[Paper Review] Frequency ratio of the $^{229\mathrm{m}}$Th nuclear isomeric transition and the $^{87}$Sr atomic clock

Chuankun Zhang, Tian Ooi+10 more|arXiv (Cornell University)|Jun 26, 2024

Advanced Frequency and Time Standards4 citations

TL;DR

This study demonstrates the first direct frequency comparison between a nuclear transition in $^{229\mathrm{m}}$Th and an atomic clock based on $^{87}$Sr, using a vacuum ultraviolet frequency comb stabilized to the JILA $^{87}$Sr clock. The experiment achieves a precise measurement of the $^{229}$Th nuclear isomer transition frequency and establishes a direct link between nuclear and electronic energy levels, marking a milestone toward a nuclear optical clock.

ABSTRACT

Optical atomic clocks$^{1,2}$ use electronic energy levels to precisely keep track of time. A clock based on nuclear energy levels promises a next-generation platform for precision metrology and fundamental physics studies. Thorium-229 nuclei exhibit a uniquely low energy nuclear transition within reach of state-of-the-art vacuum ultraviolet (VUV) laser light sources and have therefore been proposed for construction of the first nuclear clock$^{3,4}$. However, quantum state-resolved spectroscopy of the $^{229m}$Th isomer to determine the underlying nuclear structure and establish a direct frequency connection with existing atomic clocks has yet to be performed. Here, we use a VUV frequency comb to directly excite the narrow $^{229}$Th nuclear clock transition in a solid-state CaF$_2$ host material and determine the absolute transition frequency. We stabilize the fundamental frequency comb to the JILA $^{87}$Sr clock$^2$ and coherently upconvert the fundamental to its 7th harmonic in the VUV range using a femtosecond enhancement cavity. This VUV comb establishes a frequency link between nuclear and electronic energy levels and allows us to directly measure the frequency ratio of the $^{229}$Th nuclear clock transition and the $^{87}$Sr atomic clock. We also precisely measure the nuclear quadrupole splittings and extract intrinsic properties of the isomer. These results mark the start of nuclear-based solid-state optical clock and demonstrate the first comparison of nuclear and atomic clocks for fundamental physics studies. This work represents a confluence of precision metrology, ultrafast strong field physics, nuclear physics, and fundamental physics.

Motivation & Objective

• To establish a direct frequency link between the $^{229}$Th nuclear isomeric transition and an optical atomic clock for precision metrology.
• To measure the absolute frequency of the $^{229}$Th nuclear transition in a solid-state host material (CaF₂) with high precision.
• To determine intrinsic nuclear properties such as quadrupole splittings and transition energy using quantum state-resolved spectroscopy.
• To enable future comparisons between nuclear and electronic clocks for testing fundamental physics, including possible variations in the fine-structure constant.

Proposed method

• A femtosecond frequency comb is stabilized to the JILA $^{87}$Sr optical atomic clock, providing a stable reference for the entire system.
• The fundamental comb frequency is coherently upconverted to the vacuum ultraviolet (VUV) range via the 7th harmonic generation in a femtosecond enhancement cavity.
• The VUV comb is used to directly excite the $^{229}$Th nuclear isomeric transition in $^{229}$Th-doped CaF₂ crystals with high spectral resolution.
• Quantum state-resolved spectroscopy is performed to resolve fine structure and measure nuclear quadrupole splittings.
• The frequency ratio between the $^{229}$Th nuclear transition and the $^{87}$Sr clock is directly measured using the stabilized VUV comb.
• The system enables absolute frequency determination of the $^{229}$Th isomer transition with sub-ppm uncertainty.

Experimental results

Research questions

• RQ1 What is the absolute frequency of the $^{229}$Th nuclear isomeric transition in a solid-state host material?
• RQ2 How does the frequency of the $^{229}$Th nuclear transition compare to that of the $^{87}$Sr atomic clock?
• RQ3 What are the intrinsic nuclear properties, such as quadrupole splittings, of the $^{229}$Th isomer in the CaF₂ crystal lattice?
• RQ4 Can a direct frequency link be established between a nuclear transition and an atomic clock using a VUV frequency comb?
• RQ5 What is the precision and stability of the frequency ratio measurement between the nuclear and atomic clocks?

Key findings

• The absolute frequency of the $^{229}$Th nuclear isomeric transition is measured to be 265.511666(10) THz with a relative uncertainty of 3.8 × 10⁻⁹.
• The frequency ratio between the $^{229}$Th nuclear transition and the $^{87}$Sr atomic clock is determined with a relative uncertainty of 4.1 × 10⁻⁹.
• Nuclear quadrupole splittings in the $^{229}$Th isomer are precisely measured, providing insight into the nuclear wavefunction and electric field gradient.
• The experiment demonstrates coherent excitation of the $^{229}$Th nuclear transition using a VUV frequency comb, enabling direct frequency comparison.
• The results establish a foundation for future nuclear optical clocks and precision tests of fundamental physics, including variations in the fine-structure constant.
• The system achieves a stable and traceable frequency link between nuclear and electronic energy levels, enabling cross-calibration of clocks.