Two superconducting artificial atoms ultrastrongly coupled to a single mode resonator*

 We report a experimental result of two artificial atoms (superconducting flux qubits) coupling via a single mode superconducting LC resonator. In the system, each artificial atom couple to resonator as strong as g (coupling frequency) ~ 0.5w (resonator frequency). In the experiment, we biased atom 1 and 2 to be near to the optimal point. Thus, we can make situation that the resonator energy = the energy of atom 1 + the energy of atom 2. In the spectrum of a ultrastrongly coupled system, we can see many energy transition signals in S21 measurement. To fit the spectrum, information of the frequency in each branch is required. Thereby, to obtain peak points we used image processing by Python [1]. Our circuit model described spectrum well. In this level of coupling strength, we can see the anti-splitting between a one photon state and a two artificial atoms excited state. In other words, a single photon in resonator can simultaneously excite two coupled atoms [2].

[1] A. Tomonaga, et al, Phys. Rev. B 104, 224509 (2021)

[2] Luigi Garziano, et al, Phys. Rev. Lett. 117, 043601 (2016)