Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2308.03335

Standard quantum limit of finite-size optical lattice clock in estimating gravitational potential

Fumiya Nishimura, Yui Kuramochi, Kazuhiro Yamamoto

Published Aug 7, 2023• 0 citations
arXivHTMLPDF

Abstract

We evaluated the accuracy limit for estimating gravitational potential using optical lattice clocks by utilizing the quantum Cramér--Rao bound. We then compared the results for single-layer and multilayer optical lattice clocks. The results indicate that the lower bound of variance of the estimator of gravitational potential using finite-size optical lattice clocks diverges and recovers repeatedly as a function of time. Namely, the accuracy of the gravitational potential estimation is not a monotonic function of time owing to the effect of gravitational dephasing in finite-size optical lattice clock. Further, this effect creates an estimation accuracy limit when attempting to avoid the divergence of the lower bound. When the number of layers in the optical lattice clock is sufficiently large, the limit is independent of the optical lattice clock details. The time required to reach this limit is calculated to be approximately 33 hours for a three-dimensional optical lattice clock consisting of one million cadmium atoms due to Earth's gravity, and approximately the same for other atoms.

DOI
10.48550/arxiv.2308.03335

Related papers

Classical gravitational effect on the standard quantum limit of finite-size optical lattice clocks in estimating gravitational potential

Fumiya Nishimura, Yui Kuramochi, Kazuhiro Yamamoto

We evaluated the accuracy limit for estimating gravitational potential using optical lattice clocks by utilizing the quantum Cram\'er-Rao bound. We then compared the results for single-layer and multilayer optical lattice clocks. The results indicate that the lower bound of variance of the estimator of gravitational potential using finite-size optical lattice clocks diverges and recovers repeatedly as a function of time. Namely, the accuracy of the gravitational potential estimation is not a monotonic function of time owing to the effect of gravitational dephasing in finite-size optical lattice clocks. Further, this effect creates an estimation accuracy limit when attempting to avoid the divergence of the lower bound. When the number of layers in the optical lattice clock is sufficiently large, the limit is independent of the optical lattice clock details. The time required to reach this limit is calculated to be approximately 33 h for a three-dimensional optical lattice clock consisting of one million cadmium atoms due to Earth's gravity, and approximately the same for other atoms. This time is much longer than the current coherence time of $26\phantom{\rule{0.16em}{0ex}}\mathrm{s}$.

Physical Review A•Dec 28, 2023•0 citations

Decoherence of Atomic Ensembles in Optical Lattice Clocks by Gravity

Akio Kawasaki

Optical lattice clocks can now resolve the height difference below 1 mm within an atomic ensemble by means of gravitational redshift with integration over sufficient amount of time. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state in a single Ramsey sequence, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of a stability of $\lesssim 10^{-21}$ by introducing a single-layer-resolved imaging system for a three-dimensional optical lattice, and limits the 1 s stability of the clock around $10^{-19}$ for an atomic ensemble distributing symmetrically for the three axes, which is also a signal of the decoherence. With atoms in an entangled state, this can be the first observation of the decoherence of a quantum state by a gravitational effect, and the suppression of other systematic shifts to observe this decoherence seems feasible.

arXiv:2107.02405•Journal of the Physical Society of Japan•Feb 2, 2022•1 citation

Gravitational Dephasing in Optical Lattice Clocks

Akio Kawasaki

Optical lattice clocks can now resolve the height difference below 1 cm by means of the gravitational redshift. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of the stability of $\sim 10^{-21}$ by introducing single layer resolved imaging system for three dimensional optical lattice, and limits the 1 s stability of the clock at $10^{-19}$ without proper compensations. This can be the first observation of the decoherence of a quantum state by a gravitational effect, and the suppression of other systematic shifts to observe this gravitational dephasing seems feasible.

•Jul 6, 2021•0 citations

Resolving gravitational redshift with sub-millimeter height differences using spin-squeezed optical clocks

Deshui Yu, Jia Zhang, Shougang Zhang +2 more

Abstract The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential, also known as gravitational redshift, is one of the classical tests of Einstein’s theory of general relativity. Owing to their ultra-high accuracy and stability, state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference. Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing. Here, we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of 171Yb atoms. The numerical results illustrate that for a sample of 104 atoms, the atomic-collision-limited resolution of the vertical separation between two clocks can reach 0.48 mm, corresponding to a fractional gravitational redshift at the 10−20 level. In addition, the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms. Our work opens a door to the future spin-squeezing-enhanced test of general relativity.

Chinese Physics B•Apr 8, 2025•0 citations

Multiparameter quantum estimation in a photon system induced by gravitational redshift

Wei Ye, Hui Cao, Songtao Zhang +6 more

As photons propagate through curved spacetime, gravitational effects become unavoidable. In particular, gravitational redshift can induce significant distortion in photon wave packets, making it es?sential to investigate parameter estimation within this context. While previous research has focused on single-parameter estimation using the quantum Cramer-Rao bound, the multiparameter scenario remains largely unexplored. In this work, we investigate multiparameter quantum estimation for a photon system subject to gravitational redshift under both amplitude-damping and Ohmic-like dephasing channels. Our analysis reveals that the quantum Cramer-Rao bound fails to provide a tight error bound for the two-parameter estimation involving the initial phase and weight parameters inboth types of noisy channels. To overcome this limitation, we numerically compute two tighter error bounds, i.e., the Holevo Cramer-Rao bound and the Nagaoka bound, when utilizing a semidefinite program. We demonstrate that the Nagaoka bound yields the tightest error bound among all considered bounds, consistent with the general hierarchy of multiparameter quantum estimation. Furthermore, for the three-parameter estimation, including the initial weight parameter, the phase parameter, and the strength of gravitational redshift, we observe significantly enhanced estimation precision in the strong-coupling regime compared to the weak-coupling regime under the amplitude-damping channel. Similarly, in the Ohmic-like dephasing channel, the sub-Ohmic regime consistently affords higher precision than the Ohmic and super-Ohmic regimes.

quant-pharXiv:2608.00550•Aug 4, 2026•0 citations

Optical-lattice-clock-network Technology for Gravitational Potential Sensing

Katsuya Oguri, Tomoya Akatsuka, Hiromitsu Imai +2 more

Optical lattice clocks have an ultrahigh frequency accuracy that exceeds that of cesium atomic clocks by a few orders of magnitude, enabling quantum sensing of gravitational potential equivalent to an altitude difference of only 1 cm on the Earth's surface.An optical-lattice-clock network, in which multiple optical lattice clocks are interconnected by optical fibers, is expected to become a new infrastructure, such as for a real-time sensing network of crustal movements with 1-cm-level accuracy.In this article, we introduce the elemental technologies comprising an optical-lattice-clock network.We also report on the construction of the ultrahigh-precision optical frequency transmission fiber link in the Tokyo metropolitan area and the experiment to evaluate its transmission stability.

NTT technical review•Jun 1, 2023•3 citations
We evaluated the accuracy limit for estimating gravitational potential using optical lattice clocks by utilizing the quantum Cramér--Rao bound. We then compared the results for single-layer and multilayer optical lattice clocks. The results indicate that the lower bound of variance of the estimator of gravitational potential using finite-size optical lattice clocks diverges and recovers repeatedly as a function of time. Namely, the accuracy of the gravitational potential estimation is not a monotonic function of time owing to the effect of gravitational dephasing in finite-size optical lattice clock. Further, this effect creates an estimation accuracy limit when attempting to avoid the divergence of the lower bound. When the number of layers in the optical lattice clock is sufficiently large, the limit is independent of the optical lattice clock details. The time required to reach this limit is calculated to be approximately 33 hours for a three-dimensional optical lattice clock consisting of one million cadmium atoms due to Earth's gravity, and approximately the same for other atoms.
We evaluated the accuracy limit for estimating gravitational potential using optical lattice clocks by utilizing the quantum Cram\'er-Rao bound. We then compared the results for single-layer and multilayer optical lattice clocks. The results indicate that the lower bound of variance of the estimator of gravitational potential using finite-size optical lattice clocks diverges and recovers repeatedly as a function of time. Namely, the accuracy of the gravitational potential estimation is not a monotonic function of time owing to the effect of gravitational dephasing in finite-size optical lattice clocks. Further, this effect creates an estimation accuracy limit when attempting to avoid the divergence of the lower bound. When the number of layers in the optical lattice clock is sufficiently large, the limit is independent of the optical lattice clock details. The time required to reach this limit is calculated to be approximately 33 h for a three-dimensional optical lattice clock consisting of one million cadmium atoms due to Earth's gravity, and approximately the same for other atoms. This time is much longer than the current coherence time of 26s26\phantom{\rule{0.16em}{0ex}}\mathrm{s}26s.
Optical lattice clocks can now resolve the height difference below 1 mm within an atomic ensemble by means of gravitational redshift with integration over sufficient amount of time. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state in a single Ramsey sequence, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of a stability of ≲10−21\lesssim 10^{-21}≲10−21 by introducing a single-layer-resolved imaging system for a three-dimensional optical lattice, and limits the 1 s stability of the clock around 10−1910^{-19}10−19 for an atomic ensemble distributing symmetrically for the three axes, which is also a signal of the decoherence. With atoms in an entangled state, this can be the first observation of the decoherence of a quantum state by a gravitational effect, and the suppression of other systematic shifts to observe this decoherence seems feasible.
Optical lattice clocks can now resolve the height difference below 1 cm by means of the gravitational redshift. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of the stability of ∼10−21\sim 10^{-21}∼10−21 by introducing single layer resolved imaging system for three dimensional optical lattice, and limits the 1 s stability of the clock at 10−1910^{-19}10−19 without proper compensations. This can be the first observation of the decoherence of a quantum state by a gravitational effect, and the suppression of other systematic shifts to observe this gravitational dephasing seems feasible.
Abstract The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential, also known as gravitational redshift, is one of the classical tests of Einstein’s theory of general relativity. Owing to their ultra-high accuracy and stability, state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference. Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing. Here, we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of 171Yb atoms. The numerical results illustrate that for a sample of 104 atoms, the atomic-collision-limited resolution of the vertical separation between two clocks can reach 0.48 mm, corresponding to a fractional gravitational redshift at the 10−20 level. In addition, the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms. Our work opens a door to the future spin-squeezing-enhanced test of general relativity.
As photons propagate through curved spacetime, gravitational effects become unavoidable. In particular, gravitational redshift can induce significant distortion in photon wave packets, making it es?sential to investigate parameter estimation within this context. While previous research has focused on single-parameter estimation using the quantum Cramer-Rao bound, the multiparameter scenario remains largely unexplored. In this work, we investigate multiparameter quantum estimation for a photon system subject to gravitational redshift under both amplitude-damping and Ohmic-like dephasing channels. Our analysis reveals that the quantum Cramer-Rao bound fails to provide a tight error bound for the two-parameter estimation involving the initial phase and weight parameters inboth types of noisy channels. To overcome this limitation, we numerically compute two tighter error bounds, i.e., the Holevo Cramer-Rao bound and the Nagaoka bound, when utilizing a semidefinite program. We demonstrate that the Nagaoka bound yields the tightest error bound among all considered bounds, consistent with the general hierarchy of multiparameter quantum estimation. Furthermore, for the three-parameter estimation, including the initial weight parameter, the phase parameter, and the strength of gravitational redshift, we observe significantly enhanced estimation precision in the strong-coupling regime compared to the weak-coupling regime under the amplitude-damping channel. Similarly, in the Ohmic-like dephasing channel, the sub-Ohmic regime consistently affords higher precision than the Ohmic and super-Ohmic regimes.
Optical lattice clocks have an ultrahigh frequency accuracy that exceeds that of cesium atomic clocks by a few orders of magnitude, enabling quantum sensing of gravitational potential equivalent to an altitude difference of only 1 cm on the Earth's surface.An optical-lattice-clock network, in which multiple optical lattice clocks are interconnected by optical fibers, is expected to become a new infrastructure, such as for a real-time sensing network of crustal movements with 1-cm-level accuracy.In this article, we introduce the elemental technologies comprising an optical-lattice-clock network.We also report on the construction of the ultrahigh-precision optical frequency transmission fiber link in the Tokyo metropolitan area and the experiment to evaluate its transmission stability.