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Ramsey spectroscopy measures a transition frequency by comparing the relative quantum phase acquired between two coherent interactions with the reference oscillator. In a beam, a state selector and apertures admit particular internal quantum states and trajectories; an analyzer and detector measure state-dependent transmission. In an optically prepared atomic clock, optical pumping and fluorescence can perform those functions. The preparation and readout determine which part of the beam contributes; they are not themselves the two coherent interactions.

For an ideal accepted particle, the first resonant half-duration Rabi pi pulse splits the probability amplitude between $|g⟩$ and $|e⟩$. The second combines two indistinguishable alternatives: a transition in the first region followed by no transition in the second, or the reverse. Their relative quantum phase depends on the dark flight and the drive oscillation phases. Adding probability amplitudes gives quantum interference; adding only the two alternatives' probabilities would erase the fringe. “Dark” means that the transverse drive is absent: a static magnetic field and the internal Hamiltonian operator can still act.

The useful separation is between pulse duration and phase-accumulation time. Short regions can share one coherent oscillator while a long drive-free interval resolves small frequency differences. A scan over reference frequency locates a fringe pattern; controlled changes of the second pulse's oscillation phase distinguish that coherent signal from phase-insensitive background. A reference scan must also identify the central fringe before atomic clock frequency lock, because neighboring fringes provide competing lock points.