Exploring the dynamical interplay between mass-energy equivalence, interactions and entanglement in an optical lattice clock

TL;DR

This paper proposes protocols to investigate mass-energy equivalence effects in optical lattice clocks using entangled states, revealing how gravitational and quantum effects interplay to influence synchronization and entanglement.

Contribution

It introduces a dressing protocol to distinguish mass-energy effects and analyzes the interplay between interactions and gravitational redshift in quantum states.

Findings

Synchronization time depends on initial entanglement.

Entanglement can be generated through photon-mediated interactions.

Synchronization can serve as a metrological proxy.

Abstract

We propose protocols that probe manifestations of the mass-energy equivalence in an optical lattice clock (OLC) interrogated with spin coherent and entangled quantum states. To tune and uniquely distinguish the mass-energy equivalence effects (gravitational redshift and second order Doppler shift) in such a setting, we devise a dressing protocol using an additional nuclear spin state. We then analyze the dynamical interplay between photon-mediated interactions and gravitational redshift and show that such interplay can lead to entanglement generation and frequency synchronization dynamics. In the regime where all atomic spins synchronize, we show the synchronization time depends on the initial entanglement of the state and can be used as a proxy of its metrological gain compared to a classical state. Our work opens new possibilities for exploring the effects of general relativity on quantum coherence and entanglement in OLC experiments.