  We proposed a spectroscopic method that extends Ramsey's atomic spectroscopy
to detect the transition frequency of a qubit fabricated on a superconducting
circuit. The method uses a multi-interval train of qubit biases to implement an
alternate resonant and dispersive couplings to an incident probe field. The
consequent absorption spectrum of the qubit has a narrower linewidth at its
transition frequency than that obtained from constantly biasing the qubit to
resonance while the middle dispersive evolution incurs only a negligible shift
in detected frequency. Modeling on transmon qubits, we find that the linewidth
reduction reaches 23% and Ramsey fringes are simultaneously suppressed at
extreme duration ratio of dispersion over resonance for a double-resonance
scheme. If the scheme is augmented by an extra resonance segment, a further 37%
reduction can be achieved.
