  Single-, two-, and three-photon transitions were driven amongst five quantum
states of a niobium persistent-current qubit. A multi-level energy-band diagram
was extracted using microwave spectroscopy, and avoided crossings were directly
measured between the third and fourth excited states. The energy relaxation
times between states connected by single-photon and multi-photon transitions
were approximately 30 - 100 microseconds. Three-photon coherent oscillations
were observed between the qubit ground and fourth excited states with a
decoherence time of approximately 50 nanoseconds.
