Sr Optical Lattice Clock Research Articles

Improved frequency ratio measurement with 87Sr and 171Yb optical lattice clocks at NMIJ

We report improved frequency ratio measurement with 87Sr and 171Yb optical lattice clocks at the National Metrology Institute of Japan. The 87Sr optical lattice clock is enhanced with several major modifications and is re-evaluated with a reduced uncertainty of 1.1 × 10−16. We employed a 171Yb optical lattice clock with an uncertainty of 4 × 10−16 that was developed for contributing to International Atomic Time. The measurement result is ν Yb/ν Sr = 1.207 507 039 343 338 58(49)sys(6)stat with a fractional uncertainty of 4.1 × 10−16, which is 3.4 times smaller than our previous measurement result.

Evaluation of systematic uncertainty for transportable <sup>87</sup>Sr optical lattice clock

Transportable optical clocks have broad applications in scientific research and engineering. Accurate evaluation of systematic uncertainty for the transportable <sup>87</sup>Sr optical lattice clock is a prerequisite for the practical realization of the optical clock. Four main frequency shifts of the <sup>87</sup>Sr optical lattice clock are measured, i.e. blackbody-radiation (BBR) shift, collision shift, lattice alternating current (AC) Stark shift, and second-order Zeeman shift. Firstly, by measuring the temperature distribution on the surface of the magneto-optical trap cavity and analyzing the influence of different heat sources on atomic cloud, the BBR shift correction is measured to be 50.4 × 10<sup>–16</sup> Hz with an uncertainty of 5.1 × 10<sup>–17</sup>. Secondly, the time-interleaved self-comparison method is used under high and low atom density condition to evaluate the collision shift of the system. The correction of collision shift is 4.7 × 10<sup>–16</sup> with an uncertainty of 5.6 × 10<sup>–17</sup>. Thirdly, the lattice AC Stark shift is evaluated by the time-interleaved self-comparison method. By measuring the dependence of the lattice AC Stark shift on the wavelength of the lattice light, the magic wavelength is measured to be 368554393(78) MHz. As a result, the lattice AC Stark shift correction is 3.0 × 10<sup>–16</sup> with an uncertainty of 2.2 × 10<sup>–16</sup>. Finally, using the time-interleaved self-comparison technology, the second-order Zeeman frequency shift is evaluated by measuring the fluctuation of the difference in center frequency between the <inline-formula><tex-math id="M300">\begin{document}${m_{\text{F}}} = + {9 / 2} \to {m_{\text{F}}} = + {9 / 2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M300.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M300.png"/></alternatives></inline-formula> polarization spectrum and <inline-formula><tex-math id="M301">\begin{document}${m_{\text{F}}} = - {9 / 2} \to {m_{\text{F}}} = - {9 / 2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M301.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M301.png"/></alternatives></inline-formula> polarization spectrum. The correction of second-order Zeeman shift is calculated to be 0.7 × 10<sup>–16</sup>, and corresponding uncertainty is 0.2 × 10<sup>–17</sup>. Experimental results indicate that the frequency shift correction due to the blackbody radiation is the largest, while the uncertainty caused by the lattice AC Stark effect is the largest in the evaluated shifts. The systematic shift is 58.8 × 10<sup>–16</sup>, the total uncertainty is 2.3 × 10<sup>–16</sup>. In the next work, the magneto-optical trap cavity will be placed in a blackbody-radiation cavity to reduce the blackbody-radiation shift. The uncertainty of the collision shift will be reduced by increasing the beam waist of the lattice and reducing the potential well depth of the lattice, which will reduce the density of atoms. What is more, the light source for the optical lattice after spectral filtering will be measured by an optical frequency comb locked to the hydrogen clock signal to reduce the uncertainty of the lattice AC Stark frequency shift. The systematic uncertainty is expected to be on the order of 10<sup>–17</sup>. The evaluation of the systematic uncertainty for the transportable <sup>87</sup>Sr optical lattice clock lays the foundation for the practical application.

Synchronous frequency comparison beyond the Dick limit based on dual-excitation spectrum in an optical lattice clock

We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between |mF|=9/2 and |mF|=7/2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.

Zero-crossing temperature of ultra-stable optical reference cavity measured by optical transition spectrum

In an experimental system of <sup>87</sup>Sr atomic optical lattice clock, the free-running 698 nm diode laser is locked in an ultra-stable optical reference cavity to obtain the ultra-stable narrow linewidth laser with good short-term frequency stability. The ultra-stable optical reference cavity, which is usually composed of glass material doped with titanium dioxide for ultra-low thermal expansion coefficient and two highly reflective fused quartz mirrors, is called ULE cavity. The cavity length is prone to being affected by mechanical vibration, temperature change, airflow, etc. The stability of the cavity length determines the stability of the final laser frequency. Near the room temperature, there exists a special temperature point for the ultra-low expansion glass material, at which temperature its thermal expansion coefficient becomes zero, which is called the zero-crossing temperature. At the zero-crossing temperature, the length of the ULE cavity is not sensitive to the temperature fluctuation, reaching a minimum value, and the laser locked to the ULE cavity has a minimum frequency drift. In order to reduce the influence of temperature on the laser frequency instability, the zero-crossing temperature of the ultra-stable optical reference cavity of 698 nm ultra-stable narrow linewidth laser system is measured by using the clock transition spectrum of the strontium atomic optical lattice clock. The frequency drift and frequency instability of the 698 nm ultra-stable narrow linewidth laser system at zero-crossing temperature are measured by using the change of the in-loop locked clock frequency of strontium atomic optical lattice clock. By scanning the atomic clock transition frequencies at different temperatures, the clock transition spectra at different temperatures are obtained. The second order polynomial fitting of the central frequency of the clock transition spectrum with the change curve of temperature is carried out, and the zero-crossing temperature of the 698 nm ultra-stable narrow linewidth laser system ULE cavity is measured to be 30.63 ℃. At the zero-crossing temperature, the 698 nm ultra-stable narrow linewidth laser frequency is used for in-loop locking of <sup>87</sup>Sr atomic optical lattice clock. The linear drift rate of the ULE cavity in the 698 nm ultra-stable narrow linewidth laser system is measured to be 0.15 Hz/s, and the frequency instability of the 698 nm ultra-stable narrow linewidth laser system is 1.6 × 10<sup>–15</sup> at an average time of 3.744 s. The determination of ULE cavity zero-crossing temperature for the 698 nm ultra-stable narrow linewidth laser system is of great significance in helping to not only improve the instability of the laser system, but also increase the instability of <sup>87</sup>Sr optical lattice clock system. In the future, we will improve the temperature control system of the ULE cavity in the 698 nm clock laser system, enhancing the temperature control accuracy of the ULE cavity and reducing the measurement error, thus achieving a more accurate zero-crossing temperature and further improving the frequency instability of the 698 nm ultra-stable narrow linewidth laser system.

Frequency ratio of an 115In+ ion clock and a 87Sr optical lattice clock.

We report on the first, to the best of our knowledge, frequency ratio measurement of an 115In+ singleion clock and a 87Sr optical lattice clock. A hydrogen maser serves as a flywheel oscillator to measure the ratio by independent optical combs. From 89,000 s of measurement time, the frequency ratio fIn/fSr is determined to be 2.952 748 749 874 863 3(23) with 7.7×10-16 relative uncertainty. The measurement creates a new connection in the network of frequency ratios of optical clocks.

Demonstration of the frequency-drift-induced self-comparison measurement error in optical lattice clocks

The frequency-drift-induced self-comparison measurement error was experimentally demonstrated by measuring the frequency difference between two interleaved clock loops with the same systemic parameters in the 87Sr optical lattice clock at the National Time Service Center of China. Combining the experimental and simulated results, this error was precisely determined by the total clock laser frequency drift during the time interval between two adjacent operations of interleaved clock loops.

State-Dependent Optical Lattices for the Strontium Optical Qubit.

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than 4 orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.

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).

An Evaluation of the Zeeman Shift of the 87Sr Optical Lattice Clock at the National Time Service Center

The Zeeman shift plays an important role in the evaluation of optical lattice clocks since a strong bias magnetic field is applied for departing Zeeman sublevels and defining a quantization axis. We demonstrated the frequency correction and uncertainty evaluation due to Zeeman shift in the 87Sr optical lattice clock at the National Time Service Center. The first-order Zeeman shift was almost completely removed by stabilizing the clock laser to the average frequency of the two Zeeman components of mF = ±9/2. The residual first-order Zeeman shift arose from the magnetic field drift between measurements of the two stretched-state center frequencies; the upper bound was inferred as 4(5) × 10−18. The quadratic Zeeman shift coefficient was experimentally determined as –23.0(4) MHz/T2 and the final Zeeman shift was evaluated as 9.20(7) × 10−17. The evaluation of the Zeeman shift is a foundation for overall evaluation of the uncertainty of an optical lattice clock. This measurement can provide more references for the determination of the quadratic coefficient of 87Sr.

JILA SrI optical lattice clock with uncertainty of

We report on an improved systematic evaluation of the JILA SrI optical lattice clock, achieving a nearly identical uncertainty compared to the previous strontium record set by the JILA SrII optical lattice clock at . This improves upon the previous evaluation of the JILA SrI optical lattice clock in 2013, and we achieve a more than twenty-fold reduction in systematic uncertainty to . A seven-fold improvement in clock stability, reaching for an averaging time in seconds, allows the clock to average to its systematic uncertainty in under 10 min. We improve the systematic uncertainty budget in several important ways. This includes a novel scheme for taming blackbody radiation-induced frequency shifts through active stabilization and characterization of the thermal environment, inclusion of higher-order terms in the lattice light shift, and updated atomic coefficients. Along with careful control of other systematic effects, we achieve low temporal drift of systematic offsets and high uptime of the clock. We additionally present an improved evaluation of the second order Zeeman coefficient that is applicable to all Sr optical lattice clocks. These improvements in performance have enabled several important studies including frequency ratio measurements through the boulder area clock optical network (BACON), a high precision comparison with the JILA 3D lattice clock, a demonstration of a new all-optical time scale combining SrI and a cryogenic silicon cavity, and a high sensitivity search for ultralight scalar dark matter.

Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks

Improvements in atom-light coherence are foundational to progress in quantum information science, quantum optics, and precision metrology. Optical atomic clocks require local oscillators with exceptional optical coherence due to the challenge of performing spectroscopy on their ultra-narrow linewidth clock transitions. Advances in laser stabilization have thus enabled rapid progress in clock precision. A new class of ultrastable lasers based on cryogenic silicon reference cavities has recently demonstrated the longest optical coherence times to date. In this work we utilize such a local oscillator, along with a state-of-the-art frequency comb for coherence transfer, with two Sr optical lattice clocks to achieve an unprecedented level of clock stability. Through an anti-synchronous comparison, the fractional instability of both clocks is assessed to be $4.8\times 10^{-17}/\sqrt{\tau}$ for an averaging time $\tau$ in seconds. Synchronous interrogation reveals a quantum projection noise dominated instability of $3.5(2)\times10^{-17}/\sqrt{\tau}$, resulting in a precision of $5.8(3)\times 10^{-19}$ after a single hour of averaging. The ability to measure sub-$10^{-18}$ level frequency shifts in such short timescales will impact a wide range of applications for clocks in quantum sensing and fundamental physics. For example, this precision allows one to resolve the gravitational red shift from a 1 cm elevation change in only 20 minutes.

Dual-wavelength-pumped Tm3+-doped ZBLAN fiber MOPA at 813 nm

We report a dual-wavelength-pumped (1220 nm + 1050 nm) Tm3+-doped ZBLAN fiber master oscillator power amplifier (MOPA) system at 813 nm for the lattice laser of the Sr optical lattice clock (OLC). Since the photodarkening effect of the Tm3+-doped fiber is more serious in the 800 nm region, it was suppressed by applying real-time photobleaching with a 532 nm laser for obtaining stable output. We also investigated the dependence of conversion efficiency on the launched pump power ratio (P1220 nm/P1220+1050 nm) and found that the maximum conversion efficiency of 50% was obtained from the pump power ratio of 41%. By installing real-time photobleaching and dual-wavelength pumping, our MOPA system generated the maximum output power of 1.95 W with slope efficiency of 48%, which is the highest output power at around 810 nm from fiber laser sources, to the best of our knowledge.

Direct phase-locking of a Ti:Sapphire optical frequency comb to a remote optical frequency standard.

We report on an ultralow noise optical frequency transfer from a remotely located Sr optical lattice clock laser to a Ti:Sapphire optical frequency comb through telecom-wavelength optical fiber networks. The inherent narrow linewidth of the Ti:Sapphire optical frequency comb eliminates the need for a local reference high-finesse cavity. The relative fractional frequency instability of the optical frequency comb with respect to the remote optical reference was 6.7(1) × 10-18 at 1 s and 1.05(3) × 10-19 at 1,000 s including a 2.9 km-long fiber network. This ensured the optical frequency comb had the same precision as the optical standard. Our result paves the way for ultrahigh-precision spectroscopy and conversion of the highly precise optical frequency to radio frequencies in a simpler setup.

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.

Operational Magic Intensity for Sr Optical Lattice Clocks.

We experimentally investigate the lattice-induced light shift by the electric-quadrupole (E2) and magnetic-dipole (M1) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the E2-M1 polarizability difference. Measured polarizabilities determine an operational lattice depth to be 72(2)E_{R}, where the total light shift cancels to the 10^{-19} level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.

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.

Advanced Satellite-Based Frequency Transfer at the 10-16 Level.

Advanced satellite-based frequency transfers by two-way carrier-phase (TWCP) and integer precise point positioning have been performed between the National Institute of Information and Communications Technology and Korea Research Institute of Standards and Science. We confirm that the disagreement between them is less than at an averaging time of several days. In addition, an overseas frequency ratio measurement of Sr and Yb optical lattice clocks was directly performed by TWCP. We achieved an uncertainty at the mid-10-16 level after a total measurement time of 12 h. The frequency ratio was consistent with the recently reported values within the uncertainty.

Experimental Determination of the Landé g-Factors for 5s2 1S and 5s5p 3P States of the 87Sr Atom**Supported by the National Natural Science Foundation of China under Grant Nos 61127901, 11404025 and 91536106, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB21030700, the Key Research Project of Frontier Science of Chinese Academy of Sciences under

We present an experimental determination on the Landé g-factors for the 5s2 1S0 and 5s5p 3P0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the 87Sr optical lattice clock. The Zeeman shift of the 5s5p 3P0–5s2 1S0 forbidden transition is measured with the π-polarized and σ±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5s2 1S0 g-factor for the 87Sr atom is −1.306(52)×10−4, which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factor δg between the 5s5p 3P0 state and the 5s2 1S0 state of the 87Sr atoms is measured in the experiment as well, which are −7.67(36) × 10−5 with π-transition spectra and −7.72(43) × 10−5 with σ±-transition spectra, in good agreement with the previous report [Phys. Rev. A 76 (2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.

Months-long real-time generation of a time scale based on an optical clock

Time scales consistently provide precise time stamps and time intervals by combining atomic frequency standards with a reliable local oscillator. Optical frequency standards, however, have not been applied to the generation of time scales, although they provide superb accuracy and stability these days. Here, by steering an oscillator frequency based on the intermittent operation of a 87Sr optical lattice clock, we realized an “optically steered” time scale TA(Sr) that was continuously generated for half a year. The resultant time scale was as stable as International Atomic Time (TAI) with its accuracy at the 10−16 level. We also compared the time scale with TT(BIPM16). TT(BIPM) is computed in deferred time each January based on a weighted average of the evaluations of the frequency of TAI using primary and secondary frequency standards. The variation of the time difference TA(Sr) – TT(BIPM16) was 0.79 ns after 5 months, suggesting the compatibility of using optical clocks for time scale generation. The steady signal also demonstrated the capability to evaluate one-month mean scale intervals of TAI over all six months with comparable uncertainties to those of primary frequency standards (PFSs).

Geodesy and metrology with a transportable optical clock

The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a revision of the International System of units (SI). However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy, a major challenge remains. This is their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations. Here we report the first field measurement campaign performed with a ubiquitously applicable $^{87}$Sr optical lattice clock. We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km apart, exploiting both local and remote clock comparisons to eliminate potential clock errors. A local comparison with a $^{171}$Yb lattice clock also serves as an important check on the international consistency of independently developed optical clocks. This campaign demonstrates the exciting prospects for transportable optical clocks.