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Quantum optical frequency combs are of great significance in the fields of quantum computing, quantum information, and high precision quantum measurement, which can be produced by using a degenerate type-I synchronously pumped optical parametric oscillator (SPOPO). When anisotropic crystal is used as a nonlinear medium in the SPOPO, the spatial walk-off effect will occur due to the birefringence effect, which cannot be ignored and will adversely affect the generation of squeezed state. In this work, we investigate the influence of spatial walk-off effect on the squeezing level of quantum optical frequency combs both theoretically and experimentally. A Ti∶sapphire mode-locked femtosecond pulsed laser which produces 130 fs pulse trains at 815 nm with a repetition rate of 76 MHz is utilized as a fundamental source. Its second harmonic at 407.5 nm is used to pump the collinear BiB3O6 (BIBO) crystal for generating the squeezed vacuum frequency comb. It is indicated that as the crystal length increases, the area of interaction between pump light and signal light decreases gradually. Thus the enhancement of squeezing is eventually limited by the spatial walk-off effect. According to the simulations, the squeezing level reaches a maximum value when the crystal length is 1.49 mm. The quantum properties of squeezed vacuum optical frequency combs obtained for four crystal lengths (0.5, 1.0, 1.5 and 2.0 mm) are subsequently measured experimentally. When the length of BIBO is 1.5 mm, the maximum vacuum squeezing of (3.6±0.2) dB is obtained, which is (7.0±0.2) dB after being corrected for detection loss. The experimental results are consistent with the numerical simulations. This study demonstrates that the spatial walk-off effect in nonlinear crystal is a significant factor affecting the quantum optical frequency comb, and the theoretical model presented in this paper can be used to provide a guideline for optimizing the experimental implementation.
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Keywords:
- quantum optical frequency comb /
- squeezed state /
- spatial walk-off
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图 1 系统阈值(a)和压缩(b)随晶体长度的理论变化曲线. 黑色虚线和红色实线分别是无空间走离和有空间走离的结果.
$ {n_0} = 1.82 $ ,$\chi = 3.54~ \rm pm/V$ ,$ \delta = 0.0468 $ ,$ T = 0.1 $ Figure 1. System threshold (a) and squeezing noise levels (b) as a function of crystal length, respectively. The black dotted line and red line are the results without/with spatial walk-off respectively.
$ {n_0} = 1.82 $ ,$\chi = 3.54~\rm pm/V$ ,$ \delta = 0.0468 $ ,$ T = 0.1 $ .
图 2 量子光频梳产生和测量的实验装置图. HWP, 半波片; PBS, 偏振分束器; DBS, 双色镜; SPOPO, 同步泵浦光学参量振荡器; PZT, 压电陶瓷; SA, 频谱分析仪器
Figure 2. Experimental setup for the generation and measurement of squeezed frequency comb states. HWP, half-wave plate; PBS, polarizing beam splitter; DBS, dichroic beamsplitter; SPOPO, synchronously pumped optical parametric oscillator; PZT, piezoelectric transducer; SA, spectrum analyzer.
图 3 倍频光功率及倍频效率随基频光变化的实验结果
Figure 3. Experimentally dependence of second harmonic power and efficiency on fundamental power.
图 4 种子光与泵浦光的光谱
Figure 4. The spectral profiles of the seed and pump.
图 5 在三种不同透过率下, 系统阈值随晶体长度的变化. 方块为实验测量结果, 曲线为理论计算结果
Figure 5. Dependence of the pump threshold on the crystal length under three different transmissions. The square is the experimental measurement result, and the curve is the theoretical calculation result.
图 6 在三种不同透过率下, 真空压缩随晶体长度变化的结果. 方块为实验测量结果, 曲线为理论计算结果. RBW = 100 kHz, VBW = 100 Hz
Figure 6. Dependence of squeezing noise levels on the crystal length under three different transmission. The square is the experimental measurement result, and the curve is the theoretical calculation result. RBW = 100 kHz, VBW = 100 Hz
图 7 晶体长度1.5 mm、输出耦合镜透过率30%时的真空压缩噪声谱
Figure 7. Squeezed vacuum states versus the sweeping time with 1.5 mm crystal length and 30% transmission.
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[1] Walls D F 1983 Nature 306 141
Google Scholar
[2] Xiao M, Wu L, Kimble H J 1987 Phys. Rev. Lett. 59 278
Google Scholar
[3] Kong J, Ou Z, Zhang W 2013 Phys. Rev. A 87 023825
Google Scholar
[4] Ou Z 2012 Phys. Rev. A 85 023815
Google Scholar
[5] Xin J, Liu J, Jing J 2017 Opt. Express 25 1350
Google Scholar
[6] Liu S, Lou Y, Xin J, Jing J 2018 Phys. Rev. Appl. 10 064046
Google Scholar
[7] Li Y, Guzun D, Xiao M 1999 Phys. Rev. Lett. 82 5225
Google Scholar
[8] Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002
Google Scholar
[9] Shi S, Wang Y, Yang W, Zheng Y, Peng K 2018 Opt. Lett. 43 5411
Google Scholar
[10] Zheng S, Lin Q, Cai Y, Zeng X, Li Y, Xu S, Fan D 2018 Photonics Res. 6 177
Google Scholar
[11] Menicucci N C 2014 Phys. Rev. Lett. 112 120504
Google Scholar
[12] Chen H, Liu J 2009 Chin. Opt. Lett. 7 440
Google Scholar
[13] Vahlbruch H, Mehmet M, Chelkowski S, Hage B, Franzen A, Lastzka N, Schnabel R 2008 Phys. Rev. Lett. 100 033602
Google Scholar
[14] Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763
Google Scholar
[15] Eberle T, Steinlechner S, Bauchrowitz J, Handchen V, Vahlbruch H, Mehmet M, Schnabel R 2010 Phys. Rev. Lett. 104 251102
Google Scholar
[16] Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801
Google Scholar
[17] Driel H M V 1995 Appl. Phys. B 60 411
[18] de Valcárcel G J, Patera G, Treps N, Fabre C 2006 Phys. Rev. A 74 061801
Google Scholar
[19] Patera G, Treps N, Fabre C, de Valcárcel G J 2010 Eur. Phys. J. D 56 123
Google Scholar
[20] Cai Y, Roslund J, Ferrini G, Arzani F, Xu X, Fabre C, Treps N 2017 Nat. Commun. 8 15645
Google Scholar
[21] Lamine B, Fabre C, Treps N 2008 Phys. Rev. Lett. 101 123601
Google Scholar
[22] Wang S, Xiang X, Treps N, Fabre C, Liu T, Zhang S, Dong R 2018 Phys. Rev. A 98 053821
Google Scholar
[23] Cai, Y, Roslund J, Thiel V, Fabre C, Treps N 2021 npj Quantum Inf. 7 82
Google Scholar
[24] Wu L, Kimble H J, Hall J L, Wu H 1986 Phys. Rev. Lett. 57 2520
Google Scholar
[25] Pinel O, Jian P, de Araujo R M, Feng J, Chalopin B, Fabre C, Treps N 2012 Phys. Rev. Lett. 108 083601
Google Scholar
[26] Roslund, J, de Araújo R M, Jiang S, Fabre C, Treps N 2014 Nat. Photonics 8 109
Google Scholar
[27] Cai Y, Xiang Y, Liu Y, He Q, Treps N 2020 Phys. Rev. Res. 2 032046
Google Scholar
[28] 刘洪雨, 陈立, 刘灵, 明莹, 刘奎, 张俊香, 郜江瑞 2013 164206 164206
Google Scholar
Liu H Y, Chen L, Liu L, Ming Y, Liu K, Zhang J X, Gao J R 2013 Acta Phys. Sin. 164206 164206
Google Scholar
[29] 石顺祥, 陈国夫, 赵卫, 刘继芳 2012 非线性光学 (西安: 电子科技大学出版社) 第105页
Shi S X, Chen G F, Zhao W, Liu J F 2012 Nonlinear Optics (Xidian: University Press) p105 (in Chinese)
[30] Hellwig H, Liebertz J, Bohaty L 2000 J. Appl. Phys. 88 240
Google Scholar
[31] Drever R W P, Hall J L, Kowalski F V, Hough J, Ford G M, Munley A J, Ward H 1983 Appl. Phys. B 31 97
[32] Gehr R J, Kimmel M W, Smith A V 1998 Opt. Lett. 23 1298
Google Scholar
[33] 周绪桂, 王燕玲, 吴洪, 丁良恩 2009 光学学报 29 2630
Google Scholar
Zhou X G, Wang Y L, Wu H, Ding L E 2009 Acta Opt. Sin. 29 2630
Google Scholar
[34] 孟祥昊, 刘华刚, 黄见洪, 戴殊韬, 邓晶, 阮开明, 陈金明, 林文雄 2015 64 164205
Google Scholar
Meng X H, Liu H G, Huang J H, Dai S T, Deng J, Ruan K M, Chen J M, Lin W X 2015 Acta Phys. Sin. 64 164205
Google Scholar
[35] Perez A M, Just F, Cavanna A, Chekhova M V, Leuchs G 2013 Laser Phys. Lett. 10 125201
Google Scholar
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