Quantum Monte Carlo study of superradiant supersolid of light in the extended Jaynes-Cummings-Hubbard model

Searching for and investigating supersolids is a long-term outstanding problem in physics. In addition to the solid element $⁴\mathrm{He}$ and cold atoms as potential candidates for the supersolid, the quantum system of light realized by circuit quantum electrodynamics is also a promising platform. In this paper, we propose a supersolid phase, i.e., a superradiant supersolid of light, where superradiant, superfluid, and solid orders coexist. We theoretically simulate the extended Jaynes-Cummings-Hubbard model describing the circuit quantum electrodynamics systems, mainly by the large-scale worm quantum Monte Carlo method, and find that a superradiant supersolid phase exists on triangular lattices due to the antiferromagnetic correlation between photons via light-atom coupling. We also confirm that the previous supersolid of light given by Bujnowski et al. [Phys. Rev. A 90, 043801 (2014)] is not stable. The phase transition between our superradiant supersolid phase and the superradiant solid phase can be continuous (first order) and above (below) the ``symmetry point.'' This is not the same as the pure Bose-Hubbard model on triangular lattices. The results herein could help in the search for a new superradiant supersolid phase in circuit quantum electrodynamic experiments and other light-matter coupling systems.