Inelastic scattering of microwave radiation in the dynamical Coulomb blockade

TL;DR

This paper investigates how a Josephson junction, biased with DC voltage, scatters microwave radiation, revealing its ability to absorb, amplify, and convert microwaves, with applications in quantum information processing.

Contribution

It provides a theoretical framework for understanding microwave scattering in Josephson junctions using the $P(E)$ function, including photon state transformations and squeezing effects.

Findings

Thermal and coherent radiation can be absorbed and amplified by the junction.

A coherent input can produce a two-mode squeezed output.

Photon multiplication and absorption processes are characterized at the quantum level.

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.