Generalized hyper-Ramsey resonance with spinors

TL;DR

This paper derives a generalized hyper-Ramsey resonance formula using spinor parametrization, enabling detailed analysis and simulation of atomic clock protocols with systematic effects and pulse imperfections.

Contribution

It introduces a new derivation of the hyper-Ramsey resonance formula using Cayley-Klein spinors, allowing comprehensive modeling of pulse parameters and systematic effects in atomic clocks.

Findings

Analytical expression for Ramsey's method with quantum state control.

Simulation of clock protocols under pulse defects.

Potential for optimizing signal robustness against systematic effects.

Abstract

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.