Cold atom clocks and their applications in precision measurements

Cold atom clocks have made remarkable progresses in the last two decades and played critical roles in precision measurements. Primary Cs fountain frequency standards have achieved a total uncertainty of a few parts in 1016, and the best optical clock has reached a type B uncertainty below 10-18. Besides applications in the metrology, navigation, etc.,ultra-stable and ultra-accurate atomic clocks have also become powerful tools in the basic scientific investigations. In this paper, we focus on the recent developments in the high-performance cold atomic clocks which can be used as frequency standards to calibrate atomic time scales. The basic principles, performances, and limitations of fountain clocks and optical clocks based on signal trapped ion or neutral atoms are summarized. Their applications in metrology and other areas are briefly introduced.     

Einstein Lecture – Passion for precision

Optical frequency combs from mode‐locked femtosecond lasers have link optical and microwave frequencies in a single step, and they provide the long missing clockwork for optical atomic clocks. By extending the limits of time and frequency metrology, they enable new tests of fundamental physics laws. Precise comparisons of optical resonance frequencies of atomic hydrogen and other atoms with the microwave frequency of a cesium atomic clock are establishing sensitive limits for possible slow variations of fundamental constants. Optical high harmonic generation is extending frequency comb techniques into the extreme ultraviolet, opening a new spectral territory to precision laser spectroscopy. Frequency comb techniques are also providing a key to attosecond science by offering control of the electric field of ultrafast laser pulses. In our laboratories at Stanford and Garching, the development of new instruments and techniques for precision laser spectroscopy has long been motivated by the goal of ever higher resolution and measurement accuracy in optical spectroscopy of the simple hydrogen atom which permits unique confrontations between experiment and fundamental theory. This lecture recounts these adventures and the evolution of laser frequency comb techniques from my personal perspective.     

从引力波探测中的压缩光到光原子钟

2020 年度“墨子量子奖”授予量子精密测量领域, 获奖科学家是 Carlton Caves, 香取秀俊和叶军. 香取秀俊和叶军又获得2021 年基础物理学突破奖. 对于引力波探测中的量子噪声,Caves 分析了海森堡不确定关系所带来的测量精度极限, 并且提出用压缩光来克服这个极限. 这个方法已经被探测引力波的激光干涉仪实际采用. 原子钟基于原子中电子改变能量状态时, 发射或吸收的电磁波, 提供了最精确的时间和频率标准. 与基于微波的原子钟相比. 光原子钟, 特别是光晶格上的大量原子, 可以达到更好的精度. 叶军的研究组将约1 万个锶原子放在3 维光晶格中, 实现光原子钟, 相对精度达到2.5 × 10-19 . 香取秀俊的研究组搭建的两个可移动光原子钟, 精度达到了5 ×10-18 , 并用来测量了引力红移, 达到地面测量的最好精度.     

光和原子关联与量子计量

物理量的测量与单位标准的统一推动了计量学的发展.量子力学的建立,激光技术的发明以及原子与分子物理学的发展,在原理与技术上进一步刷新了计量学的研究内涵,特别是激光干涉与原子频标技术的发展,引起了计量学革命性的飞跃.基于激光干涉的引力波测量、激光陀螺仪,基于原子干涉的原子钟、原子陀螺仪等精密测量技术相继诞生,一个以量子物理为基础,探索与开拓物理量精密测量方法与技术的新的科学分支——量子计量学(Quantum Metrology)已然兴起.干涉是计量学中最常用的相位测量方法.量子干涉技术,其相位测量精度能够突破标准量子极限的限制,是量子计量学与量子测量技术的核心研究内容.本文重点介绍近几年我们在量子干涉方面所取得的新开拓与新发展,主要内容包括基于原子系综中四波混频过程的SU(1,1)型光量子关联干涉仪和基于原子系综中拉曼散射过程的光-原子混合干涉仪.     

Trapped ion optical clocks

A single laser-cooled ion confined in a radiofrequency ion trap comes close to the spectroscopic ideal of an absorber at rest in a perturbation-free environment. Narrow optical transitions in such systems are therefore very promising for the realisation of optical frequency standards with accuracy significantly exceeding that of current microwave primary frequency standards. When combined with femtosecond optical frequency combs, these standards can be operated as optical clocks generating a direct microwave output, raising the possibility of a future redefinition of the SI second. In this article, the fundamental aspects and current state-of-the-art of trapped ion optical clocks are reviewed, and the improvements that are likely to occur over the next few years are considered.     

The Hyperfine Transition for the Definition of the Second

The unit of time of the International System of Units (SI), the “atomic second” was defined through a constant of physics in 1967. It is derived from the frequency of the hyperfine transition of the atom of cesium 133. From the astronomical definition of the second until today, the accuracy of the realization of the second has improved by eight orders of magnitude, with a rate that has increased since the development of the cesium frequency standards, to reach parts in 10¹⁶ for the best clocks today. In 2018, when the new SI was adopted, the time metrology community proved that a new generation of frequency standards operating in optical wavelengths has uncertainties at the level of 10^–18, and challenge the implementation of high accurate frequency and time comparison techniques to decide on a revision of the definition of the second. Herein, the progress in the definition and realization of the second from astronomy until today is reviewed, an inventory of the present resources is assembled and a brief view for the future given.     

基于光纤的光学频率传递研究

随着光钟研究的发展, 光钟的稳定度和不确定度均达到10^-18量级. 通过光纤可以实现光钟频率信号的高精度传输, 有望用于未来“秒”定义的复现. 演示了百公里级实验室光纤上的光学频率传递. 对于在实验室70 km光纤盘上实现的光频传递, 光纤相位噪声抑制在1-250 Hz傅里叶频率范围内均接近于光纤延时极限, 对应传输稳定度(Allan偏差)为秒级稳定度1.2×10^-15, 10000 s稳定度为1.4×10^-18. 实验室100 km光纤的光频传递秒级稳定度也达到了5×10^-15. 提出了光纤噪声用户端补偿的方案, 可以简化星形传递网络中心站的复杂度. 在25 km光纤上演示了该传递方案, 实现的传输稳定度接近传统前置补偿传递方案.     

Generation of a broadband continuum by a Ti:sapphire femtosecond oscillator with a 1-GHz repetition rate

A five-element Ti:sapphire femtosecond ring oscillator emitting a broadband continuum that ranges from 560 to 1150 nm at -50 dB below the maximum with a repetition rate of 1 GHz is demonstrated. The key element is a slightly convex cavity mirror that increases the self-amplitude modulation of a short pulse inside the resonator. Flat negative intracavity group-delay dispersion is required only for the core spectral part of the pulse. We believe that the device presented will make optical frequency metrology and future optical atomic clocks simpler and more stable. Within the reported ultrabroad spectrum a distinct strong emission band near 655 nm occurs that can be extracted to a powerful femtosecond pulse source far out of the amplification of Ti:sapphire.     

Optical frequency comb technology for ultra‐broadband radio‐frequency photonics

The outstanding phase‐noise performance of optical frequency combs has led to a revolution in optical synthesis and metrology, covering a myriad of applications, from molecular spectroscopy to laser ranging and optical communications. However, the ideal characteristics of an optical frequency comb are application dependent. In this review, the different techniques for the generation and processing of high‐repetition‐rate (>10 GHz) optical frequency combs with technologies compatible with optical communication equipment are covered. Particular emphasis is put on the benefits and prospects of this technology in the general field of radio‐frequency photonics, including applications in high‐performance microwave photonic filtering, ultra‐broadband coherent communications, and radio‐frequency arbitrary waveform generation.     

Spatial and temporal coherence effects in interference microscopy and full‐field optical coherence tomography

Low‐coherence optical microscopy or optical coherence microscopy uses light with short coherence length. The well‐known case is: “white‐light interferometry”, which became recently more known as: “optical coherence tomography”. However, when lenses and microscope objectives are used to create interferometric images, in what is known classically as “interference microscopy” or today as “full‐field optical coherence tomography” the spatial coherence starts to play a critical role. In this article the coherence effects in low‐coherence optical microscopy are reviewed. As this technology is becoming increasingly publicized due to its importance in three‐dimensional imaging, particularly of scattering biological media and optical metrology, the understanding of the fundamental physics behind it is essential. The interplay between longitudinal spatial coherence and temporal coherence and the effects associated with them are discussed in detail particularly when high numerical apertures are used. An important conclusion of this study is that a high‐contrast, high‐resolution system for imaging of multilayered samples is the one that uses narrowband illumination and high‐NA objectives with an index‐matching fluid. Such a system, when combined with frequency‐domain operation, can reveal nearly real‐time three‐dimensional images, and is thus competitive with confocal microscopy.     

Frequency ratios of Sr,Yb, and Hg based optical lattice clocks and their applications

This article describes the recent progress of optical lattice clocks with neutral strontium (⁸⁷Sr), ytterbium (¹⁷¹Yb) and mercury (¹⁹⁹Hg) atoms. In particular, we present frequency comparison between the clocks locally via an optical frequency comb and between two Sr clocks at remote sites using a phase-stabilized fibre link. We first review cryogenic Sr optical lattice clocks that reduce the room-temperature blackbody radiation shift by two orders of magnitude and serve as a reference in the following clock comparisons. Similar physical properties of Sr and Yb atoms, such as transition wavelengths and vapour pressure, have allowed our development of a compatible clock for both species. A cryogenic Yb clock is evaluated by referencing a Sr clock. We also report on an Hg clock, which shows one order of magnitude less sensitivity to blackbody radiation, while its large nuclear charge makes the clock sensitive to the variation of fine-structure constant. Connecting all three types of clocks by an optical frequency comb, the ratios of the clock frequencies are determined with uncertainties smaller than possible through absolute frequency measurements. Finally, we describe a synchronous frequency comparison between two Sr-based remote clocks over a distance of 15 km between RIKEN and the University of Tokyo, as a step towards relativistic geodesy.     

光晶格原子钟研究进展

钟跃迁频率在光学频段的光晶格原子钟已经实现了10-19 量级的频率稳定度和10-18 量级的频率不确定度, 在量子频标、 量子模拟和精密测量等领域有着重要的应用. 本文综述了光晶格原子钟的发展历史、 工作原理、 性能评估和应用与展望.     

光辐射计量测试技术

简要介绍国外光辐射计量采用的主要方法、测试手段和发展趋势。为了满足国防系统对光辐射计量的需要建立了一批计量标难，解决了光辐射源辐射特性和探测器特性计量测试问题。     

Suppression of servo error uncertainty to 10~(-18) level using double integrator algorithm in ion optical clock

A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator.Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10~(-18), which is meaningful for the systematic uncertainty of the transportable single ~(40)Ca~+ ion optical clock entering the 10~(-18) level.     

A simplified optical lattice clock

Existing optical lattice clocks demonstrate a high level of performance but they remain complex experimental devices. In order to address a wider range of applications including those requiring transportable devices, it will be necessary to simplify the laser systems and reduce the amount of support hardware. Here we demonstrate two significant steps towards this goal: demonstration of clock signals from a Sr lattice clock based solely on semiconductor laser technology, and a method for finding the clock transition (based on a coincidence in atomic wavelengths) that removes the need for extensive frequency metrology hardware. Moreover, the unexpected high contrast in the signal revealed evidence of density dependent collisions in ⁸⁸Sr atoms.     

Delivering pulsed and phase stable light to atoms of an optical clock

In optical clocks, transitions of ions or neutral atoms are interrogated using pulsed ultra-narrow laser fields. Systematic phase chirps of the laser or changes of the optical path length during the measurement cause a shift of the frequency seen by the interrogated atoms. While the stabilization of cw-optical links is now a well-established technique even on long distances, phase stable links for pulsed light pose additional challenges and have not been demonstrated so far. In addition to possible temperature or pressure drift of the laboratory, which may lead to a Doppler shift by steadily changing the optical path length, the pulsing of the clock laser light calls for short settling times of stabilization locks. Our optical path length stabilization uses retro-reflected light from a mirror that is fixed with respect to the interrogated atoms and synthetic signals during the dark time. Length changes and frequency chirps are compensated for by the switching AOM. For our strontium optical lattice clock, we have ensured that the shift introduced by the fiber link including the pulsing acoustooptic modulator is below 2×10^-17.     

Long-distance frequency dissemination with a resolution of 10(-17)

We use a new technique to disseminate microwave reference signals along ordinary optical fiber. The fractional frequency resolution of a link of 86 km in length is 10(-17) for a one day integration time, a resolution higher than the stability of the best microwave or optical clocks. We use the link to compare the microwave reference and a CO2/OsO4 frequency standard that stabilizes a femtosecond laser frequency comb. This demonstrates a resolution of 3 x 10(-14) at 1 s. An upper value of the instability introduced by the femtosecond laser-based synthesizer is estimated as 1 x 10(-14) at 1 s.     

Fractal surface for calibration of an optical profiler

The surface profiler has become a basic metrology tool for the characterization of high-quality optical surfaces. The unknown effective resolution of the surface profiler is problematic in using the instrument, as it distorts the measured surface profile. In this paper, we suggest and describe the use of a fractal surface as a standard test surface with which to calibrate the effective resolution of a surface profiler. Fractal surfaces have the characteristics of irregularity, self-similarity and low correlation, with the correlation length being approximately equal to the length of the profile; therefore, a log-log plot of the power spectral density curve is a straight line. The power spectral density curves of fractal surfaces, which can be acquired through surface characterization techniques such as atomic force microscopy, are fitted to a straight line to act as a standard with which to calibrate an optical profiler in different ranges. Through calibration, we can obtain the effective resolution of the optical profiler, and the surface profiler is found to have good transmission capacity within the effective spatial frequency range.     

Interaction between atom and radiation with sinusoidally shaped amplitude: Applications to frequency standards

The study of the evolution of a two-level atom crossing an electromagnetic field with a sinusoidally shaped amplitude is of interest in frequency metrology because a few Cs beam standards share this type of realization. The Magnus expansion method helps to find a solution to this problem giving approximate analytical results, which are made easy to handle by a series expansion in the detuning between atom resonance and radiation frequency. Numerical checks show that rather simple expressions provide an accuracy better than 10^–3 in the matrix elements of the evolution operator for useful ranges of power levels and frequency differences. Two examples concerned with Cs beam standards are discussed.At the time of this work A.G. Shahian was a guest at Politecnico di Milano, with a grant of the Ministry for Foreign Affairs of Italy     

Long-external-cavity distributed Bragg reflector laser with subkilohertz intrinsic linewidth

We report on a simple, compact, and robust 780 nm distributed Bragg reflector laser with subkilohertz intrinsic linewidth. An external cavity with optical path length of 3.6 m, implemented with an optical fiber, reduces the laser frequency noise by several orders of magnitude. At frequencies above 100 kHz the frequency noise spectral density is reduced by over 33 dB, resulting in an intrinsic Lorentzian linewidth of 300 Hz. The remaining low-frequency noise is easily removed by stabilization to an external reference cavity. We further characterize the influence of feedback power and current variation on the intrinsic linewidth. The system is suitable for experiments requiring a tunable laser with narrow linewidth and low high-frequency noise, such as coherent optical communication, optical clocks, and cavity QED experiments.