Frequency ratio of the $^{229\mathrm{m}}$Th nuclear isomeric transition and the $^{87}$Sr atomic clock (2406.18719v2)

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.

Direct Frequency Link Between a Thorium-229 Nuclear Transition and Strontium Atomic Clock

This paper investigates the linking of the frequency ratio of Thorium-229 ($^{229m}$Th) nuclear transition and the strontium (Sr) atomic clock, introducing a sophisticated method that may herald advancements in precision metrology and fundamental physics. A low-energy nuclear transition in $^{229m}$Th, uniquely accessible with vacuum ultraviolet (VUV) sources, has long been proposed as a promising cornerstone for nuclear clocks. However, a crucial gap has been direct spectroscopy of the nuclear structure and its frequency connectivity to atomic clocks. This paper makes significant strides to bridge this gap by embedding $^{229m}$Th in a CaF$_2$ solid-state host and performing VUV frequency comb spectroscopy.

Key Methodological Contributions

• The use of a VUV frequency comb, frequency-stabilized to correspond to the JILA strontium clock, allows for direct excitation of the $^{229m}$Th nuclear transition. This innovative approach establishes an absolute frequency link between nuclear and electronic transitions.
• The experimental setup featured a femtosecond enhancement cavity with coherent high harmonic generation, providing the necessary VUV radiation. The harmonic coherence and narrow pulse durations facilitated precision spectroscopy of the $^{229m}$Th transition.

Results and Interpretations

• Direct resonant excitation of the $^{229m}$Th transition was achieved with an unprecedented precision down to the kHz level in absolute frequency, narrowing down the transition frequency uncertainty by approximately six orders of magnitude compared to previous estimates.
• The paper revealed the nuclear quadrupole structure of the isomeric transition, identifying four dominant spectral peaks corresponding to quadrupole interactions of $^{229m}$Th nuclei with the crystal's electric field gradient. These findings are pivotal in understanding the nuclear hyperfine structure.

Theoretical and Practical Implications

• The refined frequency determination of the $^{229m}$Th nuclear transition offers prospects for testing fundamental physics constants, such as probing variations in the fine structure constant and strong interaction parameters. The insensitivity of the $^{229m}$Th transition to environmental disturbances heightens its suitability for portable, high-precision clock applications.
• The realization of a nuclear-based optical clock taps into long-lived nuclear states, augmenting the ability to conduct timekeeping with potential impacts on quantum technology, metrology, and various fields requiring extreme precision.

Prospective Developments

The successful linkage of nuclear and atomic clocks portends future attempts to further refine transition measurements. It also opens avenues for the development of continuous wave VUV lasers for coherent control over nuclear states, potentially enhancing accuracy and coherence in clock operations. Avenues for exploration include the impact of material properties on nuclear transitions, which could provide vital insights into nuclear physics and crystal engineering.

This paper demonstrates a major advancement in the interplay of precision spectroscopy, ultrafast optics, and nuclear physics, paving pathways for the future evolution of next-generation timekeeping technologies and their myriad applications across scientific disciplines.