High sensitivity spectral characterization of local microwave fields using two-photon absorption processes of a transmon qudit

Optimal control methods for quantum information processing require precise knowledge of the local microwave amplitudes generated by control pulses arriving at the cryogenic stage of the quantum processor. We present a scheme for characterizing the spectral transfer function of a superconducting transmon qudit capacitively coupled to a 3D cavity resonator. We apply two simultaneous drive tones close to the transmon's 0-1 and 1-2 state transition frequencies while varying both the duration of the pulses as well as their relative detuning. Through measurement of the 0-, 1-, and 2-state occupations, we map out the 0 to 2 state two-photon absorption process.The relative occupation of the three lowest transmon levels provides a sensitive probe of the local microwave field over a large range of detuning. By comparing our measurement results to master equation simulations incorporating a spectral filter, we recover the amplitude-corrected transfer function over an approximately 200 MHz bandwidth.