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高精细度光学谐振腔辅助的量子非破坏(quantum nondemolition, QND)测量可产生原子自旋/动量压缩态, 是提升原子干涉灵敏度以突破标准量子极限的重要手段. 传统Fabry-Perot腔内驻波场结构导致的光与原子相互作用不均匀性, 使得原子自旋压缩度在演化过程中逐渐衰退. 本文研究一种面向原子干涉仪均匀QND测量的光学环形腔, 分析环形腔内行波场结构对光与原子相互作用均匀性的影响, 设计并研制了高精细度($ {\cal{F}} = 2.4(1)\times 10^{4} $)高真空兼容型光学环形腔, 并测试了环形腔特性. 在此基础上, 制备88Sr冷原子系综并与环形腔模式耦合, 通过环形腔差分测量方式提取原子经过腔模过程中对环形腔造成的色散相移, 实现对原子数目的非破坏测量. 实验结果表明在探测光功率为20 μW条件下, 测得环形腔色散相移为40 mrad, 耦合进腔内原子数目约为$ 1\times 10^{5} $. 调节原子与腔模位置匹配及探测光失谐量等参数, 验证了环形腔色散相移与QND测量理论的一致性. 本文研制的光学环形腔为原子干涉仪中自旋/动量压缩态的产生提供重要解决途径, 有望进一步提升原子干涉灵敏度, 并广泛应用于腔增强型量子精密测量中.High-finesse optical cavity assisted quantum nondemolition (QND) measurement is an important method of generating high-gain spin or momentum squeezed states, which can enhance the sensitivity of atom interferometers beyond the standard quantum limit. Conventional two-mirror Fabry-Perot cavities have the drawback of a standing wave pattern, leading to inhomogeneous atom-light coupling and subsequent degradation of metrological gain. In this study, we present a novel method of achieving homogeneous quantum nondemolition measurement by using an optical ring cavity to generate momentum squeezed states in atom interferometers. We design and develop a high-finesse ($ {\cal{F}} = 2.4(1) \times 10^{4} $), high-vacuum compatible ($ 1\times 10^{-10} \;{\rm mbar}$) optical ring cavity. It utilizes the properties of traveling wave fields to address the issue of inhomogeneous atom-light interaction. A strontium cold atomic ensemble is prepared and coupled into the cavity mode; the nondemolition measurement of atom number is achieved by extracting the dispersive cavity phase shift caused by the passage of atoms through differential Pound-Drever-Hall measurement. Experimental results indicate that under a probe laser power value of 20 μW, the dispersive phase shift of the ring cavity is measured to be 40 mrad. The effective number of atoms coupled into the cavity mode is around $ 1 \times 10^{5} $. The consistency between the ring cavity dispersive phase shift and QND measurement theory is verified by adjusting parameters such as matching the atomic position with the cavity mode and tuning the frequency of the probe laser. The optical ring cavity developed in this work provides an important method for generating spin or momentum squeezed states in atom interferometers. Therefore it holds promise for enhancing their sensitivity, and it is expected to be widely applied to cavity-enhanced quantum precision measurements.
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Keywords:
- optical ring cavity /
- quantum nondemolition measurement /
- spin squeezing /
- atom interferometer
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图 1 (a)原子与光学环形腔耦合模型, 一对Bragg激光($ \text{B}_{1} $和$ \text{B}_{2} $)用于制备基态的动量叠加态, 探测光和参考光沿相反方向耦合至腔内, 且与环形腔同时共振; (b) $ ^{88} {\mathrm{Sr}}$原子能级跃迁示意图, 其中$ \varDelta_{1} $和$ \varDelta_{2} $分别为参考光和探测光相对于$ ^{1} {\mathrm{S}} _{0} $—$ ^{3} {\mathrm{P}} _{1} $跃迁的失谐量; (c)光学环形腔内光束腰半径沿切平面(tangential plane, T-plane)和矢状面(sagittal plane, S-plane)的演化规律
Fig. 1. (a) Atom-optical ring cavity coupling model. A pair of Bragg beams ($ \text{B}_{1} $ and $ \text{B}_{2} $) are used to induce the momentum state superposition on the ground state, the probe and reference beams are coupled into the cavity with counter-propagating directions and are resonant with the cavity simultaneously; (b) $ ^{88} {\mathrm{Sr}}$ atomic transition energy diagram, where $ \varDelta_{1} $ and $ \varDelta_{2} $ are detunings of the reference and probe beam with respect to the $ ^{1} {\mathrm{S}} _{0} $–$ ^{3} {\mathrm{P}} _{1} $ transition; (c) optical ring cavity beam waist evolution at the tangential plane (T-plane) and the sagittal plane (S-plane).
图 2 自制腔镜支架原理图, 右插图为用于俯仰角度调节的分立零件
Fig. 2. Schematic for the homemade cavity mirror holder, right inset shows the parts for adjusting the rolling direction.
图 3 (a)光纤EOM输出的探测光束腰半径演化规律, 实线为拟合曲线; (b)探测光与光学环形腔模式匹配光路示意图(EOM, 电光调制器; PBS, 偏振分束器; CCD, 电荷耦合器件; PC, 计算机; PD, 光电探测器; Scope, 示波器; HW, 半波片)
Fig. 3. (a) Probe beam waist propagation at the output of the fiber-EOM, solid traces are fitting results; (b) mode-matching schematic for the probe beam and the optical ring cavity. EOM, electro-optic modulator; PBS, polarization beam splitter; CCD, charge coupled device; PC, personal computer; PD, photo detector; Scope, oscilloscope; HW, half-wave plate.
图 4 (a)利用翻转光学面板的方式实现环形腔腔镜整体粘连; (b)光学环形腔粘连至真空法兰示意图; (c)真空装配光学环形腔实物图
Fig. 4. (a) Schematic for epoxying the cavity mirrors by flipping the optical breadboard; (b) optical ring cavity schematic assembled on a vacuum flange; (c) optical ring cavity assembled into a vacuum chamber.
图 5 实验测试装置, 详见正文阐述. ECDL, 外腔半导体激光器; TA, 锥形放大器; PID, PID控制器; AOM, 声光调制器; OI, 光学隔离器; MOD, 调制信号; LO, 本振信号; MX, 混频器; ADC, 模数转换器; PZT, 压电传感器; HW, 半波片; QW, 1/4 波片
Fig. 5. Schematic for the experimental setup, see main text for more details. ECDL, external cavity diode laser; TA, tapered amplifier; PID, proportional-integral-derivative controller; AOM, acousto-optic modulator; OI, optical isolator; MOD, modulation; LO, local oscillator; MX, mixer; ADC, analog to digital converter; PZT, piezoelectric transducer; HW, half-wave plate; QW, quarter- wave plate.
图 6 (a) 光学环形腔自由光谱区测量, 蓝色实线为拟合曲线, 插图为电光调制产生的载波和边带; (b) 环形腔真空装配前后腔内光子数衰减振荡时间测量, 实线为指数衰减拟合曲线
Fig. 6. (a) Measurement of the FSR of the optical ring cavity. The blue solid trace is a fit of the data. Inset shows the carrier and sidebands as a result of electro-optic modulation. (b) Cavity photon decay time constant measurement before and after the cavity assembly. The solid traces are exponential decay fits of the data.
图 7 (a)锶原子冷却和环形腔内QND测量时序; (b)环形腔内QND测量结果. 蓝色点线为磁场梯度变化, 提供时序参考; 灰色虚线为环形腔透射信号, 监测PDH锁定状态; 红色实线为滤波处理后的差分PDH误差信号; 粉红色区域内显示原子对腔造成的相移
Fig. 7. (a) Experimental sequence for Sr atom cooling and QND measurement in the optical ring cavity; (b) QND measurement results in the optical ring cavity. The blue dotted trace shows the recording of the magnetic gradient, which provides a reference for time sequence; the gray dashed trace shows the cavity transmission signal, which monitors the PDH locking state; the red solid trace is the filtered differential PDH error signal, where the atom-induced cavity phase shift is shown in the pink shaded region.
图 8 (a)耦合进腔内原子数目随x方向补偿磁场电流大小变化, 蓝色实线为高斯拟合; (b)腔色散相移随探测光失谐量变化, 蓝色实线为基于函数$ y=a+b/x $的拟合
Fig. 8. (a) Effective atom number coupled into the cavity mode as a function of the current for the x-compensation coils. The blue trace is the Gaussian fit. (b) Cavity dispersive phase shift as a function of the frequency detuning of the probe beam. The blue trace is a fit with function $ y=a+b/x $.
表 1 光学环形腔真空制备前后主要参数测试结果
Table 1. Test results of the relevant optical ring cavity parameters before and after vacuum assembly.
Parameter Symbol Value (before) Value (after) Units Free spectral range FSR $ 1.4475(5) $ $ 1.4475(5) $ GHz Linewidth $ {\text{δ}}\nu $ $ 56.9(4) $ $ 60.4(1) $ kHz Finesse $ {\cal{F}} $ $ 2.5(4)\times 10^{4} $ $ 2.4(1)\times 10^{4} $ — 
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[1] Pezzè L, Smerzi A, Oberthaler M K, Schmied R, Treutlein P 2018 Rev. Mod. Phys. 90 035005
Google Scholar
[2] 鹿博, 韩成银, 庄敏, 柯勇贯, 黄嘉豪, 李朝红 2019 物理学报 68 040306
Google Scholar
Lu B, Han C Y, Zhuang M, Ke Y G, Huang J H, Li C H 2019 Acta Phys. Sin. 68 040306
Google Scholar
[3] Leroux I D, Schleier-Smith M H, Vuletić V 2010 Phys. Rev. Lett. 104 250801
Google Scholar
[4] Hosten O, Engelsen N J, Krishnakumar R, Kasevich M A 2016 Nature 529 505
Google Scholar
[5] Pedrozo-Peñafiel E, Colombo S, Shu C, Adiyatullin A F, Li Z, Mendez E, Braverman B, Kawasaki A, Akamatsu D, Xiao Y, Vuletić V 2020 Nature 588 414
Google Scholar
[6] Eckner W J, Darkwah Oppong N, Cao A, Young A W, Milner W R, Robinson J M, Ye J, Kaufman A M 2023 Nature 621 734
Google Scholar
[7] Greve G P, Luo C, Wu B, Thompson J K 2022 Nature 610 472
Google Scholar
[8] 黄馨瑶, 项玉, 孙风潇, 何琼毅, 龚旗煌 2015 物理学报 64 160304
Google Scholar
Huang X Y, Xiang Y, Sun F X, He Q Y, Gong Q H 2015 Acta Phys. Sin. 64 160304
Google Scholar
[9] Bao H, Duan J, Jin S, Lu X, Li P, Qu W, Wang M, Novikova I, Mikhailov E E, Zhao K F, Mølmer K, Shen H, Xiao Y 2020 Nature 581 159
Google Scholar
[10] Bornet G, Emperauger G, Chen C, Ye B, Block M, Bintz M, Boyd J A, Barredo D, Comparin T, Mezzacapo F, Roscilde T, Lahaye T, Yao N Y, Browaeys A 2023 Nature 621 728
Google Scholar
[11] Malia B K, Wu Y, Martínez-Rincón J, Kasevich M A 2022 Nature 612 661
Google Scholar
[12] 王恩龙, 王国超, 朱凌晓, 卞进田, 王玺, 孔辉 2024 激光与光电子学进展 61 050001
Google Scholar
Wang E L, Wang G C, Zhu L X, Bian J T, Wang X, Kong H 2024 Laser Optoelectron. Prog. 61 050001
Google Scholar
[13] Wineland D J, Bollinger J J, Itano W M, Heinzen D J 1994 Phys. Rev. A 50 67
Google Scholar
[14] Louchet-Chauvet A, Appel J, Renema J J, Oblak D, Kjaergaard N, Polzik E S 2010 New J. Phys. 12 065032
Google Scholar
[15] Bowden W, Vianello A, Hill I R, Schioppo M, Hobson R 2020 Phys. Rev. X 10 041052
Google Scholar
[16] Muniz J A, Young D J, Cline J R, Thompson J K 2021 Phys. Rev. Res. 3 023152
Google Scholar
[17] Cox K C, Greve G P, Wu B, Thompson J K 2016 Phys. Rev. A 94 061601
Google Scholar
[18] Salvi L, Poli N, Vuletić V, Tino G M 2018 Phys. Rev. Lett. 120 033601
Google Scholar
[19] Tino G M 2021 Quantum Sci. Technol. 6 024014
Google Scholar
[20] Cox K C, Meyer D H, Schine N A, Fatemi F K, Kunz P D 2018 J. Phys. B: At. Mol. Opt. Phys. 51 195002
Google Scholar
[21] Kawasaki A, Braverman B, Pedrozo-Peñafiel E, Shu C, Colombo S, Li Z, Özel Ö, Chen W, Salvi L, Heinz A, Levonian D, Akamatsu D, Xiao Y, Vuletić V 2019 Phys. Rev. A 99 013437
Google Scholar
[22] Braverman B, Kawasaki A, Pedrozo-Peñafiel E, Colombo S, Shu C, Li Z, Mendez E, Yamoah M, Salvi L, Akamatsu D, Xiao Y, Vuletić V 2019 Phys. Rev. Lett. 122 223203
Google Scholar
[23] Chen Y T, Szurek M, Hu B, de Hond J, Braverman B, Vuletić V 2022 Opt. Express 30 37426
Google Scholar
[24] Manzoor S, Tinsley J N, Bandarupally S, Chiarotti M, Poli N 2022 Opt. Lett. 47 2582
Google Scholar
[25] Heinz A, Trautmann J, Šantić N, Park A J, Bloch I, Blatt S 2021 Opt. Lett. 46 250
Google Scholar
[26] Zhang L, Wu M, Gao J, Liu J, Fan L, Jiao D, Xu G, Dong R, Liu T, Zhang S 2023 Appl. Phys. B 129 149
Google Scholar
[27] 姜海峰 2018 物理学报 67 160602
Google Scholar
Jiang H F 2018 Acta Phys. Sin. 67 160602
Google Scholar
[28] Bowden W, Hobson R, Hill I R, Vianello A, Schioppo M, Silva A, Margolis H S, Baird P E, Gill P 2019 Sci. Rep. 9 11704
Google Scholar
[29] Bernon S, Vanderbruggen T, Kohlhaas R, Bertoldi A, Landragin A, Bouyer P 2011 New J. Phys. 13 065021
Google Scholar
[30] Chen Z, Bohnet J G, Weiner J M, Cox K C, Thompson J K 2014 Phys. Rev. A 89 043837
Google Scholar
[31] Tanji-Suzuki H, Leroux I D, Schleier-Smith M H, Cetina M, Grier A T, Simon J, Vuletić V 2011 Adv. Mol. Opt. Phys. 60 201
Google Scholar
[32] Kogelnik H, Li T 1966 Appl. Opt. 5 1550
Google Scholar
[33] Carstens H, Holzberger S, Kaster J, Weitenberg J, Pervak V, Apolonski A, Fill E, Krausz F, Pupeza I 2013 Opt. Express 21 11606
Google Scholar
[34] Black E D 2001 Am. J. Phys. 69 79
Google Scholar
[35] Wang E, Verma G, Tinsley J N, Poli N, Salvi L 2021 Phys. Rev. A 103 022609
Google Scholar
[36] Sun Y L, Ye Y X, Shi X H, Wang Z Y, Yan C J, He L L, Lu Z H, Zhang J 2019 Class. Quantum Gravity 36 105007
Google Scholar
[37] Serra E, Borrielli A, Cataliotti F S, Marin F, Marino F, Pontin A, Prodi G A, Bonaldi M 2012 Phys. Rev. A 86 051801
Google Scholar
[38] Verma G, Wang E, Assendelft J, Poli N, Rosi G, Tino G M, Salvi L 2022 Appl. Phys. B 128 1
Google Scholar
[39] Han J X, Lu B Q, Yin M J, Wang Y B, Xu Q F, Lu X T, Chang H 2019 Chin. Phys. B 28 013701
Google Scholar
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