Igor Pikovski

Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity by resolving time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts (SODS) due to the vacuum energy (vSODS), squeezing (sqSODS) and quantum corrections to the dynamics (qSODS) arise. We also demonstrate that the entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach to probe relativistic evolution of clocks for which a quantum description of proper time becomes necessary.

Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here we propose a quantum network of alkaline earth(-like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over $\sim$km-scale elevation differences and distributing one clock between them via a W-state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our non-local observable. We further demonstrate that $N$-atom entanglement within each node enhances the interrogation bandwidth by a factor of $N$. We discuss how our system can probe new facets of fundamental physics, such as the linearity, unitarity and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of curved spacetime uniquely enabled by quantum networks.