Quantum signatures of proper time in optical ion clocks

Abstract

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.

10 pages, 2 Figures

References in corpus (15)

• Resolving the gravitational redshift within a millimeter atomic sample
• High precision differential clock comparisons with a multiplexed optical lattice clock
• General relativistic effects in quantum interference of photons
• High-Stability Single-Ion Clock with $5.5\times 10^{-19}$ Systematic Uncertainty
• Will a decaying atom feel a friction force?
• General relativistic effects in quantum interference of "clocks"
• Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks
• Entanglement dynamics of photon pairs and quantum memories in the gravitational field of the earth
• A coupling prescription for post-Newtonian corrections in Quantum Mechanics
• Testing quantum theory on curved space-time with quantum networks
• Quantum time dilation in a gravitational field
• Probing curved spacetime with a distributed atomic processor clock
• Atomic clock interferometry using optical tweezers
• Witnessing mass-energy equivalence with trapped atom interferometers
• On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks