  In this work, we measure longitudinal dressed states of a superconducting
qubit, the single Cooper-pair box, and an intense microwave field. The dressed
states represent the hybridization of the qubit and photon degrees of freedom,
and appear as avoided level crossings in the combined energy diagram. By
embedding the circuit in an rf oscillator, we directly probe the dressed
states. We measure their dressed gap as a function of photon number and
microwave amplitude, finding good agreement with theory. In addition, we
extract the relaxation and dephasing rates of these states.
