Session G03: Atomic Clocks

Systematic accuracy of the JILA strontium 1D optical lattice clock

We report an accuracy evaluation of our 1D strontium optical lattice clock operated in the Wannier-Stark regime. This recently constructed system relies on 10⁵ neutral fermionic strontium atoms trapped in the ground band of a shallow 1D optical lattice oriented along gravity. We perform recoil free spectroscopy of the least magnetically sensitive ¹S₀ to ³P₀ transition. A key feature of this system is in-situ imaging that allows us to resolve local frequency shifts such as the gravitational redshift [1]. Imaging also allows us to measure and correct for the density shift in real time. Ultimately, we entirely eliminate this shift by tuning atomic interactions [2]. Formed within an in-vacuum buildup cavity, the magic wavelength lattice has excellent homogeneity and repeatable control, allowing us to calibrate the lattice light fractional frequency shift to 3 x 10^-19 [3]. The largest uncorrected systematic shift is due to black body radiation. Improving the ³D₁ lifetime uncertainty, we reduce this shift uncertainty. In sum, the excellent stability and accuracy of this system opens the door to a host of new sensing regimes in relativistic geodesy, quantum measurement, and fundamental physics. 

[1] Bothwell et al., Nature 602, 2022.

[2] Aeppli et al., Science Advances 8 (41), eadc9242, 2022.

[3] Kim et al., Physical Review Letters 113203, 2023.   

Contribution of negative-energy states to multipolar polarizabilities of the Sr optical lattice clock

We address the problem of lattice light shifts in the Sr clock caused by multipolar M1 and E2 atom-field interactions. We present a simple but accurate formula for the magnetic-dipole polarizability that takes into account the contributions of both the positive- and negative-energy states. We calculate the contribution of

negative-energy states to the M1 polarizabilities of the clock ¹S₀ and ³P₀ states at the magic frequency. Taking these contributions into account, we obtain good agreement with the experimental results, explaining the major discrepancy between theory and experiment.   

Towards an optical frequency standard for the NIST timescale

To correct frequency drifts and random-walk of phase in hydrogen masers and cesium beam clocks that form the timescale at NIST, and to support incorporation of ultra-stable oscillators into the clock ensemble, it is desirable to have an optical frequency standard with high operational uptime with inaccuracy < 1 × 10^-16. Following related work (e.g., [1]), we report progress on development of an optical clock based on the S_1/2 -> D_5/2 transition of a single trapped ⁸⁸Sr⁺ ion. We report ion trapping with a novel manufacturable spherical radio frequency (RF) trap design [2] using a single optical photonic crystal fiber to deliver the necessary wavelengths (all between 400 nm and 1100 nm) to the ion. Operating the trap at the “magic” trap RF drive frequency [3] should enable low systematic uncertainty related to micromotion without complex experimental overhead.

[1] B Jian, J Bernard, M Gertsvolf, P Dubé, Metrologia 60 015007 (2023)

[2] DR Leibrandt, DB Hume, RC Brown, JA Sherman, US Patent 11651949B2 (2023)

[3] A Madej, APS DAMOP 2013 T7-001 (2013).   

The Next-Generation NIST 27Al+ Clock

The NIST aluminum ion optical clock operates based on quantum logic spectroscopy of the 1S0 ⟷ 3P0 transition in ²⁷Al⁺, together with a ²⁵Mg⁺ ion for three-dimensional ground-state cooling and state readout. The previous clock achieved a systematic uncertainty below 10^-18 and clock stability of 1.2x10^-15/√(τ) [1]. The leading systematic uncertainty of this clock was due to time dilation from driven micromotion, and the stability was limited by quantum projection noise. The next-generation NIST aluminum-ion clock will improve on both of these limitations. A redesigned ion trap demonstrates significantly reduced residual micromotion, while a new vacuum system and larger usable trap volume will enable operation with multiple ²⁷Al⁺ ions. Simultaneous interrogation of multiple aluminum ions will reduce quantum projection noise below the single-ion limit. Here, we report the design and commisioning of the new trap, including measurements of systematic shifts for a single ion and preparation for multi-ion operation.

[1] Brewer et al., PRL 123, 033201 (2019)   

Towards an optical clock with 173Yb+ ions

Clocks based on optical reference transitions are the most accurate measurement devices ever built. Among them, the single-ion clock based on the ²S_1/2-²F_7/2 electric octupole transition of a ¹⁷¹Yb⁺ ion is one of the systems that have the lowest uncertainty [1]. A recent theoretical study shows that the coupling between the excited and ground states for this transition in ¹⁷³Yb⁺ isotope is significantly stronger [2]. Consequently, the radiative lifetime will be reduced from 1.6 years [3] to days. While the stronger coupling in 173Yb⁺ will  largely reduce the light shift introduced when exciting the highly forbidden transition, the reduced lifetime in ¹⁷³Yb⁺ will still be significantly longer than any laser coherence time envisioned to date and hence enable very good clock stability. Here, we report on progress at PTB in cooling and trapping ¹⁷³Yb⁺ ions, and searching for clock transitions in this isotope with richer hyperfine structure (I=5/2). 

[1] Sanner et al., Nature 567, 204 (2019). 

[2] V. A. Dzuba and V. V. Flambaum, Phys. Rev. A 93, 052517 (2016). 

[3] R. Lange, et al. Phys. Rev. Lett. 127 213001 (2021).     

Auto-cancellation of motional frequency shifts in optical ion clocks

Motion-induced frequency shifts significantly contribute to the uncertainty budgets of state-of-the-art optical ion clocks. For clock transitions with second-order Doppler and quadratic Stark shifts of opposite signs it is possible to engineer electrodynamic ion confinement such that these two shift effects become anticorrelated causing zero net shift. Here we introduce a spectroscopic interrogation protocol which leads to first-order auto-cancellation of motional frequency shifts without requiring the opposite sign configuration. Particularly for ultranarrow clock lines like the electric octupole transition in singly-charged ytterbium, this novel method helps to reach total systematic uncertainties at or below the 1e-18 level.   

Progress Towards a 229Th3+ Nuclear Clock

Atomic clocks are the most precise instruments in existence today, with current state of the art clocks achieving fractional accuracies at the level of 10^-18. Atomic clocks work by locking the frequency of a local oscillator (typically a laser) to an atomic transition. In general, the precision of an atomic clock is improved with higher frequency clock transitions and transitions which are less sensitive to external perturbations. To develop a next generation clock, it is natural then to seek a clock candidate which has a transition meeting both requirements. The ²²⁹Th³⁺ ion offers one such transition, having an anomalously low-energy (about 8 eV) nuclear isomer transition with wavelength of about 149 nm, just on the edge of what is experimentally achievable with VUV lasers. Furthermore, this clock transition is very narrow and is less sensitive to external perturbations due to the strong suppression of external field-shifts. Experimental progress towards the development of a next generation clock utilizing this ²²⁹Th³⁺ nuclear isomer transition will be presented.   

Progress toward direct VUV frequency comb spectroscopy of the 229Th nuclear clock transition

Atomic nuclei are known to possess isomeric transitions that are typically in the X-ray energy range. The ²²⁹Th nucleus offers a uniquely low energy, narrow linewidth transition at 8.338(24) eV, corresponding to a wavelength of 148.71(47) nm in the vacuum ultraviolet (VUV). This ²²⁹Th transition is expected to have a high quality factor and a low sensitivity to external perturbations, and has been proposed as a nuclear-based optical frequency reference.

However, direct laser excitation of this transition has yet to be achieved. Based on recent nuclear physics experiments that significantly reduced the transition energy uncertainty, we are currently searching for this transition using a VUV optical frequency comb. We will present our recent attempt on optical excitation of the nuclear transition in a thin-film solid-state environment, aiming for building a nuclear-based clock. We will also discuss our efforts developing alternative spectroscopy target systems for the nuclear transition search.   

Direct VUV Laser Search for the $^{229}$Th Transition

The nucleus of $^{229}$Th has an exceptionally low-energy isomeric transition in the vacuum-ultraviolet (VUV) spectrum around 8.338(24) eV [1] that, if measured with spectroscopic precision, holds much promise for future timekeeping and quantum logic operations. Our group has pursued the development of thorium-doped crystals [2], both as a way to search for the transition, as well as a potential platform for a solid state nuclear clock. Here we will present the results of an ongoing direct VUV laser search for the isomeric transition, during which fluorescence has been observed that may provide evidence of optical driving and quenching of the nuclear transition in the crystal environment. Possible interpretations will be discussed.

[1] Kraemer, S., et. al. Observation of the radiative decay of the ²²⁹Th nuclear clock isomer. Nature (2023).

Operational optimization of a fully-crystalline optical cavity

Optical cavities with crystalline optical coatings offer reduced thermal noise and lower drift rates, but must be operated at low intracavity power due to power-dependent coating noise.[1] We use a modified PDH scheme where an AOM generates an FM-triplet.[2] This allows cavity stabilization to a sub-ppm fraction of the cavity linewidth, while coupling <100nW of light into the cavity. Precision cryogenic thermometry stabilises the cavity at a zero-crossing of the thermal-expansion coefficient of silicon near 16K, suppressing temperature driven fluctuations. Comparison with a Sr clock [3] allows characterization of the long-term stability of the cavity, and has previously shown drift at the level of a few Hz per day. Improvements in cavity performance suggest that optical local oscillators could replace traditional hydrogen masers where long-term stability is required, as in timescale applications.[4] 

 

[1] Kedar et al., Optica 10, 464-470 (2023); Yu et al., Phys. Rev. X 13, 041002 (2023) 

[2] Kedar et al., Optica 11, 58-63 (2024) 

[3] Bothwell et al., Metrologia 56, 065004 (2019); 

[4] Milner et al., Phys. Rev. Lett. 123, 173201 (2019).    

Direct Laser Excitation of the Th-229 Nucleus in the CaF2 Crystal Environment Using a VUV Tunable Laser

We report on the resonant excitation of the low energy nuclear isomer state of the Th-229 using a tabletop tunable vacuum ultraviolet (VUV) laser system, and measured its long-lived fluorescence signal. To achieve this, we dope Th-229 nuclei as Th⁴⁺ ions into calcium fluoride (CaF₂) crystals [1]. The solid-state approach allows for a high Thorium concentration (up to 10¹⁹ cm⁻³) resulting in a high signal yield. The isomer signal was observed in two different crystals with different doping concentrations but was absent in a control experiment with a Th-232 doped crystal. These results are significant because they pave the way for Th-229 nuclear laser spectroscopy with a hertz-level resolution, similar to what has been achieved in the most advanced optical atomic clocks. This brings us one step closer to the development of the first nuclear clock.

[1] Beeks, K. et al. Sci Rep 13, 3897 (2023).