a, Energy diagram showing the first- and second-order manifolds of the strongly coupled cavity/quantum-dot system. The energy difference between consecutive manifolds is not constant, as shown by the blue and the red arrows. This anharmonic spacing of the levels causes phenomena such as photon blockade12 and photon-induced tunnelling. b, Simulated output intensity for a probe beam frequency tuned through the strongly coupled cavity/quantum-dot system (solid line). The dotted line shows the bare-cavity reflectivity corresponding to the quantum dot in the dark state. The blue and red lines indicate the frequencies for the |0〉→|1,+〉 and |1,+〉→|2,+〉 transitions. c, Computed second-order correlation g(2)(0) for a coherent laser probe reflected from the cavity. The inset shows that photon blockade is expected when the probe detuning is Δωp/g∼1.5 because the absorption of a photon into |1,+〉 suppresses the probability of absorbing a second photon of the same energy for a transition to |2,+〉. The blockade does not occur exactly at Δωp/g=1 because of the finite linewidth of the polaritons. As Δωp→0, the absorption of a photon into the first manifold enhances the absorption probability into higher-order manifolds (photon-induced tunnelling) and results in a bunched output field. d, Simulated time dependence of the second-order correlation for Δωp=0. The value for g(2)(τ) drops rapidly for time delays greater than ∼5 ps, corresponding to the cavity photon lifetime.