Photon number splitting in a multilevel transmon with different microwave photon sources

We present the observation of photon number splitting (PNS) in a superconducting transmon qubit with different microwave photon sources. Such PNS is not limited to the lower energy levels and can also be observed in the higher energy levels of a superconducting transmon qubit. The sideband transition, Autler-Townes splitting, and the absence of PNS are demonstrated under certain conditions. Furthermore, we investigate the PNS induced by the nonclassical microwave photons emitted from a dual-mode Josephson parametric amplifier, which can operate in either the single mode or dual mode. The evolution from the dual-mode squeezing to the self-oscillation light emission is demonstrated. Our results provide a useful reference for future investigations, such as the exploration of more nonlinear effects in strongly driven circuit QED systems, the manipulation of quantum states, and the characterization of the quantum microwave source by utilizing PNS.