Strontium Optical Lattice Clock Research Articles

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.

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.

Strontium optical lattice clock at the National Time Service Center**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474282 and 61775220), the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC004), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030700).

We report the 87Sr optical lattice clock developed at the National Time Service Center. We achieved a closed-loop operation of the optical lattice clock based on 87Sr atoms. The linewidth of the spin-polarized clock peak is 3.9 Hz with a clock laser pulse length of 300 ms, which corresponds to a Fourier-limited linewidth of 3 Hz. The fitting of the in-loop error signal data shows that the instability is approximately , affected primarily by the white noise. The fractional frequency difference averages down to for an averaging time of 3000 s.

Strontium optical lattice clock

The strontium optical lattice clock has experienced a rapid development since the beginning of the 21st century. Its relative frequency uncertainty, on the order of 10-18, has surpassed that of the cesium fountain clock, the current primary standard for time and frequency. This supreme level of precision reflects one of the most advanced measurement capabilities of mankind. This article reviews the current progress of the strontium optical lattice clock, and describes its key components and techniques, including high-resolution spectroscopy, close-loop operation, evaluation of systematic shifts, and absolute frequency measurement. The applications and future outlook of the strontium clock are also summarized.

Interrogation of spin polarized clock transition in strontium optical lattice clock

We demonstrate a spin-polarized clock transition spectrum of the 87Sr optical lattice clock. The clock transition 5s2 1S05s5p 3P0 of isotope 87Sr has a hyperfine structure due to non-zero nuclear spin, inducing ten -polarized transitions from each individual mF state under the condition of a bias magnetic field along the probing polarization axis. In this experiment, atoms are driven to a certain mF state by a circular-polarization pump light to maximize the atomic population, which is beneficial to the stability and uncertainty evaluation of the optical lattice clock. After two stages cooling and trapping, about 3.5106 atoms are trapped in the red magneto-optical trap with a temperature of 3.9 K. A grating-feedback external cavity diode laser with a tapered amplifier is used to build the optical lattice with a magic-wavelength of 813.426 nm. Both waists of the counter-propagating lattice beam along the horizontal direction are overlapped to form a one-dimensional (1D) optical lattice. The lifetime of the atoms trapped in the 1D optical lattice is 1600 ms. The clock laser at 698 nm is a grating-feedback diode laser, which is locked to an ultra-low expansion cavity by the Pound-Drever-Hall technique to stabilize the frequency and phase. As a result, the linewidth of clock laser is narrowed to Hz level. By the normalized shelving method, we obtain a resolved sideband spectrum of 87Sr 5s2 1S05s5p 3P0 transition. According to the spectrum, the lattice temperature along the longitudinal direction is approximately 4.2 K. After that a linewidth of 6.7 Hz of the degenerate clock transition is obtained at a probing time of 150 ms by utilizing a three-dimensional (3D) bias magnetic field, which is used to eliminate the stray magnetic fields. Then a small bias magnetic field of 300 mGs is applied along the polarization axis of the lattice light to achieve the spectrum of Zeeman magnetic sublevels of the clock transition. Furthermore, the mF=+9/2 and mF=-9/2 magnetic sublevels are picked to be respectively pumped by the +-polarized and --polarized light at 689 nm, a variable liquid crystal wave plate is employed to switch on both polarizations. Finally, the spin polarized clock transition spectrum is obtained at the interrogating pulse of 150 ms, and the linewidths of the mF=+9/2, mF=-9/2 magnetic sublevel transitions are 6.8 Hz and 6.2 Hz respectively.