We propose a superconducting circuit that shows a superradiant phase transition (SRPT) in thermal equilibrium. The existence of the SRPT is confirmed analytically in the limit of an infinite number of artificial atoms. We also perform a 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.

Full text

Motoaki Bamba, Kunihiro Inomata, and Yasunobu Nakamura
Superradiant Phase Transition in a Superconducting Circuit in Thermal Equilibrium
Physical Review Letters 117, 173601 (2016)