Super-radiant phase transition in superconducting circuit in thermal equilibrium

TL;DR

This paper introduces a superconducting circuit capable of exhibiting a super-radiant phase transition in thermal equilibrium, confirmed analytically and numerically, with potential classical interpretation.

Contribution

It demonstrates the existence of SRPT in superconducting circuits at thermal equilibrium, supported by analytical and numerical evidence, and provides an intuitive classical understanding.

Findings

Analytical proof of SRPT in infinite atom limit

Numerical results showing asymptotic behavior with finite atoms

Classical interpretation of the super-radiant phase transition

Abstract

We propose a superconducting circuit that shows a super-radiant phase transition (SRPT) in the thermal equilibrium. The existence of the SRPT is confirmed analytically in the limit of an infinite number of artificial atoms. We also perform numerical diagonalization of the Hamiltonian with a finite number of atoms and observe an asymptotic behavior approaching the infinite limit as the number of atoms increases. The SRPT can also be interpreted intuitively in a classical analysis.