Generalized hyper-Ramsey resonance with spinors

The generalized hyper-Ramsey resonance formula originally published in Phys. Rev. A vol 92, 023416 (2015) is derived using a Cayley-Klein spinor parametrization. The shape of the interferometric resonance and the associated composite phase-shift are reformulated including all individual laser pulse parameters. Potential robustness of signal contrast and phase-shift of the wave-function fringe pattern can now be arbitrarily explored tracking any shape distortion due to systematic effects from the probe laser. An exact and simple analytical expression describing a Ramsey's method of separated composite oscillating laser fields with quantum state control allows us to accurately simulate all recent clock interrogation protocols under various pulse defects.