Multiphoton pumping between two microwaves mediated by transmon qubit

In this work, we analyze the interference patterns, observed in the multiphoton absorption spectrum of a transmon qubit, when it is driven by a pair of microwaves, tuned near and far off the qubit resonance. The appearance of such structures in the spectrum is explained as various photon contributions from the two microwave drives. We show that each of these manifolds demonstrates single or multiphoton pumping from one microwave to another. A many-mode Floquet formalism, with longitudinal coupling, is used to simulate the observed
quantum interference. An intuitive graph theoretic approach is introduced to derive the effective Hamiltonian that elucidate main features of the Floquet results. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide frequency range. The proposed experimental design and the theoretical approach can be extended to tunable qubit circuits or solid state semiconductors, in general, which offer full controllability of the energy gaps.