Exponential scaling of clock stability with atom number

TL;DR

This paper proposes a method to exponentially improve clock stability by combining multiple atomic ensembles, leveraging phase noise reduction techniques and quantum phase measurement, leading to significant performance gains in trapped-atom clocks.

Contribution

It introduces a theoretical framework for exponentially enhancing clock stability using multiple atomic ensembles with different frequencies or probe periods.

Findings

Frequency variance reduced by M 2^-M times with M ensembles

Exponential improvement achievable with ensembles of lower-frequency transitions

Quantum phase measurement enables smaller ensemble sizes

Abstract

In trapped-atom clocks, the primary source of decoherence is often the phase noise of the oscillator. For this case, we derive theoretical performance gains by combining several atomic ensembles. For example, M ensembles of N atoms can be combined with a variety of probe periods, to reduce the frequency variance to M 2^-M times that of standard Ramsey clocks. A similar exponential improvement is possible if the atomic phases of some of the ensembles evolve at reduced frequencies. These ensembles may be constructed from atoms or molecules with lower-frequency transitions, or generated by dynamical decoupling. The ensembles with reduced frequency or probe period are responsible only for counting the integer number of 2 pi phase wraps, and do not affect the clock's systematic errors. Quantum phase measurement with Gaussian initial states allows for smaller ensemble sizes than Ramsey spectroscopy.