# Photonic heat transport across a Josephson junction

## TL;DR

This paper investigates how photonic heat is transported across a Josephson junction in various circuit configurations, analyzing effects of anharmonicity and coupling strength to inform quantum thermodynamics experiments.

## Contribution

It provides a comprehensive analysis of photonic heat transport in Josephson junctions, including effects of anharmonicity and different coupling regimes, with analytical approximations for heat flux.

## Key findings

- Analytical expressions for photonic heat flux in different regimes
- Effects of junction anharmonicity on heat transport
- Potential for quantum thermodynamics experiments using Josephson circuits

## Abstract

We present a detailed study of photonic heat transport across a Josephson junction coupled to two arbitrary linear circuits having different temperatures. First, we consider the linear approximation, in which a nonlinear Josephson potential is replaced by a quadratic one and the junction acts as an inductor. Afterwards, we discuss the effects of junction anharmonicity. We separately consider the weak-coupling limit, in which the Bloch band structure of the junction energy spectrum plays an important role, and the opposite strong-coupling regime. We apply our general results to two specific models: a Josephson junction coupled to two Ohmic resistors and two resonators. We derive simple analytical approximations for the photonic heat flux in many limiting cases. We demonstrate that electric circuits with embedded Josephson junctions provide a useful platform for quantum thermodynamics experiments.