SU(2) hyper-clocks: quantum engineering of spinor interferences for time and frequency metrology

Abstract: In 1949, Ramsey's method of separated oscillating fields was elaborated boosting over many decades metrological performances of atomic clocks and becoming the standard technique for very high precision spectroscopic measurements. A generalization of this interferometric method is presented replacing the two single coherent excitations by arbitrary composite laser pulses. The rotation of the state vector of a two-level system under the effect of a single pulse is described using the Pauli matrices basis of the SU(2) group. It is then generalized to multiple excitation pulses by a recursive Euler-Rodrigues-Gibbs algorithm describing a composition of rotations with different rotation axes. A general analytical formula for the phase-shift associated with the clock's interferometric signal is derived. As illustrations, hyper-clocks based on three-pulse and five-pulse interrogation protocols are studied and shown to exhibit nonlinear cubic and quintic sensitivities to residual probe-induced light-shifts. The presented formalism is well suited to optimize composite phase-shifts produced by tailored quantum algorithms in order to design a new generation of optical frequency standards and robust engineering control of atomic interferences in AMO physics with cold matter and anti-matter.