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arXiv:2507.00533

Gravitational photon echo

Wen-Te Liao, Sven Ahrens

Published Jul 1, 2025• 0 citations
arXivHTMLPDF

Abstract

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 $10^{19}$, 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.

DOI
10.48550/arxiv.2507.00533

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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.
Abstract Gravitational redshift, a striking prediction of Einstein’s theory of general relativity, has been experimentally confirmed on Earth. Yet, exploiting this effect as a controllable resource in coherent quantum systems remains challenging. Here, we theoretically demonstrate gravitationally induced γ -ray photon echoes in solid-state Thorium-229 targets using the 8.4 eV nuclear clock transition, which, owing to its nuclear origin, extends the definition of γ rays down into the vacuum ultraviolet regime. With its ultranarrow linewidth (1 mHz), exceptional quality factor (10 19 ), and long 1740 s isomeric half-life, this transition offers a compact solid-state platform sensitive to millimeter-scale gravitational variations. We further investigate the gravitational photon echo in a spinless crystal with a coherence time on the order of seconds. Controlled target rotations enable the generation, manipulation, and storage of γ -ray echoes, paving the way for a gravitationally driven γ -ray memory, a narrowband γ -ray source, and relativistic geodesy.
Atomic clocks achieve extraordinary precision through quantum control over large ensembles of atoms, with precision increasing and atom number advancing steadily. Emerging nuclear clock technology encodes clock states in nuclear rather than electronic transitions, offering a new frontier for precision measurement. Here we study whether a large ensemble of such clock nuclei could be used to observe their mutual gravitational interaction. We investigate the gravitational redshift induced by neighboring atoms, including nuclear energy superpositions as sources of gravity, giving rise to a genuinely quantum gravitational interaction between pairs of nuclei. We find that the resulting clock frequency shift due to mutual gravity may become non-negligible for a macroscopic number of nuclei, for instance in a solid-state thorium clock, and we propose approaches to mitigate electromagnetic field effects by exploiting spatial symmetry and high-precision spectroscopy. We further discuss how energy-induced mass superpositions could be directly probed using external gravitational field sensors. By contrast, observing gravity-induced entanglement involving clocks would require substantially greater experimental advances due to decoherence from spontaneous emission. Taken together, our results suggest that nuclear clocks, either alone or in combination with complementary sensors such as optomechanical systems, may offer a future route toward probing gravity at short distances and testing gravitating quantum source masses beyond the Newtonian limit.
The laser-accessible nuclear transition in the thorium-229 isotope has been identified as a promising candidate for the realization of an optical nuclear clock. Such a nuclear clock might rival or outperform current optical clocks based on electron-shell transitions in atoms or ions, is expected to be more robust against external perturbations, and provides enhanced sensitivity in clock-based tests of fundamental principles of physics. Here, we implement a thorium-229 nuclear clock by stabilizing a continuous-wave laser to the 148 nm nuclear transition with rapid feedback based on continuous absorption spectroscopy. The thorium-229 nuclei are embedded into a millimeter-sized, room temperature calcium fluoride crystal. A subharmonic of the 148 nm radiation is continuously compared to a Yb+ single-ion clock. The nuclear clock shows a simple shot-noise limited scaling of the fractional frequency instability of 3⋅10−12τ/s3\cdot 10^{-12} \sqrt{τ/\text{s}}3⋅10−12τ/s​ where τττ is the averaging time, approaching 10−1510^{-15}10−15 instabilities over 1 day of continuous operation. Improvements of the instability by several orders of magnitude can be projected for future solid-state nuclear clocks. We use the nuclear clock to constrain models of ultralight dark matter by searching for periodic fluctuations and slow drifts in the nuclear transition energy, on time scales between 20 s and 1 day. Drawing benefit from the enhanced sensitivity of the thorium-229 transition, these constraints compete with the best atomic clocks concerning dark matter coupling to photons and go beyond previous measurements regarding coupling to the strong force and quarks.
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.
Gravitational time dilation implies that clocks held at different heights accumulate different proper times. We analyze a memory-assisted quantum clock interferometer in which a frequency-bin photonic clock is stored in two vertically separated quantum memories for a controllable duration, such that the joint state evolves in a quantum superposition of two proper times. After retrieval, the photonic modes interfere in a Hong-Ou-Mandel (HOM) interferometer, for which we derive analytic expressions for the resulting multiphoton detection statistics. Extending this HOM-based scheme from entangled photon pairs to frequency-entangled 2N-photon inputs, we show that the proper-time dependent phase is amplified by a factor N, leading to an N-times faster collapse and revival of the interference signal compared with the two-photon case. Incorporating finite memory efficiency and lifetime, we identify regimes where this modulation remains observable. For parameters compatible with demonstrated Rb and Cs memories and achievable optical frequency separations, the first collapse occurs for height differences in the order of 10-100 m with subsecond to few-second storage times, while suitable rare-earth ion and alkali memory combinations can reduce the required height to the few-metre scale. These results establish near-term laboratory conditions for observing entanglement dynamics driven by gravitational time dilation in a photonic platform.
The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics.This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined.Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field.All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times.This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available.Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations.Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed.It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations.As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too.Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.