Detecting gravitational decoherence with clocks: Limits on temporal resolution from a classical channel model of gravity

TL;DR

This paper explores how classical models of gravity impose fundamental limits on the precision and coherence of quantum clocks, revealing intrinsic decoherence and temporal resolution constraints.

Contribution

It introduces a classical channel model of gravity to analyze decoherence and temporal resolution limits in quantum clocks, linking gravitational effects to clock dephasing.

Findings

Decoherence rates scale with the number of clocks and their configuration.

Classical gravity models predict finite dephasing rates due to non-local interactions.

A fundamental limit on time accuracy is intrinsic to each clock.

Abstract

The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modelled as a two level systems. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. In particular, we focus on the decoherence rates and temporal resolution of arrays of $N$ clocks showing how the minimum dephasing rate scales with $N$, and the spatial configuration. Furthermore, we consider the gravitational redshift between a clock and massive particle and show that a classical channel model of gravity predicts a finite dephasing rate from the non-local interaction. In our model we obtain a fundamental limitation in time accuracy that is intrinsic to each clock.