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The squeezed light field in the band of alkali metal atomic transitions is an important quantum resource in the field of quantum information and precision measurement. The wavelengths of atomic transition lines (760–860 nm) are relatively short. Limited by the gray-tracking effect of nonlinear crystals, the squeezing degree of the squeezed light in this band generated by the optical parametric amplifiers is low. Now, the squeezing is about 3–5 dB. Considering the problems in the experimental generation of the squeezed light at the wavelengths of atomic transitions, the variation law of quantum noise of the light field output from the single optical parametric amplifier with its physical parameters is studied theoretically, and the optimal physical parameters are obtained. To further improve the squeezing in the band of alkali metal atomic transitions, the cascaded optical parametric amplifiers are considered. Based on the basic theory of the optical parametric amplifiers, the theoretical model of the cascaded optical parametric amplifiers is constructed, in which the optical loss and phase noise of the cascaded optical loops are considered. Based on this, the quantum noise characteristics of the light field output from the cascaded system versus the optical loss and phase noise are analyzed at the frequencies of 2 MHz and 100 kHz, respectively. It is found that for the squeezing at 2 MHz, cascading 2 to 3 optical parametric amplifiers can significantly improve the squeezing under the premise of the low optical path loss and phase noise; for the squeezing in the low-frequency band, the enhancement of the squeezing for the cascaded system is quite weak. Under the current experimental parameters, the squeezing at 2 MHz of the squeezed light on rubidium resonance can be improved from –5 dB to –7 dB by cascading another DOPA. For the squeezing at low frequency band, the cascaded system proves to be useless, and the efforts should be made to reduce the technique noise in the low frequency band. Furthermore, the quantum limit and spectral characteristics of the squeezed light field output from the cascaded system are further explored. This study can provide reference and guidance for the improvement in the squeezing degree of the band of atomic transitions.
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Keywords:
- optical parametric amplifiers /
- the squeezed light field /
- the cascaded system /
- squeezing enhancement
[1] Li B B, Bilek J, Hoff U B, Madsen L S, Forstner S, Prakash V, Schäfermeier C, Gehring T, Bowen W P, Andersen U L 2018 Optica 5 850
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[10] Sun X C, Wang Y J, Tian L, Zheng Y H, Peng K C 2019 Chin. Opt. Lett. 17 072701
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[12] Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321
Google Scholar
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Zuo G H, Yang C, Zhao J X, Tian Z Z, Zhu S Y, Zhang Y C, Zhang T C 2020 Acta Phys. Sin. 69 014207
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Google Scholar
[15] Hétet G, Glöckl O, Pilypas K A, Harb C C, Buchler B C, Bachor H A, Lam P K 2007 J. Phys. B 40 221
Google Scholar
[16] Han Y S, Wen X, He J, Yang B D, Wang Y H, Wang J M 2016 Opt. Express 24 2350
Google Scholar
[17] 温馨, 韩亚帅, 刘金玉, 白乐乐, 何军, 王军民 2018 物理学报 67 024207
Google Scholar
Wen X, Han Y S, Liu J Y, Bai L L, He J, Wang J M 2018 Acta Phys. Sin. 67 024207
Google Scholar
[18] Yang W H, Wang Y J, Zheng Y. H, Lu H D 2015 Opt. Express 23 19624
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 DOPA腔示意
Figure 1. Schematic diagram of theDOPA cavity.
图 2 级联DOPA结构示意图
Figure 2. Schematic diagram of cascade DOPA.
图 3 DOPA输出光场压缩度随输出耦合镜透过率的变化
Figure 3. Squeezing degree of the output field versus the transmissivity of output coupler for the DOPA.
图 4 在各个分析频率对应的最佳输出耦合镜透过率Topt下, DOPA输出的光场压缩度随分析频率f的变化, 插图给出了Topt与分析频率f的依赖关系
Figure 4. Squeezing degree of the output filed versus analysis frequency for the DOPA at Topt of each frequency, inset shows dependence of Topt versus analysis frequency f.
图 5 级联DOPA输出光场压缩度随传输光路损耗L的变化 (a)分析频率f = 2 MHz; (b)分析频率f = 100 kHz
Figure 5. Squeezing degree of the output field versus the loss of optical loop for the cascaded DOPA: (a) f = 2 MHz; (b) f = 100 kHz.
图 6 (a)和(c)为级联DOPA系统输出光场压缩度随传输光路位相延迟
$\phi $ 的变化; (b)和(d)为级联DOPA可实现压缩增强的相位区间RE随级联DOPA个数的变化 (a)和(b)为分析频率f = 2 MHz的结果; (c)和(d)为分析频率f = 100 kHz结果Figure 6. (a) and (c) are the results for squeezing degree of the output field versus the phase delay
$\phi $ of optical loop for the cascaded DOPA; (b) and (d) are the results for the phase region RE versus numbers of DOPA; (a) and (b) are the results for f = 2 MHz; (b) and (d) are the results for f = 100 kHz.
图 7 考虑传输光路损耗以及位相噪声情况下, 级联DOPA系统输出光场在2 MHz分析频率处的压缩度随DOPA数目的变化
Figure 7. The squeezing of the output field at 2 MHz from the cascaded DOPA versus the numbers of DOPA, at the circumstance of considering the loss and phase noise induced by optical loop.
图 8 级联DOPA输出光场的压缩特性随分析频率的变化 (a)忽略传输光路位相噪声结果; (b)考虑4.42 mrad位相噪声的结果
Figure 8. Squeezing characteristics of the output light for the cascaded DOPA versus analysis frequency: (a) The result when the phase noise induced by optical loop is ignored; (b) the result when the phase noise of 4.42 mrad is considered.
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[1] Li B B, Bilek J, Hoff U B, Madsen L S, Forstner S, Prakash V, Schäfermeier C, Gehring T, Bowen W P, Andersen U L 2018 Optica 5 850
Google Scholar
[2] Lawrie B J, Lett P D, Marino A M, Pooser R C 2019 ACS Photonics 6 1307
Google Scholar
[3] Su X L, Hao S H, Deng X W, Ma L Y, Wang M H, Jia X J, Xie C D, Peng K C 2013 Nat. Commun. 4 2828
Google Scholar
[4] Usenko V C 2018 Phys. Rev. A 98 032321
Google Scholar
[5] Yan Z H, Wu L, Jia X J, Liu Y H, Deng R J, Li S J, Wang H, Xie C D, Peng K C 2017 Nat. Commun. 8 718
Google Scholar
[6] Wolfgramm F, Cerè A, Beduini F A, Predojević A, Koschorreck M, Mitchell M W 2010 Phys. Rev. Lett. 105 053601
Google Scholar
[7] Bai L L, Wen X, Yang Y L, Zhang L L, He J, Wang Y H, Wang J M 2021 J. Opt. 23 085202
Google Scholar
[8] Wu L A, Kimble H J, Hall J L, Wu H F 1986 Phys. Rev. Lett. 57 2520
Google Scholar
[9] Vahlbruch H, Mehmet M, Danzmann K, R Schnabel 2016 Phys. Rev. Lett. 117 110801
Google Scholar
[10] Sun X C, Wang Y J, Tian L, Zheng Y H, Peng K C 2019 Chin. Opt. Lett. 17 072701
Google Scholar
[11] Suzukia S, Yonezawa H, Kannari F, Sasaki M, Furusawa A 2006 Appl. Phys. Lett. 89 061116
Google Scholar
[12] Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321
Google Scholar
[13] 左冠华, 杨晨, 赵俊祥, 田壮壮, 朱诗尧, 张玉驰, 张天才 2020 物理学报 69 014207
Google Scholar
Zuo G H, Yang C, Zhao J X, Tian Z Z, Zhu S Y, Zhang Y C, Zhang T C 2020 Acta Phys. Sin. 69 014207
Google Scholar
[14] Tanimura T, Akamatsu D, Yokoi Y, Furusawa A, Kozuma M 2006 Opt. Lett. 31 2344
Google Scholar
[15] Hétet G, Glöckl O, Pilypas K A, Harb C C, Buchler B C, Bachor H A, Lam P K 2007 J. Phys. B 40 221
Google Scholar
[16] Han Y S, Wen X, He J, Yang B D, Wang Y H, Wang J M 2016 Opt. Express 24 2350
Google Scholar
[17] 温馨, 韩亚帅, 刘金玉, 白乐乐, 何军, 王军民 2018 物理学报 67 024207
Google Scholar
Wen X, Han Y S, Liu J Y, Bai L L, He J, Wang J M 2018 Acta Phys. Sin. 67 024207
Google Scholar
[18] Yang W H, Wang Y J, Zheng Y. H, Lu H D 2015 Opt. Express 23 19624
Google Scholar
[19] Wang Y J, Yang W H, Li Z X, Zheng Y H 2017 Sci. Rep. 7 41405
Google Scholar
[20] Wang S, Pasiskevicius V, Laurell F 2004 J. Appl. Phys. 96 2023
Google Scholar
[21] Boulanger B, Rousseau I, Fève J P, Maglione M, Ménaert B, Marnier G 1999 IEEE J. Quantum. Electron. 35 281
Google Scholar
[22] Zhang J, Ye C G, Gao F, Xiao M 2008 Phys. Rev. Lett. 101 233602
Google Scholar
[23] Wang D, Zhang Y, Xiao M 2013 Phys. Rev. A 87 023834
Google Scholar
[24] Ye C, Zhang J 2006 Phys. Rev. A 73 023818
Google Scholar
[25] Shi S P, Wang Y J, Yang W H, Zheng Y H, Peng K C 2018 Opt. Lett. 43 5411
Google Scholar
[26] He W P, Li F L 2007 Phys. Rev. A 76 012328
Google Scholar
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