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Письма в журнал технической физики

Measuring the effect of gravitational frequency shift doubling using a hydrogen clock-based quantum level

Vyacheslav F. Fateev, Fedor R. Smirnov, E. A. Rybakov

Published Jan 1, 2022• 1 citation
Publisher

Abstract

The effect of gravitational frequency shift doubling in a system of stationary and transported hydrogen quantum clocks in the Earth's gravitational field has been measured for the first time with an instability of 1·10-15. The clocks were separated in height by 34 m and connected by a radio channel based on optical fiber. The measured relative doubled "redshift" effect at this altitude was Delta fGR/fref=(-7.73± 1.61)· 10-15. Keywords: time dilation gravitational effect, gravitational frequency shift, quantum hydrogen clock.

DOI
10.21883/tpl.2022.04.53574.19062

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The effect of gravitational frequency shift doubling in a system of stationary and transported hydrogen quantum clocks in the Earth's gravitational field has been measured for the first time with an instability of 1·10-15. The clocks were separated in height by 34 m and connected by a radio channel based on optical fiber. The measured relative doubled "redshift" effect at this altitude was Delta fGR/fref=(-7.73± 1.61)· 10-15. Keywords: time dilation gravitational effect, gravitational frequency shift, quantum hydrogen clock.
According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.
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The generation, controls, and storage of the gravitationally induced photon echo using the 8.4 eV Thorium-229 nuclear clock transition on Earth are theoretically investigated. With its exceptionally narrow linewidth of approximately 1 mHz and high quality factor in the order of 101910^{19}1019, the Thorium-229 clock transition allows for the potential detection of gravitational-redshift effects at millimeter-scale altitude variations. Moreover, the 1740-second half lifetime of the Thorium-229 isomeric state allows for the slow movement of the system within its coherence time. Along this line, we explore the generation, controls, and storage of photon echo arising from a rotation induced inversion of the gravitational frequency shift in a single target or in multiple equally spaced samples. Our approach lays the foundation for the controllable gravitational quantum optics on Earth.