Strontium Optical Lattice Clock Research Articles

An ultrastable1397-nm laser stabilized by a crystalline-coated room-temperature cavity.

State-of-the-art optical cavities are pivotal in pushing the envelope of laser frequency stability below 10-16. This is often achieved by extending the cavity length or cooling the system to cryogenic temperatures to reduce the thermal noise floor. In our study, we present a 30-cm-long cavity that operates at room temperature and is outfitted with crystalline coatings. The system has a predicted ultralow thermal noise floor of 4.4 × 10-17, comparable to what is observed in cryogenic silicon cavities. A 1397-nm laser is stabilized in this advanced cavity, and the stable frequency is then transferred to the clock transition in strontium optical lattice clocks via a frequency-doubling process. We have meticulously minimized and assessed the technical noise contributions through comparisons with an ultrastable reference laser that is locked to a commercially available 30-cm cavity. The frequency instability of the system is rigorously evaluated using a three-cornered-hat method. The results demonstrate that the laser frequency instability remains below 2 × 10-16 for averaging times ranging from 1 to 50s. These findings underscore the significant potential of room-temperature cavities with crystalline coatings in high-precision metrology and pave the way for further improvements in optical lattice clocks.

Fiber-coupled 2 mL vacuum-gap Fabry-Perot reference cavity for portable laser stabilization.

Vacuum-gap Fabry-Perot cavities are indispensable for the realization of frequency-stable lasers, with applications across a diverse range of scientific and industrial pursuits. However, making these cavity-based laser stabilization systems compact, portable, and rugged enough for use outside of controlled laboratory conditions has proven difficult. Here, we present a fiber-coupled 1396 nm laser stabilization system requiring no free-space optics or alignment, built for a portable strontium optical lattice clock. Based on a 2 mL vacuum-gap Fabry-Perot cavity, this system demonstrates thermal noise-limited performance and 1 × 10-14 fractional frequency instability. Fiber-integrated optical components have been instrumental in both advancing the field of optics and leveraging those advances across disciplines to facilitate other fields of study. This portable system represents a major step toward making the frequency stability of cavity-based systems broadly accessible.

Development of Compact and Robust Physical System for Strontium Optical Lattice Clock

Compact and robust optical clocks are significant in scientific research and engineering. Here, we present a physical system for a strontium atomic optical clock with dimensions of 465 mm × 588 mm × 415 mm and a weight of 66.6 kg. To date, this is one of the most compact physical systems ever reported. The application of the magnetic shielding box in this physical system allowed the effect of external magnetic field fluctuation on cold atoms to be negligible. The physical system passed rigorous environmental tests and remained operational. A wavelength meter integrated in this physical system could monitor the wavelengths of the incident laser, and it could automatically calibrate the wavelengths of all lasers using a microcomputer. This compact and robust physical system could be a hardware basis for demonstrating a portable optical clock or even a space optical clock.

Reducing the Instability of an Optical Lattice Clock Using Multiple Atomic Ensembles

The stability of an optical atomic clock is a critical figure of merit for almost all clock applications. To this end, much optical atomic clock research has focused on reducing clock instability by increasing the atom number, lengthening the coherent interrogation times, and introducing entanglement to push beyond the standard quantum limit. In this work, we experimentally demonstrate an alternative approach to reducing clock instability using a phase estimation approach based on individually controlled atomic ensembles in a strontium (Sr) optical lattice clock. We first demonstrate joint Ramsey interrogation of two spatially resolved atom ensembles that are out of phase with respect to each other, which we call “quadrature Ramsey spectroscopy,” resulting in a factor of 1.36(5) reduction in absolute clock instability as measured with interleaved self-comparisons. We then leverage the rich hyperfine structure of Sr87 to realize independent coherent control over multiple ensembles with only global laser addressing. Finally, we utilize this independent control over four atom ensembles to implement a form of phase estimation, achieving a factor of greater than 3 enhancement in coherent interrogation time and a factor of 2.08(6) reduction in instability over an otherwise identical single-ensemble clock with the same local oscillator and the same number of atoms. We expect that multiensemble protocols similar to those demonstrated here will result in reduction in the instability of any optical lattice clock with an interrogation time limited by the local oscillator. Published by the American Physical Society 2024

Improved Limits on the Coupling of Ultralight Bosonic Dark Matter to Photons from Optical Atomic Clock Comparisons.

We present improved constraints on the coupling of ultralight bosonic dark matter to photons based on long-term measurements of two optical frequency ratios. In these optical clock comparisons, we relate the frequency of the ^{2}S_{1/2}(F=0)↔^{2}F_{7/2}(F=3) electric-octupole (E3) transition in ^{171}Yb^{+} to that of the ^{2}S_{1/2}(F=0)↔^{2}D_{3/2}(F=2) electric-quadrupole (E2) transition of the same ion, and to that of the ^{1}S_{0}↔^{3}P_{0} transition in ^{87}Sr. Measurements of the first frequency ratio ν_{E3}/ν_{E2} are performed via interleaved interrogation of both transitions in a single ion. The comparison of the single-ion clock based on the E3 transition with a strontium optical lattice clock yields the second frequency ratio ν_{E3}/ν_{Sr}. By constraining oscillations of the fine-structure constant α with these measurement results, we improve existing bounds on the scalar coupling d_{e} of ultralight dark matter to photons for dark matter masses in the range of about (10^{-24}-10^{-17}) eV/c^{2}. These results constitute an improvement by more than an order of magnitude over previous investigations for most of this range. We also use the repeated measurements of ν_{E3}/ν_{E2} to improve existing limits on a linear temporal drift of α and its coupling to gravity.

Photoionization cross sections of ultracold 88Sr in 1P1 and 3S1 states at 390 nm and the resulting blue-detuned magic wavelength optical lattice clock constraints.

We present the measurements of the photoionization cross sections of the excited 1P1 and 3S1 states of ultracold 88Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the 1S0-3P0 clock transition. The photoionization cross section of the 1P1 state is determined from the measured ionization rates of 88Sr in the magneto-optical trap in the 1P1 state to be 2.20(50)×10-20 m2, while the photoionization cross section of 88Sr in the 3S1 state is inferred from the photoionization-induced reduction in the number of atoms transferred through the 3S1 state in an operating optical lattice clock to be 1.38(66) ×10-18 m2. Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the 3S1 state would make the use of the 3S1 state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used 3D1,2 states during the detection part of the optical clock cycle.

Magnetic field analysis and active compensation system for strontium optical lattice clock in space

Magnetic field analysis and active compensation system for strontium optical lattice clock in space

Dual-axis cubic cavity for drift-compensated multi-wavelength laser stabilisation.

We describe a 'clock control unit' based on a dual-axis cubic cavity (DACC) for the frequency stabilisation of lasers involved in a strontium optical lattice clock. The DACC, which ultimately targets deployment in space applications, provides a short-term stable reference for all auxiliary lasers-i.e. cooling, clear-out, and optical lattice-in a single multi-band cavity. Long-term cavity drift is compensated by a feed-forward scheme exploiting a fixed physical relation to an orthogonal second cavity axis; either by reference to an ultrastable 698 nm clock laser, or by exploiting the differential drift between orthogonal axes extracted by a single laser in common view. Via a change of mirror set in the cavity axis accessed by the clock laser, the system could also provide stabilisation for sub-Hz linewidths at the 698 nm clock wavelength, fulfilling all stabilisation requirements of the clock.

Theoretical calculation of the quadratic Zeeman shift coefficient of the clock state for strontium optical lattice clock

In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of clock state for 88Sr and 87Sr atoms. By using this formula and the multi-configuration Dirac–Hartree–Fock theory, the quadratic Zeeman shift coefficients were calculated. The calculated values C 2 = –23.38(5) MHz/T2 for 88Sr and the , F = 9/2, MF = ±9/2 clock states for 87Sr agree well with the other available theoretical and experimental values, especially the most accurate measurement recently. In addition, the calculated values of the , F = 9/2, MF = ±9/2 clock states were also determined in our 87Sr optical lattice clock. The consistency with measurements verifies the validation of our calculation model. Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition, for example, the new proposed 1 S 0, F = 9/2, MF = ±5/2–, F = 9/2, MF = ±3/2 transitions.

Transportable Strontium Optical Lattice Clocks Operated Outside Laboratory at the Level of 10−18 Uncertainty

AbstractTransportable strontium optical lattice clocks are developed with a fractional uncertainty of 5.5 × 10−18 for applications outside laboratories. A single clock consists of a spectroscopy chamber and two laser boxes, where all lasers are based on external cavity diode lasers with an adjustment‐free, laser‐welded output coupler. When this system is transported from the laboratory at RIKEN to a broadcasting tower, the instruments experience acceleration change of 4 G at maximum. However, no serious optical misalignments are found. The demonstration opens up field applications of optical atomic clocks resolving a centimeter height difference.

Precision Metrology Meets Cosmology: Improved Constraints on Ultralight Dark Matter from Atom-Cavity Frequency Comparisons.

We conduct frequency comparisons between a state-of-the-art strontium optical lattice clock, a cryogenic crystalline silicon cavity, and a hydrogen maser to set new bounds on the coupling of ultralight dark matter to standard model particles and fields in the mass range of 10^{-16}-10^{-21} eV. The key advantage of this two-part ratio comparison is the differential sensitivity to time variation of both the fine-structure constant and the electron mass, achieving a substantially improved limit on the moduli of ultralight dark matter, particularly at higher masses than typical atomic spectroscopic results. Furthermore, we demonstrate an extension of the search range to even higher masses by use of dynamical decoupling techniques. These results highlight the importance of using the best-performing atomic clocks for fundamental physics applications, as all-optical timescales are increasingly integrated with, and will eventually supplant, existing microwave timescales.

A strontium optical lattice clock with 1 × 10−17 uncertainty and measurement of its absolute frequency

We present a measurement of the absolute frequency of the 5 s2 1S0 to 5s5p 3P0 transition in 87Sr which is a secondary representation of the SI second. We describe the optical lattice clock apparatus used for the measurement, and we focus in detail on how its systematic frequency shifts are evaluated with a total fractional uncertainty of 1 × 10−17. Traceability to the International System of Units is provided via comparison to International Atomic Time (TAI). Gathering data over 5- and 15-day periods, with the lattice clock operating on average 74% of the time, we measure the frequency of the transition to be 429 228 004 229 873.1 (5) Hz, which corresponds to a fractional uncertainty of 1 × 10−15. We describe in detail how this uncertainty arises from the intermediate steps linking the optical frequency standard, through our local time scale UTC(NPL), to an ensemble of primary and secondary frequency standards which steer TAI. The calculated absolute frequency of the transition is in good agreement with recent measurements carried out in other laboratories around the world.

Direct measurement of the frequency ratio for Hg and Yb optical lattice clocks and closure of the Hg/Yb/Sr loop.

We performed the first direct measurement of the frequency ratio between a mercury (199Hg) and an ytterbium (171Yb) optical lattice clock to find νHg/νYb = 2.177 473 194 134 565 07(19) with the fractional uncertainty of 8.8 × 10-17. The ratio is in excellent agreement with expectations from the ratios νHg/νSr and νYb/νSr obtained previously in comparisons against a strontium (87Sr) optical lattice clock. The completed closure (νHg/νYb)(νYb/νSr)(νSr/νHg) - 1 = 0.4(1.3) × 10-16 tests the frequency reproducibility of the optical lattice clocks beyond what is achievable in comparison against the current realization of the second in the International System of Units (SI).

Toward a quantum-enhanced strontium optical lattice clock at INRIM

The new strontium atomic clock at INRIM seeks to establish a new frontier in quantum measurement by joining state-of-the-art optical lattice clocks and the quantized electromagnetic field provided by a cavity QED setup. The goal of our experiment is to apply advanced quantum techniques to state-of-the-art optical lattice clocks, demonstrating enhanced sensitivity while preserving long coherence times and the highest accuracy. In this paper we describe the current status of the experiment and the prospected sensitivity gain for the designed cavity QED setup.

Cavity-enhanced non-destructive detection of atoms for an optical lattice clock.

We demonstrate a new method of cavity-enhanced non-destructive detection of atoms for a strontium optical lattice clock. The detection scheme is shown to be linear in atom number up to at least 2×104 atoms, to reject technical noise sources, to achieve signal to noise ratio close to the photon shot noise limit, to provide spatially uniform atom-cavity coupling, and to minimize inhomogeneous ac Stark shifts. These features enable detection of atoms with minimal perturbation to the atomic state, a critical step towards realizing an ultra-high-stability, quantum-enhanced optical lattice clock.

A pyramid MOT with integrated optical cavities as a cold atom platform for an optical lattice clock

We realize a two-stage, hexagonal pyramid magneto-optical trap (MOT) with strontium, and demonstrate loading of cold atoms into cavity-enhanced 1D and 2D optical lattice traps, all within a single compact assembly of in-vacuum optics. We show that the device is suitable for high-performance quantum technologies, focusing especially on its intended application as a strontium optical lattice clock. We prepare 2 × 104 spin-polarized atoms of 87Sr in the optical lattice within 500 ms; we observe a vacuum-limited lifetime of atoms in the lattice of 27 s; and we measure a background DC electric field of 12 V m−1 from stray charges, corresponding to a fractional frequency shift of (−1.2 ± 0.8) × 10−18 to the strontium clock transition. When used in combination with careful management of the blackbody radiation environment, the device shows potential as a platform for realizing a compact, robust, transportable optical lattice clock with systematic uncertainty at the 10−18 level.

A scalable arbitrary waveform generator for atomic physics experiments based on field-programmable gate array technology.

We present a field-programmable gate array (FPGA) based control system that has been implemented to control a strontium optical lattice clock at the National Physical Laboratory, UK. Bespoke printed circuit boards have been designed and manufactured, including an 8-channel, 16-bit digital to analog converter board with a 2 μs update rate and a 4-channel direct-digital synthesis board clocked at 1 GHz. Each board includes its own FPGA with 28 digital output lines available alongside the specialized analog or radio frequency outputs. The system is scalable to a large number of control lines by stacking the individual boards in a master-slave arrangement. The timing of the digital and analog outputs is based on the FPGA clock and is thus very predictable and exhibits low jitter. A particular advantage of our hardware is its large data buffers that, when combined with a pseudoclock structure, allow complex waveforms to be created. A high reliability of the system has been demonstrated during extended atomic clock frequency comparisons.

Development of 8-branch Er:fiber frequency comb for Sr and Yb optical lattice clocks.

We demonstrate an 8-branch Er:fiber frequency comb with seven application ports, which can be individually optimized for applications with different wavelengths. The beat between the comb and a cw laser has a signal-to-noise ratio exceeding 30 dB at a resolution bandwidth of 300 kHz. The 8-branch frequency comb is used to perform frequency locking for four repumping and lattice lasers, and the frequency measurement of two clock lasers of strontium and ytterbium optical lattice clocks. We have achieved reliable optical lattice clock operation, thanks to the stable frequency locking and measurement obtained by using the 8-branch frequency comb. The developed frequency comb is a powerful experimental tool for various applications, including not only optical lattice clocks, but also research on quantum optics that use many frequency-stabilized lasers.

Recent Advances Concerning the 87Sr Optical Lattice Clock at the National Time Service Center

We review recent experimental progress concerning the 87Sr optical lattice clock at the National Time Service Center in China. Hertz-level spectroscopy of the 87Sr clock transition for the optical lattice clock was performed, and closed-loop operation of the optical lattice clock was realized. A fractional frequency instability of 2.8 × 10−17 was attained for an averaging time of 2000 s. The Allan deviation is found to be 1.6 × 10−15/τ1/2 and is limited mainly by white-frequency-noise. The Landé g-factors of the (5s2)1S0 and (5s5p)3P0 states in 87Sr were measured experimentally; they are important for evaluating the clock’s Zeeman shifts. We also present recent work on the miniaturization of the strontium optical lattice clock for space applications.

Lattice-induced photon scattering in an optical lattice clock

We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several tens of seconds. Rayleigh scattering does not cause significant decoherence of the atomic superposition state near a magic wavelength. Among the Raman scattering processes, lattice-induced decay of the excited state $(5s5p)\,{}^{3}\mathrm{P}_{0}$ to the ground state $(5s^2)\,{}^{1}\mathrm{S}_{0}$ via the state $(5s5p)\,{}^{3}\mathrm{P}_{1}$ is particularly relevant, as it reduces the effective lifetime of the excited state and gives rise to quantum projection noise in spectroscopy. We observe this process in our experiment and find a decay rate of $556(15)\times 10^{-6}\,\mathrm{s}^{-1}$ per photon recoil energy $E_\mathrm{r}$ of effective lattice depth, which agrees well with the rate we predict from atomic data. We also derive a natural lifetime $\tau = 330(140)\,\mathrm{s}$ of the excited state ${}^{3}\mathrm{P}_{0}$ from our observations. Lattice-induced decay thus exceeds spontaneous decay at typical lattice depths used by present clocks. It eventually limits interrogation times in clocks restricted to high-intensity lattices, but can be largely avoided, e.g., by operating them with shallow lattice potentials.