Interaction between light and matter results in several physical phenomena that have and continue to fascinate scientists. One such phenomenon, predicted more than 40 years ago, is the “superradiant phase transition” (SRPT), which is characterized by the spontaneous appearance of coherence in electromagnetic field amplitudes (spontaneous appearance of static electromagnetic field) due to ultra-strong coupling between light and matter at thermal equilibrium. Its occurrence under thermal equilibrium is what primarily differentiates it from all spontaneous coherence achieved so far, including that in laser light generation and that in phase transitions of only matter. Unfortunately, SRPT has not yet been experimentally observed, the reason being that both experimental and theoretical scientists do not know where to look! 

Now, with the present new insights, perhaps we will. In the present study, we have identified a system that can theoretically demonstrate SRPT at thermal equilibrium. We have shown, based on analytical and numerical calculations, that a superconducting Josephson junction circuit can exhibit a superconducting current analogue of the SRPT. This finding can potentially pave the way for a new discipline at the intersection of optics, electronics, and thermodynamics, taking research on superconductors down a new path beyond the current scheme of quantum computing.

To arrive at these findings, we began by deriving the circuit Hamiltonian using standard quantization and showed SRPT emerge at the thermodynamic limit. Next, we numerically diagonalized the Hamiltonian for a small number of atoms and observed its asymptotic behavior as we increased the number of atoms. Sure enough, it reproduced the behavior analytically obtained at the thermodynamic limit, signifying the appearance of SRPT. 

While we await experimental confirmation of our prediction, we explore an interesting implication of our work. By controlling SRPT, it may become possible to convert heat energy directly to coherent light—a process that, if efficient enough, can help us utilize waste heat and save energy. Furthermore, the light obtained can be transferred via optical cables to places that are lacking in light or other energy sources, thereby enabling better access to energy for all. While mere speculations at the moment, these possibilities may be realized in the next 50 years. For now, our study could be the next step in a new direction of investigation aimed at experimentally realizing SRPT at thermal equilibrium.

Motoaki Bamba, Kunihiro Inomata, and Yasunobu Nakamura
“Superradiant Phase Transition in a Superconducting Circuit in Thermal Equilibrium”
Physical Review Letters 117, 173601 (2016)
https://arxiv.org/abs/1605.01124