Gravitationally Induced Non-Markovianity in Quantum Clocks

We show that general relativistic time dilation can act as a controllable source of non-Markovianity in the dynamics of delocalized quantum clocks coupled to structured environments. As a concrete setting, we model a delocalized quantum clock, a two-level Unruh-DeWitt detector interacting with a thermal scalar field with finite correlation time in a weak, static gravitational field. The gravitational redshift between spatially sepa- rated branches leads to a path-dependent sampling of the bath correlation functions and to an effective spectral mismatch between the arms of the interferometer. Within a second-order time-convolutionless expansion we derive a time-local master equation whose time-dependent rates depend explicitly on the redshift parameter and reduce to the usual Markovian Gorini-Kossakowski-Sudarshan-Lindblad generator when gravity is switched off or the bath becomes memoryless. Numerical evaluation for an Ohmic environment reveals gravitationally in- duced coherence revivals and information backflow, providing a genuine non-Markovian signature that can be quantified by standard trace-distance measures. We identify a resonance-like regime in which the gravitational detuning becomes comparable to the dominant bath frequencies, leading to a suppression of decoherence and an enhancement of entanglement lifetimes relative to the flat-space Markovian case. Finally, by comparing the size of the gravity-induced deviations to quantum projection noise in state-of-the-art optical clocks, we derive an analytic signal-to-noise ratio and show that, within our model, engineered low-frequency reservoirs could al- low gravity-controlled memory effects to be resolved above the shot-noise limit on few-hour integration times, whereas for fast thermal baths the effect remains QPN-limited and effectively unobservable.