  Rydberg atoms have large transition electric dipole moments and high
sensitivity to electric fields. We describe a new method for microwave field
sensing in a vapor cell consisting of separate excitation, quantum evolution
between two Rydberg levels in the dark and state-dependent detection with probe
laser transmission. Using microwave pulse techniques we study homogeneous and
inhomogeneous relaxation of the coherence between Rydberg levels and
demonstrate detection of a 10 GHz signal with electric field sensitivity of 10
nV/cm/Hz$^{1/2}$.
