Creating photon-number squeezed strong microwave fields by a Cooper-pair injection laser

The use of artificial atoms as an active lasing medium opens a way to construct novel sources of nonclassical radiation. An example is the creation of photon-number squeezed light. Here we present a design of a laser consisting of multiple Cooper-pair transistors coupled to a microwave resonator. Over a broad range of experimentally realizable parameters, this laser creates photon-number squeezed microwave radiation, characterized by a Fano factor $F \ll 1$, at a very high resonator photon number. We investigate the impact of gate-charge disorder in a Cooper-pair transistor and show that the system can create squeezed strong microwave fields even in the presence of maximum disorder.Comment: extended and revised version, equivalent to the published article. 11 pages, 3 figure

Correlated transport through junction arrays in the small Josephson energy limit: incoherent Cooper-pairs and hot electrons

We study correlated transport in a Josephson junction array for small Josephson energies. In this regime transport is dominated by Cooper-pair hopping, although we observe that quasiparticles can not be neglected. We assume that the energy dissipated by a Cooper-pair is absorbed by the intrinsic impedance of the array. This allows us to formulate explicit Cooper-pair hopping rates without adding any parameters to the system. We show that the current is correlated and crucially, these correlations rely fundamentally on the interplay between the Cooper-pairs and equilibrium quasiparticles.Comment: 11 pages, 9 figures - Published Versio

Input-output description of microwave radiation in the dynamical Coulomb blockade

We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.Comment: 29 pages, 4 figure

Nonclassical photon pair production in a voltage-biased Josephson junction

We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the electromagnetic environment. For weak tunneling couplings and typical ohmic transmission lines, the corresponding photon flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.Comment: 5 pages, 2 figures. This version accepted in Physical Review Letter