[Paper Review] Optical Clocks in Space

S. Schiller, Theodor W. Hänsch+19 more|ArXiv.org|Aug 17, 2006

Advanced Frequency and Time Standards3 citations

TL;DR

This paper proposes using optical clocks on board Earth-orbiting satellites to enable ultra-precise tests of gravitational redshift and local position invariance, leveraging stable frequency comparisons between space-based and ground-based clocks. With sub-10−18 instability and accuracy, such missions could test the universality of fundamental constants' dependence on gravity with unprecedented precision, achieving 10−9 relative accuracy in LPI tests.

ABSTRACT

The performance of optical clocks has strongly progressed in recent years, and accuracies and instabilities of 1 part in 10^18 are expected in the near future. The operation of optical clocks in space provides new scientific and technological opportunities. In particular, an earth-orbiting satellite containing an ensemble of optical clocks would allow a precision measurement of the gravitational redshift, navigation with improved precision, mapping of the earth's gravitational potential by relativistic geodesy, and comparisons between ground clocks.

Motivation & Objective

• To enable high-precision tests of Einstein's gravitational redshift using optical clocks in space.
• To test the universality of local position invariance (LPI) by comparing clocks of different physical nature in Earth orbit.
• To map Earth's gravitational potential via relativistic geodesy using frequency comparisons between space and ground clocks.
• To improve space-based navigation and time dissemination with optical master clocks.
• To develop space-qualified optical frequency standards for future fundamental physics missions.

Proposed method

• Utilize a satellite-borne ensemble of optical clocks, including ion, cold-atom, and molecular clocks, to achieve high stability and accuracy.
• Perform frequency comparisons between space-based clocks and ground-based clocks to measure gravitational redshift via the relation (ν₁−ν₂)/ν = (U(r₂)−U(r₁))/c².
• Employ highly elliptical orbits to modulate the gravitational redshift signal over time, enabling high-stability tests without requiring absolute accuracy.
• Use laser ranging and precise orbit determination to determine the gravitational potential U(t) along the satellite trajectory with high accuracy.
• Stabilize clock lasers to ultra-stable optical cavities to minimize frequency instability and enable tests of local Lorentz invariance.
• Implement coherent optical time transfer links, potentially using femtosecond frequency combs and continuous-wave laser signals, to achieve sub-10−18 time transfer accuracy.

Experimental results

Research questions

• RQ1 Can optical clocks in space achieve the required stability and accuracy to test the gravitational redshift at the 10−8 relative level per orbit?
• RQ2 To what extent can the universality of local position invariance be tested using frequency comparisons between different types of optical clocks in Earth orbit?
• RQ3 What is the achievable sensitivity to variations in fundamental constants such as the fine structure constant α and the electron-to-nucleon mass ratio me/mN?
• RQ4 How accurately can the Earth's gravitational potential be mapped using relativistic geodesy with space-based optical clocks?
• RQ5 Can coherent optical time transfer links achieve the 10−18-level stability required for space-based optical frequency comparisons?

Key findings

• A satellite-based optical clock system could test the gravitational redshift with a relative accuracy of 1 part in 10^8 per orbital period, improving to better than 1 part in 10^9 after averaging over one year.
• An LPI test using a comparison between electronic and vibrational optical clocks in space could achieve a relative accuracy of 1×10−9, representing a 5–6 order of magnitude improvement over previous tests.
• The gravitational potential variation along a highly elliptical orbit (apogee ~36,000 km, perigee ~10,000 km) leads to a ΔU/c² ≈ 2×10−10, enabling measurable redshift modulation.
• The use of optical cavities in microgravity minimizes mechanical distortions, enhancing stability and enabling tests of the isotropy of light propagation.
• Time transfer with sub-10−18 stability over several hours is feasible only with advanced optical links, such as coherent continuous-wave laser systems or femtosecond frequency combs.
• Demonstrations like T2L2 (laser time transfer to Jason) are promising but fall short of the required 10−18 accuracy, necessitating new optical time transfer technologies.