Precisely Reconstructing Phase Space Distribution of Different Chaotic Lasers Using Maximum Likelihood Method

Mengyu Xing; Xiaomin Guo; Haojie Zhang; Jianchao Zhang; Yanqiang Guo

doi:10.3788/CJL220768

Chinese Journal of Lasers, Volume. 50, Issue 6, 0612002(2023)

Precisely Reconstructing Phase Space Distribution of Different Chaotic Lasers Using Maximum Likelihood Method

Mengyu Xing^1,2, Xiaomin Guo^1,2, Haojie Zhang^1,2, Jianchao Zhang^1,2, and Yanqiang Guo^1,2、*

¹Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

²State Key Laboratory of Cryptology, Beijing 100878, China

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Figures & Tables(8)

Fig. 1. Schematic of experimental setup for precisely reconstructing Wigner quasi-probability distribution of chaotic lasers through maximum likelihood method

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Fig. 2. Sequence, spectrum and autocorrelation diagrams of chaotic lasers measured under different $I$ and $η$ . (a1)-(a3) $I =$ 1.5I_th， $η =$ 0.2; (b1)-(b3) $I =$ 2.5I_th， $η =$ 0.043; (c1)-(c3) $I =$ 2.5I_th， $η =$ 0.079

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Fig. 3. Measured fluctuation results of quadrature components between chaotic lasers in different states and shot noise limits in vacuum state. (a) QCL with 3.2 GHz bandwidth ; (b) MCL with 7.3 GHz bandwidth ; (c) CCL with 11.5 GHz bandwidth

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Fig. 4. Experimental reconstruction results of chaotic laser. (a1)-(a3) QCL with 3.2 GHz bandwidth; (b1)-(b3) MCL with 7.3 GHz bandwidth; (c1)-(c3) CCL with 11.5 GHz bandwidth

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Fig. 5. Reconstructed diagonal element distributions of density matrixes before and after removing background noise.（a1）-（b1）QCL with 3.2 GHz bandwidth；（a2）-（b2）MCL with 7.3 GHz bandwidth；（a3）-（b3）CCL with 11.5 GHz bandwidth

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Fig. 6. Fidelity of Wigner quasi-probability distribution versus mean photon number for QCL，MCL，and CCL before and after considering system loss and background noise.（a）Before considering system loss and background noise；（b）after considering system loss and background noise

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Table 1. Measured diagonal elements of density matrixes for QCL, MCL,and CCL
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Table 1. Measured diagonal elements of density matrixes for QCL, MCL,and CCL
Laser n=0 n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10
QCL 0.26 0.35 0.19 0.13 0.04 0.01 0.01 0.01 0 0 0
MCL 0.07 0.18 0.22 0.25 0.18 0.04 0.03 0.02 0.01 0 0
CCL 0.05 0.09 0.21 0.26 0.20 0.15 0.02 0.01 0.01 0 0

Table 2. Measured diagonal elements of density matrixes for QCL, MCL,and CCL after removing background noise
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Table 2. Measured diagonal elements of density matrixes for QCL, MCL,and CCL after removing background noise
Laser n=0 n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10
QCL 0.24 0.34 0.19 0.14 0.05 0.02 0.01 0.01 0 0 0
MCL 0.07 0.19 0.22 0.25 0.16 0.06 0.03 0.02 0.01 0 0
CCL 0.05 0.09 0.20 0.26 0.21 0.12 0.05 0.01 0.01 0 0

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Mengyu Xing, Xiaomin Guo, Haojie Zhang, Jianchao Zhang, Yanqiang Guo. Precisely Reconstructing Phase Space Distribution of Different Chaotic Lasers Using Maximum Likelihood Method[J]. Chinese Journal of Lasers, 2023, 50(6): 0612002

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