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

Li Ting; Lu Xiao-Tong; Zhou Chi-Hua; Yin Mo-Juan; Wang Ye-Bing; Chang Hong

doi:10.7498/aps.70.20201721

Abstract

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1. 引　言
2. 实验装置及原理
2.1 理论分析
2.2 实验装置
3. 测量结果与分析
4. 结　论

References

Cited By

Abstract

In an experimental system of ⁸⁷Sr 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 ⁸⁷Sr 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^–15 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 ⁸⁷Sr 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.

Keywords:

PACS:

37.10.Jk	(Atoms in optical lattices)
42.62.Fi	(Laser spectroscopy)
32.70.Jz	(Line shapes, widths, and shifts)

Authors and contacts

1.
Key Laboratory of Time and Frequency Primary Standards of Chinese Academy of Sciences, National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China
2.
School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Wang Ye-Bing, wangyebing@ntsc.ac.cn ; Chang Hong, changhong@ntsc.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11803042, 61775220), the National Key R&D Program of China (Grant No. 2016YFF0200201), the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC004), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2019400)

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1. 引　言

通常原子钟由量子参考体系、本地振荡器和锁定系统三部分构成. 对于最可能成为新一代的基准原子钟—光钟, 本地振荡器是超稳窄线宽激光系统^[1]. 在超稳窄线宽激光系统中, 由超低膨胀系数(ULE)的玻璃材料构成的高精细度超稳光学参考腔(ULE腔), 为超稳窄线宽激光的实现提供了一个稳定的频率基准. 锁定于ULE腔的超稳窄线宽激光具有优异的短期频率稳定性和极低的频率噪声. 除此之外, 超稳窄线宽激光系统在物理基本常数的测量^[2-4]、暗物质的寻找^[5-8]和引力波的探测^[9,10]等方面也有广泛的应用.

ULE腔通常由掺杂二氧化钛的玻璃材料和两个高反射的熔融石英镜组成, 其腔长容易受到温度变化、机械振动和气流等因素的影响^[11,12]. ULE腔腔长的稳定性决定了最终激光频率能够达到的稳定度. 在室温附近, ULE材料存在一个使其热膨胀系数为零的特殊温度点, 称为零温漂点^[13]. 在零温漂点处, ULE腔的腔长对温度的变化非常不敏感^[14], 并且ULE腔的长度为最小值^[15]. 因此, 为了降低ULE腔腔长对温度的敏感性, 使激光频率具有更好的稳定性和更小的漂移, 测量ULE腔的零温漂点尤为重要.

测量ULE腔的零温漂点的方法通常有以下几种: 第一种方法是使用锁定于高精度频率基准的光学频率梳, 通过测量不同温度下锁定于ULE腔的激光器的绝对频率, 得到ULE腔的零温漂点. 例如, 2018年中国科学院武汉物理与数学研究所利用该方法测得ULE腔的零温漂点, 测量误差为3 ℃^[13]. 第二种方法是使用稳定性更高的ULE腔作为参考, 通过测量ULE腔共振频率随温度的变化, 得到ULE腔的零温漂点. 例如, 2011年美国国家标准与技术研究所(National Institute of Standards and Technology, NIST)利用该方法测得ULE腔的零温漂点, 测量误差为0.1 ℃^[12]. 第三种方法是利用原子的钟跃迁谱或者饱和吸收谱作为参考, 通过测量不同温度下ULE腔共振频率, 得到ULE腔的零温漂点. 例如, 2018年中国科学院武汉物理与数学研究所利用原子的钟跃迁谱测得ULE腔的零温漂点, 其量误差为0.36 ℃^[13]; 2019年山西大学利用原子的饱和吸收谱测得ULE腔的零温漂点, 测量误差为0.22 ℃^[16]. 原子的钟跃迁谱相比于饱和吸收谱, 其谱线线宽更窄, 更适用于测量超稳窄线宽激光系统ULE腔的零温漂点. 在锶原子光晶格钟实验中, 通过扫描声光调制器(acousto-optic modulator, AOM)的频率, 得到原子的钟跃迁谱线, 然后根据不同温度下钟跃迁谱线的中心频率得到ULE腔的共振频率, 从而得到ULE腔的零温漂点^[13]. 这三种方法相比较而言, 由于实验条件的限制, 以原子的钟跃迁谱线来测量超稳窄线宽激光系统ULE腔的零温漂点, 测量精度更高、实验操作更方便.

2. 实验装置及原理

2.1 理论分析

在零温漂点处, ULE腔的腔长随温度波动的变化率具有最小值, 锁定到ULE腔的超稳窄线宽激光具有最小的频率漂移率^[12]. ULE腔的温度及其波动会引起腔长的变化, ULE腔的长度与温度变化关系^[17,18]为

$\Delta L/{L}_{0}=\frac{1}{2}\alpha {\left(T-{T}_{0}\right)}^{2}+\frac{1}{3}\beta {\left(T-{T}_{0}\right)}^{3},$

(1)

其中, ΔL为腔长变化量, L₀为ULE腔的腔长, α为有效热膨胀系数的线性温度系数, 其单位为ppb/K², β为二阶温度系数, T为实际温度, T₀为有效零温漂点. 在一阶近似下, ULE腔的长度变化量与温度的关系可表示为

$\Delta L=\frac{1}{2}{L}_{0}\alpha {\left(T-{T}_{0}\right)}^{2}.$

(2)

由于腔长变化量很小, 实验中不易测量, 所以通常转化为测量其共振频率的变化量^[19]. ULE腔的腔长与共振频率的关系为

$-\Delta L/{L}_{0}=\Delta v/{\nu }_{0},$

(3)

其中, v₀为共振频率, Δv为共振频率变化量. 则ULE腔的共振频率变化量与温度之间的变化关系为:

$\Delta v=-\frac{1}{2}\alpha {\nu }_{0}{\left(T-{T}_{0}\right)}^{2}.$

(4)

由(4)式可知, ULE腔的共振频率与温度是二次方的关系, 通过二项式拟合ULE腔共振频率随温度的变化关系, 可知ULE腔共振频率变化率最小值所对应的温度即为零温漂点.

2.2 实验装置

在⁸⁷Sr光晶格钟实验系统中, 利用锶原子(5s²)¹S₀—(5s5p)³P₀能级跃迁作为参考, 超稳窄线宽激光作为本地振荡器, 通过测量锶原子的跃迁几率得到频率的误差信号, 把超稳窄线宽激光系统的频率锁定到锶原子的钟跃迁谱线上, 从而实现⁸⁷Sr光晶格钟的闭环锁定. 量子参考体系的制备一般分为一级冷却、二级冷却以及光晶格装载. 经过一级冷却后, 获得的冷原子数目在10⁷量级、温度为5 mK. 为了进一步降低冷原子的温度, 进行二级冷却. 二级冷却结束后, 获得冷原子的数目在10⁶量级、温度为3.9 μK. 利用波长为813.42 nm (即“魔数波长”)、束腰为120 μm、光功率为300 mW的晶格光, 将冷原子囚禁在由其驻波光场形成的周期势阱(光晶格)中^[20]. 最终装载进光晶格中的冷原子数目在10⁴量级、温度约为3.0 μK^[21].

实验中使用的超稳窄线宽激光器是输出波长为698 nm的半导体激光器, 对应锶原子(5s²)¹S₀—(5s5p)³P₀能级跃迁. 其ULE腔的腔长为10 cm, 精细度为400000. 为了减小外界环境的影响, 将ULE腔安装在高真空圆柱形腔体中, 并且在高真空腔体的外表面配有温度控制器, 再将高真空腔体安装在有保温隔层的金属腔中, 将整个金属腔放置在隔震平台上并封闭在隔音箱中^[22]. 通过温度控制器调节高真空腔体外表面的温度, 从而实现调节和控制698 nm超稳窄线宽激光系统ULE腔的温度, 其控制精度为0.01 °C. 通过Pound-Drever-Hall (PDH)技术^[23]将698 nm超稳窄线宽激光频率锁定到ULE腔的共振频率上, 在压窄698 nm超稳窄线宽激光线宽的同时完成频率锁定, 获得超稳窄线宽激光的线宽在1 Hz左右, 从而能够实现698 nm超稳窄线宽激光的稳定输出^[24].

当原子被装载进光晶格中, 利用698 nm超稳窄线宽激光进行钟跃迁谱线的探测, 实验装置如图1所示. 698 nm超稳窄线宽激光经过PDH技术锁定后, 利用光纤将激光传输到⁸⁷Sr光晶格钟物理系统所在的实验平台上, 然后入射到光晶格中, 用来激发锶原子(5s²)¹S₀—(5s5p)³P₀能级跃迁. 最后, 通过AOM扫描698 nm超稳窄线宽激光的频率, 得到不同频率下的原子跃迁几率, 即钟跃迁谱线. 根据探测到的钟跃迁谱线的中心频率反馈控制AOM的工作频率, 从而实现⁸⁷Sr光晶格钟的闭环锁定. 在实验中, ${f}_{\rm{atom}}={f}_{\rm{AOM}}+{f}_{\rm{ULE}}$ , f_atom为锶原子(5s²)¹S₀–(5s5p)³P₀跃迁频率, f_AOM为AOM的工作频率, f_ULE为ULE腔的共振频率. 由于f_atom是不变的, 即 ${\Delta f}_{\rm{AOM}}=\Delta {f}_{\rm{ULE}}$ (Δf_AOM为AOM的工作频率变化量, Δf_ULE为ULE腔的共振频率变化量), 所以, 通过测量不同温度下f_AOM的值, 根据二阶多项式拟合AOM的工作频率随温度的变化曲线, 可得AOM的工作频率变化率最小值所对应的温度点, 即零温漂点.

$图 1 测量零温漂点的实验装置\r\nFig. 1. Schematic setup for zero-crossing temperature measurement.$

图 1 测量零温漂点的实验装置

Fig. 1. Schematic setup for zero-crossing temperature measurement.

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3. 测量结果与分析

将ULE腔的温度设置为31.11 °C, 通过扫描AOM的工作频率, 得到的⁸⁷Sr光晶格钟的钟跃迁谱线, 如图2所示. 其中, 黑色空心圆圈表示实验数据, 红色实线为洛伦兹函数非线性拟合曲线. 从图中的拟合结果可知, AOM的工作频率为231126364 Hz, 对应的谱线线宽为9 Hz.

$图 2 归一化钟跃迁谱线\r\nFig. 2. Normalized excitation spectra of clock transition.$

图 2 归一化钟跃迁谱线

Fig. 2. Normalized excitation spectra of clock transition.

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利用温度控制器分别将ULE腔的温度设定在多个温度点上, 为了使ULE腔达到更好的热平衡状态, 温度改变5 d后再进行测量, 从而得到多个温度点对应的钟跃迁谱线. 钟跃迁谱线中心频率(即对应的AOM的工作频率)随温度的变化关系如图3所示, 其中, 黑色空心圆圈表示实验测量数据, 红色的实线表示二阶多项式拟合曲线. 根据拟合结果可得698 nm超稳窄线宽激光系统ULE腔的零温漂点为30.63 °C, 误差为0.42 °C. 与ULE腔条件相似的情况进行对比, 实验中测量得到的结果与中国科学院武汉物理与数学研究所镱原子光钟实验小组测得的结果^[13]相符合, 由于测量的温度点略少, 所以对数据进行二阶多项式拟合时, 引起的测量误差略大.

$图 3 698 nm超稳窄线宽激光系统ULE腔零漂温点的测量\r\nFig. 3. Measurements at different controlled temperatures clock transition spectra.$

图 3 698 nm超稳窄线宽激光系统ULE腔零漂温点的测量

Fig. 3. Measurements at different controlled temperatures clock transition spectra.

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锶原子钟跃迁频率为429228004229873 Hz, 通过计算得到698 nm超稳窄线宽激光系统ULE腔的共振频率v₀为429228235463189 Hz. 从二阶多项式( $y=a{x}^{2}+bx+c$ )的拟合结果, 得到二次项系数a为0.269. 通过(4)式比对, 可得 $\alpha =2 a/{v}_{0}$ , 将a与v₀的值代入, 即可得到698 nm超稳窄线宽激光系统ULE腔的热膨胀系数的有效线性温度系数α为1.25 ppb/K².

当零温漂点确定后, 将698 nm超稳窄线宽激光系统ULE腔的温度设置为零温漂点, 利用锶原子光晶格钟的闭环锁定, 测量了698 nm超稳窄线宽激光系统ULE腔零温漂点处的频率漂移以及频率不稳定度. 锶原子光晶格钟闭环锁定的钟跃迁频率随时间的变化情况如图4(a)所示. 可以看出, 698 nm超稳窄线宽激光的频率漂移总体呈线性趋势. 通过对实验数据进行线性拟合, 得到698 nm超稳窄线宽激光系统的线性漂移率为0.15 Hz/s. 图4(a)中的插图为698 nm超稳窄线宽激光频率漂移率随时间的变化情况. 由图4(a)中插图的数据可知, 在88%的测量时间内, 698 nm超稳窄线宽激光的频率漂移率都在 ± 0.3 Hz/s以内. 利用图4(a)中的数据, 计算阿仑偏差, 结果如图4(b)所示, 其中, 黑色方点为阿仑偏差数据, 方点上的线为误差棒. 从图4(b)中可以看出, 在3.744 s的平均时间内, 698 nm超稳窄线宽激光系统的不稳定度约为1.6 × 10^–15. 在3.744 s以后, 随着频率漂移的增加, 698 nm超稳窄线宽激光系统的频率不稳定度逐渐变大.

$图 4 (a) 698 nm激光频率随时间的漂移; (b) 698 nm激光系统的频率不稳定度\r\nFig. 4. (a) 698 nm laser frequency drift with the time; (b) fractional frequency instability of the 698 nm laser.$

图 4 (a) 698 nm激光频率随时间的漂移; (b) 698 nm激光系统的频率不稳定度

Fig. 4. (a) 698 nm laser frequency drift with the time; (b) fractional frequency instability of the 698 nm laser.

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4. 结　论

本文利用原子的钟跃迁谱线测量了698 nm超稳窄线宽激光系统ULE腔的零温漂点, 得到的ULE腔的零温漂点为30.63 °C. 在零温漂点处, 测得698 nm超稳窄线宽激光的线性漂移率为0.15 Hz/s, 频率不稳定度为1.6 × 10^–15 @3.744 s. 698 nm超稳窄线宽激光系统ULE腔零温漂点的确定, 对于698 nm超稳窄线宽激光系统的意义重大, 不仅有助于提高698 nm超稳窄线宽激光系统的不稳定度, 还有助于提高⁸⁷Sr光晶格钟系统的不稳定度. 在今后的工作中, 我们将对698 nm超稳窄线宽激光系统ULE腔的温度控制系统进行改进, 提高ULE腔的温度控制精度, 减小测量误差, 从而得到更精确的零温漂点, 更进一步地提高698 nm超稳窄线宽激光系统的频率不稳定度.

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[20]	卢晓同, 李婷, 孔德欢, 王叶兵, 常宏 2019 物理学报 68 233401 Google Scholar Lu X T, Li T, Kong D H, Wang Y B, Chang H 2019 Acta Phys. Sin. 68 233401 Google Scholar
[21]	Lu X T, Yin M J, Li T, Wang Y B, Chang H 2020 Appl. Sci. 10 1440 Google Scholar
[22]	高峰, 刘辉, 许鹏, 王叶兵, 田晓, 常宏 2014 物理学报 63 140704 Google Scholar Gao F, Liu H, Xu P, Wang Y B, Tian X, Chang H 2014 Acta Phys. Sin. 63 140704 Google Scholar
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Cited By

期刊类型引用(2)

1.	卢炳坤，林弋戈，方占军. 我国基准光钟及其绝对频率测量. 物理. 2023(07): 456-466 . 百度学术
2.	卢飞飞，白建东，侯晓凯，王欣，郝丽丽，何军，王军民. 置于超高真空环境且控温的超稳光学腔的腔线宽及零膨胀温度点测定. 量子光学学报. 2022(04): 288-295 . 百度学术

其他类型引用(1)

图 1 测量零温漂点的实验装置

Figure 1. Schematic setup for zero-crossing temperature measurement.

DownLoad: Full-Size Img PowerPoint

图 2 归一化钟跃迁谱线

Figure 2. Normalized excitation spectra of clock transition.

DownLoad: Full-Size Img PowerPoint

图 3 698 nm超稳窄线宽激光系统ULE腔零漂温点的测量

Figure 3. Measurements at different controlled temperatures clock transition spectra.

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图 4 (a) 698 nm激光频率随时间的漂移; (b) 698 nm激光系统的频率不稳定度

Figure 4. (a) 698 nm laser frequency drift with the time; (b) fractional frequency instability of the 698 nm laser.

DownLoad: Full-Size Img PowerPoint

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期刊类型引用(2)

1.	卢炳坤，林弋戈，方占军. 我国基准光钟及其绝对频率测量. 物理. 2023(07): 456-466 . 百度学术
2.	卢飞飞，白建东，侯晓凯，王欣，郝丽丽，何军，王军民. 置于超高真空环境且控温的超稳光学腔的腔线宽及零膨胀温度点测定. 量子光学学报. 2022(04): 288-295 . 百度学术

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