# Universal ultra-robust interrogation protocol with zero probe-field-induced frequency shift for quantum clocks and high-accuracy spectroscopy

## TL;DR

This paper introduces a universal, phase-modulated laser interrogation protocol that completely eliminates probe-induced frequency shifts in quantum clocks and spectroscopy, even with decoherence and relaxation effects.

## Contribution

It derives an exact canonical form of multi-pulse Hyper-Ramsey resonance and proposes a robust composite pulse scheme that cancels frequency shifts at all orders under dissipative conditions.

## Key findings

- Universal protocol eliminates probe-induced shifts in presence of decoherence.
- Phase modulation with $\u00b1\u03c0/4$ and $\u00b1 3\u03c0/4$ achieves shift cancellation.
- Protocol maintains clock stability and error signal robustness under various dissipative processes.

## Abstract

Optical clock interrogation protocols, based on laser-pulse spectroscopy, are suffering from probe-induced frequency shifts and their variations induced by laser power. Original Hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by laser probe by deriving the exact canonical form of a multi-pulse generalized Hyper-Ramsey (GHR) resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulses spectroscopy with phase-modulation eliminating probe-induced frequency shifts at all orders in presence of various dissipative processes. Unlike frequency shifts extrapolation-based methods, a universal interrogation protocol based on $\pm\pi/4$ and $\pm3\pi/4$ phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultra-robust error signal gradient in presence of substantial uncompensated ac Stark-shifts. Such a scheme can be implemented in two flavours: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular and nuclear frequency metrology, mass spectrometry and to the field of precision spectroscopy. It might be designed using magic-wave induced transitions, two-photon excitation and magnetically-induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement.