Inelastic scattering of microwave radiation in the dynamical Coulomb blockade
Juha Leppäkangas, Michael Marthaler · Physical review. B./Physical review. B · 2018
We study scattering of propagating microwave fields by a dc-voltage-biased Josephson junction. At subgap voltages, a small Josephson junction works merely as a nonlinear 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 occurring at the junction.