  We demonstrate rapid, first-order sideband transitions between a
superconducting resonator and a frequency-modulated transmon qubit. The qubit
contains a substantial asymmetry between its Josephson junctions leading to a
linear portion of the energy band near the resonator frequency. The sideband
transitions are driven with a magnetic flux signal of a few hundred MHz coupled
to the qubit. This modulates the qubit splitting at a frequency near the
detuning between the dressed qubit and resonator frequencies, leading to rates
up to 85 MHz for exchanging quanta between the qubit and resonator.
