Optical atomic clocks currently represent the most precise timing tools in the world, leveraging electronic energy level transitions outside the atomic nucleus to achieve unparalleled accuracy in frequency and time measurements. However, their performance is constrained by the linewidth of atomic transitions and external environmental factors. Nuclear clocks, theoretically, offer a precision ten times greater than that of atomic clocks and are impervious to environmental influences, potentially revolutionizing precision measurement and fundamental physics research. A major challenge for nuclear clocks lies in their requirement for high-energy X-rays for excitation. Fortunately, scientists have discovered an element with an upper energy level lifetime of approximately 10³-10⁴ seconds, requiring only 8.4 eV of energy—within the VUV band (150 nm)—to excite its nuclear energy level transitions. This makes it the sole known element that can be directly excited by laser light. By doping this element into a VUV-transparent crystal, researchers can utilize 150 nm lasers to stimulate nuclear energy level transitions, potentially enhancing timing precision and ushering in a new generation of nuclear clocks.

Recently, a research team led by Ye Jun at NIST employed a VUV frequency comb to directly excite nuclear transitions. This groundbreaking work determined the absolute transition frequency and established a frequency ratio between nuclear clock transitions and atomic clocks for the first time, enhancing nuclear clock precision by a millionfold [1]. The team also accurately measured nuclear quadrupole splitting and extracted the intrinsic properties of isomers, marking the dawn of solid-state optical clocks based on nuclei. This research epitomizes the convergence of precision metrology, ultrafast intense field physics, nuclear physics, and fundamental physics.

Figure 1. Schematic diagram of the VUV optical frequency comb and spectral detection setup [1]

The experimental apparatus primarily comprises a VUV optical frequency comb and a spectral detection device. The researchers coupled pulses generated by a Yb-doped femtosecond fiber laser comb, possessing a power exceeding 40 W and a pulse width of less than 200 fs, into a femtosecond enhancement cavity. This arrangement boosted the average power within the cavity to 5-7 kW while locking one comb tooth to an atomic clock. The near-infrared pulses within the cavity were focused onto a xenon gas jet, resulting in a seventh harmonic with an average power of 200 µW, a center wavelength of 148.3 nm, and a single comb tooth power of 1 nW. During the experiment, a grazing incidence plate (GIP) directed 50% of the VUV optical frequency comb outside the cavity, where it struck the crystal. The resulting photons were collected by a reflective parabolic mirror, focused onto a PMT through a lens. The Yb-doped femtosecond fiber laser comb and the atomic clock produced a beat frequency (fbeat), which was mixed with the output of a direct digital synthesizer (DDS) to adjust the frequency of the Mephisto laser. A portion of the Mephisto laser locked the oscillator's cavity length via an acousto-optic modulator (AOM), maintaining precise synchronization between the near-infrared optical frequency comb and the atomic clock. Another portion stabilized the femtosecond enhancement cavity's length through the Pound-Drever-Hall (PDH) locking scheme, ensuring the optical frequency within the cavity remained consistent with the cavity's resonance frequency. Adjusting the AOM offset frequency allowed fine-tuning of the detuning between the fundamental frequency comb and the resonant cavity, mitigating plasma instability. By modifying the DDS offset frequency, the comb light's repetition rate could be altered without impacting fceo, enabling precise spectral scanning.

Figure 2. Schematic diagram of the VUV optical frequency comb mode-locking setup [1]

The researchers conducted a comprehensive spectral scan within a repetition frequency variation range of 2.8 Hz to pinpoint the transition frequency, uncovering six distinct spectral peaks, as depicted in Figure 3. By extending the single-shot fluorescence acquisition time, the element's relaxation time was determined to be 641(4) s through fitting. The transition center frequency was established through bidirectional scanning, with an uncertainty of 4 kHz and a full width at half maximum of 300 kHz.

Figure 3. Full spectral range scan results [1]

During the initial full-range scan shown in Figure 3, the fifth spectral line 'e' of the quadrupole structure (corresponding to ) was initially undetected. This line was anticipated to exhibit an intensity one-tenth that of the strongest spectral line. After determining the expected absolute frequency of the fifth spectral line using sum rules, the researchers repeated the scan at the corresponding frequency and observed a faint transition spectral line at . Figure 4 presents the absolute transition frequencies for the entire nuclear quadrupole. By appropriately averaging the quadrupole splitting diagram (neglecting higher-order moments), the transition frequency between the ground and excited states was calculated as 2,020,407,384,335(2) kHz, yielding a frequency ratio of 4.707072615078(5) between the nuclear clock and atomic clock.

Figure 4. Direct spectroscopic measurement of the nuclear electric quadrupole moment [1]

This study marks the first demonstration of a direct frequency linkage between an isotope transition and an atomic clock, significantly enhancing the precision of nuclear clock transition frequencies and directly resolving their nuclear quadrupole splitting structure. It offers a clear roadmap for constructing and refining nuclear clocks, heralding the era of nuclear optical clocks and having profound implications for fundamental physics, quantum physics, and precision measurement technology.

References: [1] Zhang, C., Ooi, T., Higgins, J.S. et al. Frequency ratio of the 229mTh nuclear isomeric transition and the 87Sr atomic clock. Nature 633, 63–70 (2024). [2] Cingöz, A. et al. Direct frequency comb spectroscopy in the extreme ultraviolet. Nature 482, 68–71 (2012)