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

TL;DR

This paper introduces a generalized interferometric method using composite laser pulses for quantum clock precision, enabling enhanced control of atomic interferences and sensitivity to light-shifts in optical frequency standards.

Contribution

It develops a recursive algorithm for composite rotations in SU(2), deriving a formula for phase-shifts, and demonstrates hyper-clock protocols with nonlinear sensitivities for improved metrology.

Findings

Hyper-clock protocols exhibit cubic and quintic sensitivities to light-shifts.

The formalism allows optimization of phase-shifts for robust quantum control.

Potential applications in designing next-generation optical frequency standards.

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.