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

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.

6 pages, 1 figure, 1 table

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• Gravitational interaction through a feedback mechanism
• A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties
• Gravitational time dilation as a resource in quantum sensing
• Gravitational dephasing in spontaneous emission of atomic ensembles in timed Dicke states
• Gravity as a classical channel and its dissipative generalization
• Decoherence of Atomic Ensembles in Optical Lattice Clocks by Gravity