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arXiv:1812.00973

Doppler and collisional frequency shifts in trapped-atom clocks

Amar C. Vutha, Tom Kirchner, P. Dubé

Published Dec 3, 2018• 2 citations
arXivHTMLPDF

Abstract

Collisions with background gas particles can shift the resonance frequencies of atoms in atomic clocks. The internal quantum states of atoms can also become entangled with their motional states due to the recoil imparted by a collision, which leads to a further shift of the clock frequency through the relativistic Doppler shift. It can be complicated to evaluate the Doppler and collisional frequency shifts for clock atoms in such entangled states, but estimates of these shifts are essential in order to improve the accuracy of optical atomic clocks. We present a formalism that describes collisions and relativistic Doppler shifts in a unified manner, and can therefore be used to accurately estimate collisional frequency shifts in trapped-atom clocks.

DOI
10.48550/arxiv.1812.00973

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Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve 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 as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced 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 of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.