. In the strong coupling regime of cavity-QED where the coherent interaction strength between the emitter and the cavity mode exceeds the dissipative rates, the elementary excitations (polaritons) have an anharmonic spectrum (Fig. 1a). As a consequence, this system embodies the ultimate non-linear optical device enabling the observation of photon-photon interactions at the single-photon level [7]. Various implementations of cavity-QED systems have been reported with atoms in high finesse cavities [8], with quantum dots (QDs) in different types of monolithic cavities [9][10][11][12] and in the microwave domain [13][14][15]. Recent experiments in the optical domain using a single atom coupled to FabryPerot [16] or toroidal cavities [17] have demonstrated the * These authors contributed equally to this work. FIG. 1:Resonant scattering spectroscopy of a QD strongly coupled to a PC cavity. a) Non-linear JaynesCummings level scheme up to the second manifold. b) Sketch of the experimental setup with crossed-polarized laser suppression. c) On-resonance cw scattering spectrum for a probe power of 1 nW. The black trace was recorded without the additional re-pump laser. With the re-pump switched on, the resonant signal from the polaritons is restored (red trace).photon blockade effect by observing photon antibunching in correlation measurements. Photon bunching upon two-photon excitation of the second Jaynes-Cummings manifold has been observed for a single atom cavity-QED system [18]. In the solid-state, early results in quantum dot (QD) cavity-QED systems indicating optical nonlinearities have been reported [19,20].Here, we show that a single QD deterministically coupled to a photonic crystal (PC) defect cavity exhibits pronoun...