Inelastic scattering of microwave radiation in the dynamical Coulomb blockade

Abstract

We study scattering of propagating microwave fields by a DC-voltage biased Josephson junction. At sub-gap voltages, a small Josephson junction works merely as a non-linear boundary that can absorb, amplify, and diversely convert propagating microwaves. In the leading-order perturbation theory of the Josephson coupling energy, the spectral density and quadrature fluctuations of scattered thermal and coherent radiation can be described in terms of the well-known $P(E)$ function. Applying this, we study how thermal and coherent radiation is absorbed and amplified in an Ohmic transmission line and in a circuit with a resonance frequency. We show when a coherent input can create a two-mode squeezed output. In addition, we evaluate scattering amplitudes between arbitrary photon-number (Fock) states, characterizing individual photon multiplication and absorption processes occuring at the junction.

20 pages, 6 figures

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Cited by in corpus (7)

• Microwave photon-number amplification
• Photon-pair blockade in a Josephson-photonics circuit with two nondegenerate microwave resonators
• AC driven strongly correlated quantum circuits and Hall edge states: Unified photo-assisted noise and revisited minimal excitations
• Theory of double Cooper-pair tunneling and light emission mediated by a resonator
• Two-tone spectroscopy of high-frequency quantum circuits with a Josephson emitter
• Josephson junction cavity systems as cousins of the quantum optical micromaser
• Josephson Photonics with Simultaneous Resonances