Detecting Photon-Photon Interactions in a Superconducting Circuit

TL;DR

This paper proposes a method to detect photon-photon interactions in a superconducting circuit by analyzing the current-voltage characteristics of a Josephson junction coupled to a nonlinear transmission line.

Contribution

It introduces a novel approach to observe photon-photon interactions through voltage measurements in a superconducting circuit with a Josephson junction and a chain of Josephson junctions.

Findings

Features at voltages $2eV=n\u03b1 ext{h}a ext{w}_s$ indicate photon-photon interactions.

Photon-photon interactions cause distinct signatures in the current-voltage characteristic.

The method provides a direct way to detect interactions in superconducting quantum circuits.

Abstract

A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required high impedance transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\hbar\omega_s$, where $\omega_s$ is the plasma frequency of the superconducting circuit. The features at $n\ge 2$ are a direct signature of the photon-photon interaction in the system.