Current Progress on ²²⁹Th Nuclear Clock

Abstract

The ²²⁹Th nuclear clock, based on a low-energy nuclear transition, has attracted significant interest as a next-generation time and frequency standard. It is expected to surpass current leading optical atomic clocks in performance. Because nuclear transitions are naturally isolated from external electromagnetic fields, their sensitivity to blackbody radiation and environmental noise is much lower than that of electronic transitions. This gives the nuclear clock a unique advantage in both stability and accuracy. This paper reviews the current progress in nuclear clock research, focusing on the physical properties of the ²²⁹Th isomer, the operating principles, and the primary implementation methods of the nuclear clock. Comparing key technical approaches, specifically trapped ions and thorium-doped crystals, and introducing the VUV frequency comb technology used to drive the nuclear transition. Finally, we provide an outlook on the future development of the field.

1. Introduction

The earliest time standards were based on celestial motion, where one rotation of the Earth defined a day and one orbit around the Sun defined a year. While astronomical time is perceptible and direct, it is also unstable. Limited by factors such as the Earth’s irregular rotation and atmospheric dynamics, its long-term stability is only about ${10}^{-8}$, which is sufficient only for basic astronomical timekeeping [1,2]. As the demand for higher stability grew, the first cesium atomic clock (the Essen–Parry clock) was developed in 1955 [3]. The fundamental principle of the atomic clock is based on quantum transitions, utilizing the transition frequency of an atom to define the unit of time, which results in stronger resistance to environmental factors. As the technology matured, this standard was formally adopted at the 13th General Conference on Weights and Measures (CGPM) in 1967, defining the “second” as 9,192,631,770 periods of the cesium-133 atom transition. Since then, more stable clocks, such as optical lattice clocks, have rapidly emerged. In July 2025, the Marshall group [4] from the National Institute of Standards and Technology (NIST) reported the optical clock with the best performance to date; this $A{l}^{+}$ ion clock can achieve a short-term stability of $3.5\times {10}^{-16}/\sqrt{\tau }$ and an uncertainty of $5.5\times {10}^{-19}$.

However, traditional atomic clocks still face unavoidable limitations, as all existing clocks rely on transitions between electronic energy levels. Although optical clocks have significantly improved the Q-factor and reduced systematic errors, electronic levels are naturally coupled to external fields, making the electron shell highly sensitive to environmental disturbances [5]. Therefore, even though optical clocks have achieved high performance, further improvements are limited by a series of systematic errors and extreme engineering requirements. For example, it is necessary to create a near-ideal room-temperature blackbody radiation environment for the atoms, using specialized shielding to control temperature uniformity and achieve milli-Kelvin precision. Active servo electrodes and magnetic field calibration schemes are required to suppress frequency shifts caused by residual electric and magnetic fields [6]. Therefore, to break through the limitations of traditional atomic clocks and move toward even higher precision and stability, it is essential to find a new type of frequency reference that can minimize the effects of external fields, temperature, and density. This need has driven researchers to shift their focus to deeper, more robust microscopic structures, aiming to build the next generation of time and frequency standards at a more fundamental level of quantum energy.

In sharp contrast to traditional atomic clocks, the energy levels within the nucleus are governed by strong interaction. Its spatial scale is about five orders of magnitude smaller than its electron distribution, making it inherently more isolated from the external electromagnetic environment. The natural characteristic of being extremely insensitive to external perturbations makes nuclear transitions an ideal candidate for building the next generation of ultra-high-precision time and frequency standards. Their potential systematic uncertainty is far below what the most advanced optical atomic clocks can achieve. At the same time, it also shows significant application potential across a broader range of scientific and technological fields. First, in terms of the precision testing of fundamental physical constants, the nuclear clock can serve as a highly sensitive platform for detecting potential variations in fundamental physical constants (such as the fine-structure constant $\alpha$) over time [7]. Second, the nuclear clock offers unique advantages in measuring gravitational redshift and detecting topological gravitational effects. It is expected to push the testing of relativity from the current levels of ${10}^{-6}$ to ${10}^{-7}$ down to ${10}^{-8}$ or even higher precision [8]. Third, the high reproducibility of the nuclear clock and its robustness to environmental noise make it an important tool for dark matter detection [9]. Fourth, the nuclear clock holds great potential for high-demand scenarios such as deep-space navigation, the construction of inter-satellite time references, and synchronization in quantum communication networks. Its superior stability is set to significantly improve synchronization capabilities over long time scales [10].

This article systematically reviews theoretical and experimental progress in nuclear clock research, focusing on schemes represented by the low-energy nuclear isomer of ²²⁹Th. It addresses both the intrinsic physics of nuclear energy levels and transitions, while also emphasizing the key technological chain required to implement a nuclear clock—particularly the central role of optical frequency combs in frequency calibration, laser stabilization, frequency transfer, and high-precision spectroscopy. Finally, providing future perspectives on ²²⁹Th nuclear clock research.

2. Theoretical Foundations of the Nuclear Clock Transition

The energy level structure of an atomic nucleus originates from the strong interaction between nucleons. Its typical excitation energies usually range from keV to MeV, which means most nuclear transitions are far higher than electronic binding energies, making them difficult to excite directly using optical methods. Among these excited states, certain ones with long lifetimes are known as nuclear isomers. Nuclear isomers generally exhibit long lifetimes because transitions between the excited and ground states are significantly suppressed—due to differences in spin quantum numbers, structural deformation, or multipole selection rules. These lifetimes can range from seconds to hours or even longer, allowing these excited states to serve as highly stable quantum reference levels. A long lifetime implies an extremely narrow natural linewidth and an ultra-high quality factor (Q), making nuclear isomers an ideal physical platform for building ultra-stable frequency standards.

Both theoretical predictions and experimental studies indicate that the first excited state of this isotope has an energy of only a few eV (as shown in Figure 1). This is five to six orders of magnitude lower than any other known nuclear excited state, making it possible to excite it directly with vacuum ultraviolet (VUV) light. It is currently the only known nuclear excited state with an energy that falls within the VUV spectrum. This extremely low-energy nuclear state arises from a slight energy difference between two nearly degenerate quasiparticle configurations within the nuclear structure, resulting in the rare, low-energy “nuclear clock transition.” [11]. The isomeric state of ²²⁹Th offers the possibility of optical manipulation, while remaining extremely insensitive to external perturbations—since the spatial scale of the nucleus is much smaller than that of the electron cloud. These combined advantages make it a unique candidate system for building nuclear clocks. It is worth mentioning that the nucleus is not a single point relative to the electron cloud. It possesses a magnetic dipole moment, behaving much like a miniature bar magnet. Its charge distribution is typically not spherical but rather slightly prolate, resembling a rugby ball. This deformation is described by the electric quadrupole moment. At the same time, the electron cloud moving at high speeds outside the nucleus generates complex and subtle magnetic and electric field distributions at the location of the nucleus. Magnetic dipole coupling is the effect between the miniature magnet of the nucleus and the internal magnetic field generated by the electron cloud, while electric quadrupole coupling is the effect in which the shape of the nucleus perceives and responds to the electric field gradient of the electron cloud. These two extremely weak couplings are known as hyperfine structure. Physicists can employ high-precision laser spectroscopy to reverse-calculate the exact values of the magnetic moment and electric quadrupole moment of the nucleus itself based on the analysis of the hyperfine structure. In addition, an atomic nucleus in an excited state often does not tend to release energy directly by emitting a photon ($\gamma$-ray). Instead, it transfers energy directly and non-radiatively to a bound electron outside the nucleus. This process is called the internal conversion effect. The probability of internal conversion is much higher than that of direct photon emission. This discrepancy constitutes one of the primary obstacles to the direct optical detection and excitation of nuclear energy levels.

The fundamental principle of a nuclear clock is to use an ultra-narrow nuclear transition as the frequency reference. By achieving resonance between a laser and this transition, the laser frequency is locked to the nuclear transition frequency, thereby generating a stable and traceable time signal. Similarly to other optical clocks, the core architecture of a nuclear clock consists of three main components. The first is the nuclear resonance system, which serves as the physical platform hosting the target nuclear transition. This can take the form of a single ion confined in an ion trap, nuclear isotopes doped into a crystal, or other structures capable of high-coherence nuclear spectroscopy. This component acts as the “pendulum” of the nuclear clock. The second is the laser frequency stabilization system, which provides a coherent light source with a sufficiently narrow linewidth and precise frequency tunability. Its role is to excite the nuclear transition while suppressing the laser’s own phase noise and frequency drift on short timescales. Finally, there is the frequency readout system, typically an optical frequency comb. Using its frequency down-conversion capability, the system converts the optical nuclear resonance signal into a radio-frequency (RF) error signal. This signal is then used in a closed-loop control to adjust the laser frequency in real-time. This process maintains a stable lock between the nuclear transition and the output frequency over long-term operation, while providing a precise readout of the optical frequency. This component can be regarded as the “time-keeping” system of the nuclear clock.

Pálffy’s team [12] constructed a unified theoretical model coupling nuclear structure with atomic electrons, systematically analyzing the energy components of the transition between the ground state (²²⁹Th, 3/2+) and the first excited state (^229mTh, 5/2+). Based on the nuclear shell model and collective model, they calculated the effects of single-particle energy level splitting and nuclear deformation on the transition energy. They further considered the screening and polarization effects of atomic electrons on the nuclear transition energy, establishing an energy correction formula. Meanwhile, this research established a quantum field theory model of electron–nuclear interactions and described the coupling mechanism between electrons and nuclear transitions. It also calculated the dependence between internal conversion coefficients and nuclear transition energy, providing a theoretical benchmark for the interpretation of experimental data. Furthermore, the pioneering work of Flambaum [13] established a quantitative relationship between nuclear transition energy and fundamental physical constants. The research found that the low-energy nuclear transition of ²²⁹Th occurs between single-particle energy levels near the Fermi surface. These levels are highly sensitive to variations in strong interactions. The coupling of low-energy nuclear transitions with the atomic electronic structure allows changes in the fine-structure constant to be amplified through electron–nuclear interactions. The correlation effects of nucleon–nucleon interactions further enhance the response to variations in fundamental constants. Based on this, it is concluded that the response of the ²²⁹Th nuclear transition to variations in fundamental constants exhibits an exceptionally strong enhancement effect. Additionally, Safronova’s team [14] employed the relativistic coupled-cluster (RCC) method to precisely calculate the nuclear charge radius of ²²⁹Th for the first time, achieving a high-precision description of complex atomic systems. The accurate nuclear charge radius data are utilized directly for the systematic error assessment of nuclear clock frequency, providing a theoretical guarantee for nuclear clocks to reach an accuracy of the ${10}^{-19}$ order.

The performance of a nuclear clock is typically evaluated in terms of stability and uncertainty. These two parameters represent the performance limits of the time and frequency reference on short-term and long-term timescales, respectively.

Theoretically, since the traditional standard deviation fails to converge in the presence of low-frequency noise, it loses its statistical significance. Consequently, stability is typically characterized by the Allan deviation. In essence, the Allan deviation is the square root of a two-sample variance. It is primarily used to describe the frequency fluctuation characteristics of an oscillator across different averaging times $\tau$. For a set of normalized frequency error data $y\left(t\right)$, the Allan variance ${\sigma }_y^2\left(\tau \right)$ is defined as half the mean square value of the difference between the average frequencies measured over two adjacent sampling intervals. It is mathematically expressed as:

$${\sigma }_{\mathrm{y}}(\tau )=\sqrt{{\displaystyle \frac{1}{2}}〈{({\overline{y}}_{n+1}-{\overline{y}}_n)}^2〉}$$

(1)

In this expression, ${\overline{y}}_n$ represents the average fractional frequency deviation within the $n$-th measurement interval $\tau$, and $〈\dots 〉$ denotes the expectation value over an infinite time series.

On the other hand, uncertainty is the upper limit of the potential frequency deviation relative to an ideal reference, measured over a very long integration time $(\tau \to \infty )$. Unlike the Allan deviation, uncertainty does not vary with short-term integration time. Instead, it is primarily determined by systematic factors such as environmental perturbations, laser system errors, and detection noise.

At present, the most advanced optical ion clock [4] can achieve a stability of $3.5\times {10}^{-16}@1\mathrm{s}$ and an uncertainty of $5.5\times {10}^{-19}$. At the same time, this clock must operate under extremely stringent conditions: First, using six thermocouples mounted on the ion trap and the surrounding vacuum chamber, the research team constrained the blackbody radiation (BBR) environment temperature around the ion to $24.0\pm 3.3°\mathrm{C}$; Secondly, to minimize the frequency shifts and heating effects caused by collisions with background gas, a new all-titanium vacuum system was employed. This system is designed to minimize hydrogen outgassing and improve hydrogen pumping speeds to achieve ultra-high vacuum, with a measured base pressure of $\left(2.5\pm 1.3\right)\times {10}^{-10} \mathrm{P}\mathrm{a}$; In addition, the team used an active magnetic field servo system with a bandwidth of approximately 1 kHz to drive electromagnetic coils. This setup stabilizes the quantization magnetic field and minimizes noise from the 60 Hz power line and its harmonics.

Currently, of the two mainstream implementation schemes for nuclear clocks, Kazakov et al. [15] proposed that the solid-state nuclear clock is likely to achieve a systematic uncertainty of $1\times {10}^{-19}$. Furthermore, its solid-state structure offers the advantage of operating without an ultra-high vacuum environment. As for the trapped-ion nuclear clock scheme, Campbell et al. [16] also estimated a systematic uncertainty of $1.5\times {10}^{-19}$. Due to its extremely low sensitivity to blackbody radiation (BBR), the requirements for environmental temperature control are relatively relaxed. Ultimately, the uncertainty limit of nuclear clocks even has the potential to approach ${10}^{-20}$ [17].

Table 1. Comparison of the key performance indicators (KPIs) between the solid-state nuclear clock and ionic nuclear clock schemes.

KPIs	Solid-State Nuclear Clock Schemes	Ionic Nuclear Clock Schemes	Remarks
Short-term stability	${10}^{-18}/\sqrt{\tau }@1\mathrm{s}$	${10}^{-15}/\sqrt{\tau }@1\mathrm{s}$
Long-term systematic uncertainty	${10}^{-16}~{10}^{-19}$	$(1~1.5)\times {10}^{-19}$
Technical maturity	Moderate	Lower	The solid-state nuclear clock scheme has been preliminarily implemented in laboratory settings.
Implementation difficulty	High	Extremely high	Both schemes suffer from issues such as equipment complexity

compares the stability, uncertainty, technical maturity, and implementation difficulty between the solid-state nuclear clock and ionic nuclear clock schemes, with data sourced from [15,16,18,19,20].

In summary, nuclear clocks are expected to reach or even surpass the performance of current leading optical clocks without requiring extremely stringent environmental conditions.

3. Key Progress in Nuclear Clock Research

The precise determination of the ²²⁹Th isomeric transition energy is one of the most fundamental yet challenging issues in nuclear clock research. The accuracy of this transition energy directly determines the evaluation of systematic uncertainty and the feasibility limits.

Early evidence for the existence of the ²²⁹Th nuclear isomer primarily originated from high-energy $\gamma$-ray spectroscopy experiments. In 1990, Reich and Helmer [21] first indirectly inferred that the energy of the ²²⁹Th first excited state was on the order of only a few electron volts. They achieved this by measuring the $\gamma$-ray spectra of cascade transitions from high-lying excited states of ²²⁹Th produced following the alpha decay of ²³³U, combined with level fitting and energy difference analysis. At the time, this result was considered an anomaly in nuclear physics and laid the foundation for the vision of bringing nuclear transitions into the optical frequency domain. However, these indirect methods were highly sensitive to level-fitting models and spectral energy calibration. Their uncertainty remained at the sub-eV or even eV level for a long time, falling short of the requirements for precision metrology.

With the advancement of experimental techniques, the research focus gradually shifted toward indirect measurement methods based on electronic processes. Among these, internal conversion (IC) electron spectroscopy emerged as a key breakthrough direction. When the ²²⁹Th nuclear isomer de-excites via internal conversion, its energy can be transferred to the atomic electrons and released in the form of electron kinetic energy. In 2016, Von der Wense et al. [22] observed this process for the first time. The researchers utilized a beam of thorium ions produced from ²³³U decay, which was decelerated and deposited onto the surface of a metal collection plate. They successfully observed internal conversion electrons originating from the nuclear de-excitation process. This discovery confirmed that under specific conditions, internal conversion is the primary de-excitation pathway for this nuclear isomer. In 2019, Seiferle et al. [12] measured the kinetic energy distribution of electrons produced during the internal conversion process of neutral ²²⁹Th atoms using a high-resolution electron spectrometer. By combining these measurements with precise calculations of the first ionization energy of the thorium atom, they deduced a nuclear transition energy of $8.28\pm 0.17$ eV. In the VUV energy range, electron-based measurements offer a significant advantage in energy resolution compared to early indirect $\gamma$-ray spectroscopy. This approach has reduced the uncertainty of the ²²⁹Th isomeric energy to the level of hundreds of millielectronvolts (meV).

A truly landmark advancement emerged with the proposal and implementation of direct optical detection attempts. Driven by advancements in VUV laser sources, synchrotron radiation, and high-sensitivity photoelectric detection, researchers began attempting to directly excite the ²²⁹Th nuclear transition and observe it via nuclear fluorescence or related decay signals. Despite the extreme experimental challenges of direct optical detection with its weak signal strength and complex background noise, this research direction represents an essential step in bringing the nuclear clock from concept to reality.

In May 2023, Kraemer et al. [23] from KU Leuven in Belgium utilized high-energy proton bombardment to produce a radioactive isotope chain. The ²²⁹Th isomeric state was indirectly populated via the $\beta$ decay of ²²⁹Ac. The resulting thorium ions were then implanted in situ into VUV-transparent crystals with large bandgaps (CaF₂ and MgF₂), allowing a high-numerical-aperture VUV spectrometer to capture the photons emitted during nuclear de-excitation. This experiment provided the first clear observation of the radiative decay signal at a wavelength of 148.71(42) nm, determining the transition energy to be 8.338(24) eV. This achievement resolved the decades-long debate over whether this nuclear transition could emit light, providing a precise “beacon” for subsequent laser excitation.

In April 2024, the team led by Peik at the PTB in Germany and the team led by Schumm at the TU Wien [19] achieved the first direct laser excitation of an atomic nucleus. By directly illuminating a ²²⁹Th -doped CaF₂ crystal with a tunable VUV laser system, the team detected the fluorescence emitted during nuclear de-excitation after the laser was turned off. Simultaneously, a 232Th-doped crystal was used as a control to exclude any interfering background signals. The nuclear transition wavelength of ²²⁹Th⁴⁺ ions in the CaF₂ crystal was ultimately measured to be 148.3821(5) nm (as shown in Figure 2), corresponding to a photon energy of 8.35574(3) eV. This work achieved monochromatic laser resonant excitation, narrowing the search window by several orders of magnitude. However, the VUV laser linewidth of approximately 10 GHz remains far too broad compared to the mHz-level intrinsic linewidth of the ²²⁹Th nucleus. Additionally, the limited VUV laser power—typically at the nW level—results in low excitation efficiency, leaving both detection efficiency and SNR in need of improvement.

Simultaneously, the Hudson’s team at the University of California, Los Angeles (UCLA) [24] independently verified the ²²⁹Th nuclear transition by utilizing a different crystal host ($LiSrAl{F}_6$). They observed a narrow, laser-linewidth-limited spectral line within the $LiSrAl{F}_6$ crystal, featuring a center wavelength of 148.38219(4)_stat(20)_sy_s nm. This result is consistent with the measurements obtained by the PTB team in CaF₂ crystals within the margin of error. This marks the second independent research team to successfully observe the laser excitation of the ²²⁹Th nucleus utilizing a different crystal host. This cross-validation significantly enhances the credibility of the discovery, as it rules out the possibility of unknown defects or artifacts within a single crystal system. Therefore, it signifies that the confirmation of this transition has reached a field-wide consensus.

In September 2024, a team led by the Jun Ye group at JILA [20] achieved a milestone breakthrough in the field of nuclear clocks. They not only excited the atomic nucleus but also realized the first direct comparison between a nuclear transition frequency and an electronic energy level frequency (a Sr atomic clock). Using HHG technology, the researchers converted an infrared frequency comb into a narrow-linewidth, tunable VUV frequency comb to directly excite the ²²⁹Th-doped CaF₂ crystal. By locking the VUV frequency comb to the ⁸⁷Sr optical lattice clock operating in the JILA laboratory and using the comb teeth as a “bridge” (It serves as a mechanism for frequency transfer and connectivity across different frequency scales or distinct physical systems), they successfully resolved multiple hyperfine components of the nuclear excited state. Based on an averaging method derived from hyperfine structure symmetry, they calculated the transition frequency of the thorium nucleus within the crystal to be 2,020,407,384,335(2) kHz. Additionally, they measured the ratio between the Th nuclear transition frequency and the Sr atomic transition frequency to be 4.707072615078(18), corresponding to a vacuum wavelength of 148.382145(2) nm. This achievement represents a leap in measurement precision and confirms the technical feasibility of driving a solid-state nuclear clock using a VUV frequency comb. However, this scheme still faces numerous challenges. First, despite the application of the symmetry averaging method, the electric quadrupole shift (approximately on the kHz scale) generated by the crystal field remains the primary factor limiting precision. Achieving better systematic uncertainty still requires more accurate lattice field models. Second, although the power per comb tooth is sufficient to trigger the nuclear transition, it remains relatively low, thereby limiting the excitation rate and the potential for a higher SNR. This is also related to the extreme difficulty of extracting VUV light. Since most solid materials and even ambient air strongly absorb light in this spectral range, the entire system must operate under high vacuum, resulting in a very low conversion efficiency for VUV light generation. Third, using a Photomultiplier Tube (PMT) for nuclear transition detection must employ a time-domain separation strategy. This relies on the long decay lifetime of the nucleus, where the laser irradiation is rapidly cut off, followed by the detection of spontaneous emission of nuclear fluorescence during the “dark period.” Due to the inherent device limitations of PMT, the detection efficiency in the VUV range is quite low. How to achieve rapid, high-efficiency, and high-fidelity transition-state detection remains one of the urgent problems that needs to be solved.

In December 2025, the team led by Eric Hudson at UCLA [25] achieved a critical breakthrough in solid-state nuclear clock detection technology. They successfully realized laser-driven measurement of internal conversion electron Mössbauer spectroscopy of ²²⁹ThO₂. Through sophisticated thin-film fabrication techniques, the researchers achieved direct observation of nuclear transition signals within an opaque ThO₂ medium, as illustrated in Figure 3. This achievement breaks the strict reliance of traditional schemes on VUV-transparent host crystals. By employing a tunable VUV laser system to induce nuclear excitation, the team pioneered a method to extract spectral information through the detection of internal conversion electrons emitted during de-excitation. This approach enabled the successful observation of isomer shifts induced by the chemical environment, thereby elevating laser Mössbauer spectroscopy to a new peak of sub-atomic precision. This work not only confirms the possibility of constructing a nuclear frequency standard within non-transparent solid materials but also establishes the physical foundation for developing highly robust and portable solid-state nuclear clocks. However, this technical path still faces multiple technological barriers in its evolution toward higher precision. First, although ThO₂ as a homogeneous host possesses good structural stability, the interaction between the complex internal electronic density of states and the nucleus leads to significant frequency shifts. Establishing a universal and high-precision electron-nucleus coupling dynamics model to correct these systematic biases remains a severe challenge in metrology. Second, due to the extremely short mean free path of internal conversion electrons within solids, the effective signal originates only from a very thin surface layer of the film. This limitation severely constrains the number of nuclei contributing to the detection, making it difficult to improve the overall count rate.

The nuclear transition frequency of ²²⁹Th⁴⁺ ions in solid-state doped crystals has been measured with kHz-level precision; however, the direct laser excitation of isolated ²²⁹Th³⁺ ions in ion traps remains unachieved. A critical bottleneck lies in the fact that its transition frequency is unknown. In July 2025, Ma Yugang’s team at Fudan University [26] employed the non-perturbative multiconfiguration Dirac-Hartree-Fock method to precisely calculate nuclear isotope shifts and predicted the absolute transition frequency of isolated ²²⁹Th³⁺, providing a crucial theoretical target for ion trap experiments. This method distinguishes itself from the perturbation theory frequently utilized in previous studies by employing a more rigorous and self-consistent non-perturbative calculation. The team performed large-scale computations using the GRASPG package, which they independently optimized and upgraded based on GRASP2018. Ultimately, the calculated nuclear clock transition frequency of ²²⁹Th³⁺ is 639 MHz lower than that of ²²⁹Th⁴⁺, achieving a computational convergence precision of 1 MHz. This study represents the first prediction of the absolute transition frequency for isolated ²²⁹Th³⁺ at 2,020,407,009 MHz. Moreover, it provides the uncertainty derived from computational errors, nuclear radius errors, and crystal environment effects. By narrowing the laser frequency search range for ion trap experiments from an unknown span to within ±500 MHz centered on a known point, this research significantly reduces the experimental difficulty.

While the academic community currently focuses primarily on low-charge thorium ions (²²⁹Th³⁺, ²²⁹Th⁴⁺), She Lei’s team at the Chinese Academy of Science [27] has innovatively proposed a scheme utilizing the ²²⁹Th⁶⁺ ion as a nuclear clock platform. Their research indicates that the ²²⁹Th⁶⁺ ion represents a highly promising candidate for a nuclear clock platform. Its simple electronic configuration is analogous to that of Ba⁴⁺, possessing excellent ion-clock characteristics such as matched lifetimes and low state degeneracy. By selecting specific stretched states for frequency averaging, the linear Zeeman shift and electric quadrupole shift can be inherently eliminated. Other systemic frequency shifts—including the quadratic Zeeman effect, blackbody radiation, and micromotion—are evaluated to be suppressed below the 10⁻¹⁹ or even 10⁻²⁰ level. By utilizing its ion-clock transitions, the charge radius difference and magnetic moment ratio between the nuclear ground state and the isomer state can be extracted with unprecedented precision through hyperfine structure measurements. This capability significantly deepens the fundamental understanding of the ²²⁹Th nucleus itself. The study provides a complete theoretical design and feasibility demonstration—spanning atomic structure, external field evaluation, and dynamics simulations—thereby establishing a clear roadmap for future experimental research. Furthermore, this work lowers certain technical barriers and facilitates the accelerated progress of ion-trap-based experiments.

4. Key Technologies for Implementing the Nuclear Clock

4.1. Trapped-Ion Scheme

The trapped-ion scheme typically focuses on a single or a few multi-charged ions as the subjects of study. Utilizing Paul or Penning traps to achieve spatial confinement of the target nuclear clock ions. Under conditions of ultra-high vacuum and precise electromagnetic control, this scheme enables the excitation of nuclear transitions and subsequent spectroscopic detection.

The ionic charge state of the Th ion is a critical factor influencing the nuclear clock system. In most research, Th³⁺ and Th⁴⁺ are the two mainstream choices. Among them, Th³⁺ is more widely utilized due to its single-valence-electron structure, which resembles that of monovalent ion systems. This configuration not only facilitates the preparation of ions in ultracold quantum states via laser cooling [28] but also enables high SNR readout of nuclear transition states through laser-induced fluorescence (LIF) and quantum logic spectroscopy (QLS) [29]. In contrast, Th⁴⁺ possesses no valence electrons. Its closed-shell configuration ensures exceptional rigidity and minimizes sensitivity to BBR and external stray electromagnetic fields to the physical limit. Consequently, the uncertainty of the BBR frequency shift can be suppressed to the order of ${10}^{-22}$. Furthermore, the absence of outer valence electrons eliminates complex electron–nuclear coupling pathways, resulting in a more “pristine” nuclear transition. However, this also means losing the path to excite the nuclear transition via the electronic bridge effect. Because of the absence of available closed electronic transitions, Th⁴⁺ cannot perform laser cooling on its own. Instead, it must rely on sympathetic cooling techniques, which remove thermal energy via other co-trapped ions. Due to the absence of electronic transitions to generate fluorescence, it must also rely entirely on QLS techniques for state detection [30].

The role of an ion trap can be conceptually understood as “suspending and fixing charged particles using electromagnetic fields in a vacuum.” A Paul trap utilizes time-varying electric fields. Since a static electric field alone cannot simultaneously confine an ion at a stable position in three-dimensional space, the Paul trap employs high-frequency alternating voltages applied to the electrodes. This causes the ion to oscillate within the rapidly shifting electric field, as schematically illustrated in Figure 4. Even though the ion undergoes continuous “micromotion” on a microscopic scale, it remains confined near the trap center from a time-averaged perspective. Leading optical clock technology adopts the scheme of trapping target and logic ions within a Paul trap, a method that is sufficiently mature for the ion-based nuclear clock to follow. Nevertheless, research by Beloy [31] points out that the AC Zeeman frequency shift caused by parasitic RF magnetic fields is immense. This trap-induced frequency shift could potentially become the largest source of systematic frequency shifts for the ²²⁹Th nuclear clock. In specific experimental setups, this frequency shift can reach the order of 10⁻¹⁵ to 10⁻¹⁶, which is several orders of magnitude higher than the 10⁻¹⁹ uncertainty expected for the nuclear clock. Thanks to their distinct transition types, the existence of magnetic-insensitive states, and small measurable AC Zeeman coefficients, ion optical clocks can correct this frequency shift to the 10⁻²⁰ level. Yet, this issue remains a major bottleneck for the realization of the ²²⁹Th nuclear clock.

Alternatively, the Penning trap employs a strong magnetic field to force charged ions into cyclotron motion around magnetic field lines, thereby confining their transverse escape. Combined with a static electric field, this setup traps the ions in the axial direction, as illustrated in Figure 5. In this way, ions can remain stable for long periods within purely static electromagnetic fields. By contrast, the Penning trap avoids the micromotion issues inherent in Paul trap clocks due to the absence of RF driving fields. The static field confinement allows for precise control of field parameters, while also enabling the stable trapping of a large number of ions and prolonged confinement times. However, the requisite strong magnetic field exerts a fatal impact on the nuclear clock. Magnetic field drift and noise can introduce substantial systematic frequency shifts. For a nuclear clock of extreme precision, the absolute stable control of spatio-temporal magnetic fields is indispensable. Furthermore, the cooling efficiency for heavy particles such as Th ions is relatively low. How to improve this efficiency or develop novel cooling strategies remains a technical threshold that must be addressed for this scheme.

4.2. Crystal-Doping Scheme

The doped-crystal approach, also known as the solid-state nuclear clock scheme, consists of embedding a specific concentration of ²²⁹Th into a transparent solid-state crystal with a wide bandgap (the electronic transition energy of this bandgap must be significantly higher than that required for the thorium nuclear transition). This setup allows a vast number of thorium nuclei to participate in resonance simultaneously, thereby substantially enhancing the nuclear transition signal strength. This scheme is regarded as another crucial technical path for achieving high-SNR nuclear transition detection and improving short-term stability.

In practice, ²²⁹Th typically replaces a portion of the lattice sites within the crystal matrix in ionic form, as illustrated in Figure 6. Due to its wide-bandgap characteristics, the crystal exhibits a certain transparency to VUV radiation. This feature enables the nuclear transition to be optically excited and detected within a solid-state environment. Currently, most research employs CaF₂ as the substrate material. A joint research group from JILA and TU Wien [34] conducted experiments based on this substrate and identified the optimal operating point for the ²²⁹Th: CaF₂ nuclear clock to be 195(5) K (approximately the temperature of dry ice). At this temperature, the sensitivity of the nuclear transition frequency to temperature variations is precisely zero. This implies that small temperature fluctuations in the vicinity of this point do not induce noticeable frequency shifts. Furthermore, the linewidth of the nuclear transition was found to be constrained by the inherent properties of the host crystal and varies with doping concentration; specifically, crystals with lower concentrations exhibit narrower linewidths. The researchers pointed out that the solid-state nuclear clock can achieve exceptionally high frequency reproducibility by selecting specific operating temperatures and optimizing crystal growth processes. In addition, research into alternative host materials—including ThF₄ thin films [35], SrF₂ [36], LiF₂ [37], Th(SO₄)₂ [38], and a new class of materials (metallic superhalogen salts) [39]—is being conducted. These studies aim to address the existing issues of solid-state nuclear clocks, such as fabrication complexities, stringent requirements, and inadequate performance caused by material limitations.

Furthermore, the most central issue for the solid-state nuclear clock lies in the unavoidable influence of the solid-state environment on the nuclear transition frequency. Although nuclear energy levels are far less sensitive to external perturbations than electronic ones, local electric field gradients, strain, and variations in the chemical environment within the crystal can still induce frequency shifts and spectral broadening mediated by high-order nuclear multipole interactions [40]. In addition, crystal defects and radiation damage are factors that cannot be overlooked. ²²⁹Th itself is radioactive, and its decay process may generate point defects or charge-trapping centers within the crystal, which in turn modify the local lattice environment. These time-evolving effects can give rise to long-term frequency drifts, posing challenges to the accuracy and reproducibility of the nuclear clock [41].

In summary, the potential advantages and challenges of the solid-state nuclear clock largely originate from the core characteristics of the solid-state environment. On one hand, the solid-state system offers the potential for large-scale integration and engineering, providing significant advantages for practical implementation. On the other hand, the lattice environment inevitably introduces additional physical effects that constrain frequency accuracy.

4.3. Nuclear Clock Excitation and Readout Technologies

For low-energy nuclear isomers such as ²²⁹Th, two primary excitation schemes are currently in use. The first involves direct excitation of the nuclear transition utilizing a tunable VUV light source at the corresponding wavelength; the second employs resonance coupling mechanisms to transfer photon energy via electronic-nuclear coupling [42]. In terms of transition readout, schemes can be categorized into two types depending on the excitation sample and decay mode. First, during direct nuclear excitation, internal conversion or $\gamma$-decay may occur. Different readout channels are selected based on the de-excitation type; for instance, a microchannel plate (MCP) or a PMT is used to collect products as evidence of the nuclear transition and resonance. Second, for the single-ion trap scheme, quantum logic spectroscopy can be utilized. By trapping the target ion and an auxiliary ion together, the state of the target ion (ground or excited) influences the auxiliary ion via Coulomb interactions. By probing the auxiliary ion with a laser at a specific frequency, the state of the target ion can be determined based on the fluorescence signal intensity.

4.4. VUV/XUV Laser and VUV/XUV Optical Frequency Comb Technology

Since the ²²⁹Th isomeric transition energy falls within the VUV range, its direct optical excitation not only necessitates an ultra-stable laser source at approximately 148.3 nm with a narrow linewidth and high coherence, but also requires the precise and traceable synthesis and measurement of frequencies from visible or near-infrared standards to the VUV spectrum. Consequently, VUV laser generation at approximately 148.3 nm and VUV optical frequency comb technology are not merely auxiliary tools in nuclear clock research; rather, they serve as the technical backbone that determines both experimental feasibility and the ultimate performance limits.

Frequency doubling (Second Harmonic Generation, SHG) is one of the most common techniques for generating short-wavelength light from long-wavelength sources. However, researchers generally avoid utilizing this method to produce VUV light due to several factors, such as the excessive number of doubling stages required and the lack of suitable nonlinear crystals. Driven by a highly specific objective, Peik’s team [43] successfully designed and constructed an all-solid-state, continuous-wave laser system tailored for the wavelength range near 148.4 nm. Through a three-stage cascaded frequency doubling process, they achieved CW frequency doubling from 296.8 nm to 148.4 nm for the first time, leveraging a $Sr{B}_4{o}_7$ crystal with random quasi-phase-matching (RQPM). This work represents a pivotal step toward achieving high-resolution nuclear spectroscopy and the development of nuclear clocks, offering a novel perspective for fields requiring continuous-wave VUV lasers. Nonetheless, several challenges persist. First, the reproducibility of $Sr{B}_4{o}_7$ crystals, which naturally form random inversion domain structures during growth, is difficult to guarantee, leading to significant performance variations between individual crystals. Second, because this crystal suffers from performance instability in vacuum due to absorption-induced heating, the study introduced a high-purity nitrogen buffer environment to facilitate heat conduction. However, passing the VUV light through this nitrogen atmosphere inevitably results in absorption losses, thereby compromising the output power.

Four-Wave Mixing (FWM) is a typical third-order nonlinear optical process that arises from the third-order nonlinear polarizability response of a medium. When two or more coherent light beams propagate simultaneously through a medium with a non-zero third-order nonlinear susceptibility, different frequency components couple with each other via the nonlinear response of the medium. Consequently, new optical frequency components are generated, provided that the conditions for energy conservation and phase matching are satisfied. For instance, the joint team of Peik and Schumm [19] used VUV light at approximately 148.3 nm produced by four-wave mixing to excite ²²⁹Th: CaF₂, as illustrated in Figure 7. Two tunable continuous-wave Ti: Sa lasers are first amplified by dye amplifiers. One beam undergoes a third-harmonic generation process, while the other serves as a fine-tuning laser; both are injected into an Xenon gas cell to trigger FWM, which yields the VUV light.

In 2025, Shiqian Ding’s team at Tsinghua University [44] generated narrow-linewidth continuous-wave (CW) VUV laser radiation in cadmium(Cd) vapor utilizing resonance-enhanced FWM technology. Specifically, 148.4 nm VUV laser radiation is generated via FWM by employing two 375 nm photons and one 710 nm photon in cadmium vapor at 550 °C. The fundamental lasers are provided by Ti: Sa lasers and locked to ultra-stable, ultra-low expansion (ULE) cavities, which compress the fundamental linewidth to the Hz or even sub-Hz level. The linewidths of the 750 nm and 710 nm lasers are determined by measuring the beat frequency with a 1550 nm optical frequency comb. The detailed experimental setup is illustrated in Figure 8. This laser system spans a tuning range from 146.97 nm to 153.7 nm with an output power of 100 nW, which significantly exceeds the per-comb-tooth power of other laser systems whose power is diluted across millions of comb teeth. However, this system still has some issues. For example, the cadmium oven must consume a large amount of energy to maintain a high temperature, and temperature fluctuations directly affect the density homogeneity of the cadmium vapor, resulting in unstable VUV power. Furthermore, cadmium vapor is toxic, which leads to safety risks if not properly controlled.

An optical frequency comb is a femtosecond light source capable of producing spectral comb teeth with equal frequency spacing and high coherence. Figure 9 illustrates the time-domain and frequency-domain schematics of an optical comb. Its essence lies in utilizing the mode-locking mechanism to achieve a precise correspondence between ultrashort pulses in the time domain and discrete spectral lines in the frequency domain. The core characteristic of this “optical frequency ruler” is embodied in a dual unity: in the time domain, it appears as a periodic sequence of femtosecond pulses with a strictly constant time interval $\left(\tau \right)$. In the frequency domain, it presents as equally spaced spectral teeth, where the tooth spacing $\left(f_{rep}={\displaystyle \frac{1}{\tau }}\right)$ is perfectly consistent with the pulse repetition frequency. This characteristic stems from the operating mechanism of mode-locked lasers: when the laser within the resonant cavity satisfies the mode-locking condition, light waves of different longitudinal modes develop a fixed phase relationship, superimposing to form ultrashort pulses. As ultrashort pulses propagate within the resonant cavity, material and waveguide dispersions from optical components—such as the gain medium, dispersion compensation elements, and mirrors—are inevitable. Consequently, the group delay characteristics of different longitudinal modes vary significantly, thereby leading to a separation between the two key propagation velocities: the carrier phase velocity $\left(v_p\right)$ and the pulse envelope group velocity $\left(v_g\right)$. Specifically, $v_p$ is determined by the phase propagation characteristics of a single frequency component, whereas $v_g$ depends on the overall propagation of the envelope formed by the superposition of multiple longitudinal modes. The difference between the two stems from the differential modulation of the pulse phase and group delay by dispersion. When the pulse completes a round trip within the resonant cavity, the mismatch between $v_p$ and $v_g$ accumulates a non-negligible relative phase shift. This phase difference, accumulated under these specific conditions, is defined as the Carrier-Envelope Phase ${(\varnothing }_{CEP})$. Without accounting for nonlinear phase shifts within the cavity, the Carrier-Envelope Phase is primarily caused by intracavity dispersion and can be expressed as:

$${\mathsf{\Phi }}_{CEP}=({\displaystyle \frac{1}{v_g}}-{\displaystyle \frac{1}{v_p}})l_c{\omega }_c\mathrm{mod}2\pi$$

(2)

In this expression, $l_c$ is the cavity length of the laser resonant cavity, and ${\omega }_c$ is the carrier frequency. In the frequency domain, the carrier-envelope phase corresponds to the relative frequency offset of all longitudinal mode comb teeth relative to zero frequency, which is known as the carrier-envelope offset (CEO) frequency ($f_{ceo}$). The relationship between it and the carrier-envelope phase is:

$$f_{ceo}={\displaystyle \frac{{\mathsf{\Phi }}_{CEP}}{2\pi }}{f}_{rep}$$

(3)

From this, the frequency of the $n$-th comb tooth can be expressed as:

$$f_n=n\cdot f_{rep}+f_{ceo}$$

(4)

where $n$ is a very large positive integer. From this expression, it can be seen that the frequency of each tooth of the comb is uniquely determined by $f_{rep}$ and $f_{ceo}$, which constitutes the fundamental formula of the optical frequency comb.

A typical optical frequency comb spans a spectral range from 1000 nm to 2000 nm, whereas the nuclear clock transition wavelength is approximately 148.3 nm. Consequently, HHG technology must be employed to convert the wavelength into the VUV region. The HHG process is inherently a nonlinear process with extremely low efficiency. By introducing a resonance-enhanced cavity, the pulses of the infrared seed frequency comb can undergo thousands of round trips and achieve coherent superposition, thereby boosting the intracavity peak power until it reaches the critical threshold required to induce HHG. During this process, each “tooth” of the frequency comb is precisely transferred to the VUV spectral range, forming what is known as a VUV frequency comb. The experimental setup for the most accurate measurement of the nuclear transition frequency to date, achieved by Jun Ye’s group at JILA [20]. They utilize an ytterbium-doped fiber comb as the seed source; the output is first amplified and subsequently coupled into a resonance-enhanced cavity for coherent superposition. This generates high-order harmonics, from which the seventh harmonic is individually extracted to excite the ²²⁹Th nuclear transition.

In 1987, the HHG phenomenon was first experimentally observed by McPherson et al. [45] provided a pathway for obtaining XUV band lasers. Numerous scholars subsequently carried out extensive investigations in this field [46,47,48]. In 1993, Corkum et al. [49] conceptualized the “three-step model”, which provides an intuitive physical picture of electron motion. This theory elucidated the characteristics of the plateau and cutoff regions in high-order harmonic generation. In 2002, Jones et al. [50] proposed the femtosecond enhancement cavity (fsEC) amplification technique. This method utilizes the principle of coherent interference to build up laser energy within a resonant cavity, acting as a passive laser amplification technology. Subsequently, XUV frequency combs based on fsEC were successfully realized independently in 2005 by Jun Ye’s team at JILA and Hänsch’s team at MPQ. Jun Ye’s team [51] utilized a high-finesse optical resonant cavity and precisely controlled the intracavity net dispersion to amplify the pulse energy by several hundred times; Xenon gas was injected into the cavity to generate high harmonics, which were then partially reflected out of the cavity by a sapphire plate placed at Brewster’s angle relative to the fundamental light. The reflected high harmonics were detected using an aluminum grating coated with MgF₂. Due to the low detection efficiency of the components, only the 7th harmonic was observed. The schematic of the experimental setup for generating XUV femtosecond optical frequency combs within an fsEC is shown in Figure 10. Hänsch’s group [52], on the other hand, subjected the seed light to mode shaping and dispersion compensation before directing it through an input coupling mirror into the enhancement cavity. The intracavity laser was focused at a gas nozzle within a vacuum environment, generating XUV radiation via the HHG process. Finally, a sapphire plate was employed as the output coupling element to successfully extract the generated XUV frequency comb (up to the 15th harmonic) from the cavity. Following these breakthroughs, technologies related to XUV optical combs began to develop continuously and overcome numerous bottlenecks.

In the process of intracavity high-harmonic generation, effectively extracting the generated XUV light from the high-power enhancement cavity has consistently been a core challenge in precision spectroscopy. Because the wavelength of XUV light is extremely short, it is strongly absorbed by almost all conventional optical glass and mirror media, rendering traditional transmissive extraction methods completely ineffective. Initial studies attempted to place a thin sapphire plate at Brewster’s angle after the intracavity focal point. The physical logic is to have the NIR driving laser incident at Brewster’s angle to achieve reflection-free transmission, while a small fraction of the generated XUV light is “scraped” out by utilizing the minimal Fresnel reflectivity of the sapphire surface. This scheme suffers from extremely low extraction efficiency, and the thin plate is highly susceptible to thermal distortion and nonlinear phase aberration under ultra-high circulating power. In 2008, Yost et al. [53] proposed a scheme that utilizes an XUV diffraction grating as the output coupler. In 2012, researchers attempted to etch an out-coupling grating directly onto the surface of an enhancement cavity mirror. This design reflects the infrared light back into the cavity for circulation while diffracting the short-wavelength XUV light for extraction [54]. This technological breakthrough overcomes the challenge where XUV light cannot penetrate conventional reflective mirrors for extraction. By transitioning from high-loss Brewster plates to high-efficiency diffraction gratings, both the XUV output power and system stability were significantly improved. In 2025, Zhengrong Xiao et al. [55] from the Innovation Academy for Precision Measurement Science and Technology (APM), CAS, improved the performance of XUV gratings and achieved stable high-power operation within the enhancement cavity.

Additionally, extensive experiments and theoretical simulations have revealed that the accumulation of steady-state plasma at the intracavity focal point at high repetition rates hinders phase matching [56,57,58,59]. Consequently, some researchers have opted to mix different gases (such as Xe and He) to increase the flow velocity [59], thereby weakening this accumulation effect. Results showed that the photon flux of the 61 nm harmonic generated by the gas mixture was indeed approximately 30% higher than that produced by Xenon alone. In 2017, Porat et al. [60] attempted to use gas mixtures at high temperatures to increase their average velocity. This reduced the steady-state plasma at the laser focal point, weakened the impact of the accumulation effect on phase matching within the enhancement cavity, and achieved milliwatt-level harmonic power for the first time.

The research team at the Institute of Physics, Chinese Academy of Sciences, began theoretical and experimental research on femtosecond laser resonance enhancement cavities as early as 2012 [61,62,63,64]. We performed detailed calculations on various factors affecting intracavity resonance enhancement, conducting theoretical simulations on impedance matching, cavity mode matching, and chirp. Furthermore, we achieved intracavity resonance enhancement of femtosecond pulses from a Ti: Sa laser, generating 400 nm intracavity frequency-doubled light. Recently, using a 200 MHz, 20 W Yb-fiber optical frequency comb [64], we achieved an intracavity power enhancement factor exceeding 350 times. With an incident power of only 17.3 W, we realized HHG at a 200 MHz repetition rate, covering a broad spectral range from 49 nm to 148 nm. This setup generates high-order harmonics up to the 21st order within a compact and stable apparatus, as illustrated in the experimental setup in Figure 11. Utilizing a 200 MHz high repetition rate XUV frequency comb to measure the nuclear transition frequency of the Thorium (²²⁹Th) nuclear clock will significantly improve the SNR of detection signals, providing an ideal “timing” tool for the construction of high-performance Thorium nuclear clocks.

In addition to fsEC technology, researchers have explored alternative routes for generating XUV frequency combs. For instance, in 2010, Kandula et al. [65] obtained an XUV femtosecond optical frequency comb at a wavelength of 51.5 nm based on Optical Parametric Chirped-Pulse Amplification (OPCPA) technology. In 2012, Seres et al. [66] utilize a Ti: Sa oscillator to verify the feasibility of generating XUV combs directly from an oscillator. After evaluating various technical routes, scholars have concluded that despite the operational difficulties arising from the high requirements for intracavity dispersion and finesse, fsEC technology remains the most effective and straightforward solution for extending femtosecond optical frequency combs to the XUV spectral range.

5. Future Prospects and Applications of the Nuclear Clock

The fine-structure constant $\alpha$ is a fundamental dimensionless constant in physics that characterizes the strength of electromagnetic interactions, with a value of approximately 1/137. Verifying whether the fine-structure constant $\alpha$ undergoes minute drifts over cosmic time or with local gravitational potential is of profound significance for exploring new physics beyond the Standard Model, testing Einstein’s Equivalence Principle, and searching for ultralight dark matter. Due to the enormous enhancement factor (K) of its nuclear transition energy relative to minute variations in $\alpha$, the ²²⁹Th nuclear clock is widely recognized as an ideal tool for probing the time variation of fundamental constants.

In October 2025, Beeks et al. [67] calibrated the $\alpha$-sensitivity enhancement factor of the nuclear clock to be K = 5900(2300). This was achieved by utilizing the high-precision nuclear laser spectroscopy data obtained by the JILA team in 2024, incorporating a semi-classical prolate spheroidal model, and basing the calculation on key experimental parameters such as the fractional change in the nuclear quadrupole moment. This achievement eliminated the long-standing diversity of theoretical predictions and provided a definitive calibration for evaluating the performance of solid-state nuclear clock schemes in metrology. In August of the same year, Wang et al. [68] pioneered another innovative detection path. They proposed searching for variations in $\alpha$ using the Hyperfine Electronic Bridge (HEB) transitions in highly charged thorium ion systems. This scheme utilizes the coherent coupling between nuclear and electronic structures; it not only inherits the high sensitivity of the nuclear clock but also leverages the strong immunity of highly charged ions to environmental perturbations. This provides a brand-new physical mechanism and detection window for constructing highly robust and precise platforms for testing fundamental physics in the future.

In the grand background of the evolution of the International System of Units (SI) timebase, Dimarcq et al. [69] explicitly identified the ²²⁹Th nuclear clock as a critical technical route for driving the redefinition of the “second” and the development of next-generation frequency standards. As a novel quantum reference that is fundamentally different from traditional electronic transitions, the nuclear clock is expected to play multiple strategic roles in establishing an ultra-stable time and frequency system. First, regarding the evolution of primary definitions, the roadmap indicates that the nuclear clock possesses the potential to offer long-term stability superior to that of existing optical atomic clocks owing to the inherent robustness of the nucleus against external electromagnetic environments. Therefore, it could serve as a critical reference or a supplementary benchmark in the future redefinition of the SI second. Second, regarding the coordination of global timescales, the nuclear clock serves as a solid-state optical clock scheme that is expected to significantly streamline the instrumental complexity of high-performance frequency standards. Furthermore, this approach will facilitate the construction of distributed and highly robust intercontinental and global frequency comparison networks. Thirdly, the roadmap envisions the unique value of the nuclear clock in deep-space exploration and autonomous timing. Owing to its robust immunity to environmental noise, the nuclear clock is expected to be deployed on satellite platforms or deep-space probes to achieve interplanetary high-precision timing. This will establish an autonomous timebase for future deep-space navigation that is entirely independent of ground-based support. Finally, within the framework of multi-benchmark cross-verification, the integration of the nuclear clock will enable the independent validation of systematic uncertainties in existing optical lattice clocks. Moreover, this integration is poised to initiate a new era for testing the time variation of fundamental constants, thereby providing core support for constructing a more precise and robust global timebase platform at the convergence of metrology and fundamental physics research.

In addition, an absolute bottleneck that cannot be ignored before the large-scale application of ²²⁹Th nuclear clocks is the limited supply of the isotope. While thorium itself is not inherently scarce in the Earth’s crust, the restricted availability of ²²⁹Th stems from its specific production methods, high costs, and the fact that the existing supply chain is dominated by a high-priority field with immense demand: targeted alpha therapy (TAT) for cancer. Hogle et al. [70] pointed out that due to the surging demand for the clinical application of ²²⁹Ac, existing ²²⁹Th stockpiles remain insufficient. In the medical field, ²²⁹Th itself is not the end product. It is primarily utilized to produce the medical α-emitter ²²⁹Ac. Both ²²⁹Ac and its decay progeny, ²¹³Bi, serve as the core isotopes for TAT. The extreme difficulty, high cost, and inefficiency of ²²⁹Th production arise from several factors, including the scarcity of initial target materials, prolonged production cycles, low yields, and the intense radioactivity of byproduct (²²⁸Th). Tong et al. [71] also identified limited supply as the foremost of the four major challenges facing nuclear clocks. The purity requirements for ²²⁹Th in nuclear clock experiments are exceptionally stringent, and the number of facilities capable of such production is exceedingly small. Consequently, the supply of raw materials represents a formidable chasm that must be bridged on the path toward realizing the nuclear clock.