# Theory of double Cooper-pair tunneling and light emission mediated by a resonator

## TL;DR

This paper develops a theoretical framework for understanding how double Cooper-pair tunneling in Josephson junctions, mediated by a resonator, can lead to photon emission, including regimes of coherent tunneling and photon blockade.

## Contribution

It introduces an effective Hamiltonian for double Cooper-pair tunneling and identifies conditions for incoherent and coherent regimes, revealing potential for single-photon source applications.

## Key findings

- Identification of conditions for incoherent double Cooper-pair tunneling.
- Discovery of a regime of coherent double Cooper-pair tunneling.
- Prediction of photon-blockade phenomena in the system.

## Abstract

Photon emission by tunneling electrons can be encouraged by locating a resonator close to the tunnel junction and applying an appropriate voltage-bias. However, studies of normal metals show that the resonator also affects how the charges flow, facilitating processes in which correlated tunneling of two charges produces one photon. We develop a theory to analyze this kind of behavior in Josephson junctions by deriving an effective Hamiltonian describing processes where two Cooper-pairs generate a single photon. We determine the conditions under which the transport is dominated by incoherent tunneling of two Cooper-pairs, whilst also uncovering a regime of coherent double Cooper-pair tunneling. We show that the system can also display an unusual form of photon-blockade and hence could serve as a single-photon source.