Ramsey interference fringes in single pulse microwave multiphoton transitions

In microwave multiphoton transitions between Rydberg atoms driven by short microwave pulses we have observed that the rise and fall of the pulse are as important as the peak and together can produce readily visible interference in the transition probability. Furthermore, the transition probability vanishes for some tunings and can be suppressed if the ac Stark shift brings the two states into resonance at the peak of the microwave pulse with a large Rabi frequency.