Witnessing mass-energy equivalence with trapped atom interferometers

Abstract

We propose an experimental setup to probe the interplay between the quantum superposition principle and gravitational time dilation arising from the mass-energy equivalence. It capitalizes on state-of-the-art atom interferometers that can keep atoms trapped in a superposition of heights in Earth's gravitational field for exceedingly long times, reaching the minute scale. Our proposal consists of adding two additional laser pulses to the existing experiments that would set up a clock trapped at a superposition of heights, reading a quantum superposition of relativistic proper times. We develop a method to include relativistic corrections to Bloch oscillations, which describe the trapped part of the interferometer. We derive the trajectories and corresponding phases acquired in each arm of the interferometer. We then show that a superposition of proper times manifests in the interference pattern in two ways: visibility modulations and a shift of the atom's resonant frequency. We argue that the latter might be observable with current technology.

6+11 pages, 3 figures; accepted in Quantum

References in corpus (20)

• Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms
• Resolving the gravitational redshift within a millimeter atomic sample
• Quantum State Engineering and Precision Metrology using State-Insensitive Light Traps
• A clock with $8\times 10^{-19}$ systematic uncertainty
• High precision differential clock comparisons with a multiplexed optical lattice clock
• Atom interferometry with the Sr optical clock transition
• Measurement of the Gravity-Field Curvature by Atom Interferometry
• General relativistic effects in quantum interference of photons
• A trapped atom interferometer with ultracold Sr atoms
• Delocalization-enhanced Bloch oscillations and driven resonant tunneling in optical lattices for precision force measurements
• Coherence limits in lattice atom interferometry at the one-minute scale
• Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks
• Atom interferometry based on light pulses : application to the high precision measurement of the ratio h/m and the determination of the fine structure constant
• Exploring the dynamical interplay between mass-energy equivalence, interactions and entanglement in an optical lattice clock
• Atom interferometers in weakly curved spacetimes using Bragg diffraction and Bloch oscillations
• Quantum time dilation in a gravitational field
• Finite Pulse-Time Effects in Long-Baseline Quantum Clock Interferometry
• Atomic clock interferometry using optical tweezers
• Mass-energy equivalence in gravitationally bound quantum states of the neutron
• Universality of quantum time dilation

Cited by in corpus (1)

• Quantum signatures of proper time in optical ion clocks