Emission of Photon Multiplets by a dc-Biased Superconducting Circuit

We observe the emission of bunches of k >= 1 photons by a circuit made of a microwave resonator in series with a voltage-biased tunable Josephson junction. The bunches are emitted at specific values V-k of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly k photons in the resonator. The latter is a microfabricated spiral coil which resonates and leaks photons at 4.4 GHz in a measurement line. Its characteristic impedance of 1.97 k Omega is high enough to reach a strong junction-resonator coupling and a bright emission of the k-photon bunches. We show that a rotating-wave approximation treatment of the system accounts quantitatively for the observed radiation intensity, from k=1 to 6, and over 3 orders of magnitude when varying the Josephson energy E-J. We also measure the second-order correlation function of the radiated microwave to determine its Fano factor F-k, which in the low E-J limit confirms with F-k similar or equal to k the emission of k-photon bunches. At larger E-J, a more complex behavior is observed in quantitative agreement with numerical simulations.