Extending the fundamental limit of atomic clock stability

TL;DR

This paper extends the fundamental stability limits of optical atomic clocks by modeling multi-level atoms and identifying protocols that improve stability by up to 5.4 dB, especially for trapped-ion systems.

Contribution

It introduces a generalized multi-level atom model for optical clocks, enabling detection of decay events and significantly enhancing frequency stability bounds.

Findings

Frequency stability improved by up to 4.5 dB over two-level models.

Further stability enhancement of approximately 5.4 dB for Bell state comparisons.

Provides a detailed protocol for $^{27}$Al$^{+}$ optical ion clock interrogation.

Abstract

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.