  Superconducting cavities have emerged as a key tool for measuring the spin
states of quantum dots. So far however, few experiments have explored
longitudinal couplings between dots and cavities, and no solid-state qubit
experiments have explicitly probed the "adiabatic" regime, where the Purcell
decay is strongly suppressed. Here, we report measurements of a
double-quantum-dot charge qubit coupled to a high-impedance resonator via a
"flip-chip" design geometry. By applying an adiabatic ac drive to the qubit
through two different channels, and studying the effects of qubit energy
detuning, interdot tunneling, and driving strength, we are able to
unequivocally confirm the presence of a longitudinal coupling between the qubit
and cavity, while the qubit remains in its ground state. Since this coupling is
proportional to the driving amplitude, and is therefore switchable, it has the
potential to become a powerful new tool in qubit experiments.
