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.