On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks

TL;DR

This paper explores the potential to detect quantum effects on relativistic time dilation using optical lattice clocks, proposing experimental protocols and analyzing noise impacts to identify measurable quantum relativistic phenomena.

Contribution

It introduces a theoretical framework for observing quantum relativistic time dilation effects in optical clocks and assesses their detectability with current and near-future technology.

Findings

Quantum states can exhibit time dilation effects beyond classical predictions.

Current $^{24} ext{Mg}$ optical clocks could detect these effects if technical challenges are overcome.

The effect remains just out of reach for current $^{87} ext{Sr}$ clocks.

Abstract

We derive the predicted time dilation of delocalized atomic clocks in an optical lattice setup in the presence of a gravitational field to leading order in quantum relativistic corrections. We investigate exotic quantum states of motion whose relativistic time dilation is outside of the realm of classical general relativity, finding a regime where $^{24}\mathrm{Mg}$ optical lattice clocks currently in development would comfortably be able to detect this quantum effect (if the technical challenge of generating such states can be met and the expected accuracy of such clocks can be attained). We provide a detailed experimental protocol and analyse the effects of noise on our predictions. We also show that the magnitude of our predicted quantum relativistic time dilation effect remains just out of detectable reach for the current generation of $^{87}\mathrm{Sr}$ optical lattice clocks. Our calculations agree with the predicted time dilation of classical general relativity when restricting to Gaussian states.