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传统相干激光雷达的接收端与发射端均采用相干激光,在相空间中,通常使用正交振幅分量X以及正交位相分量Y描述光场的噪声特性,其噪声方差满足:
$$\left\langle {{\delta ^2}X} \right\rangle =\left\langle {{\delta ^2}Y} \right\rangle =1$$ (1) 而连续变量量子压缩态光场是某一正交分量可以突破量子噪声极限的一种非经典光场,即
$\left\langle {{\delta ^2}X} \right\rangle < 1$ 或者$\left\langle {{\delta ^2}Y} \right\rangle {\rm{ < \; }}1$ ,通过解调特定分析频率的噪声方差信号可以获得压缩态光场在特定分析频率下的时域信号,如图1所示。图 1 压缩态光场在相空间中示意图以及时域信号
Figure 1. Distribution of the squeezed state in phase space and the photon number distribution of the squeezed state
通过分析压缩态光场的特性,采用可突破量子噪声极限的压缩光代替相干激光,可在复杂的电磁环境下为提高激光雷达的探测精度提供有效的技术途径。但压缩态光场极易受光学损耗影响,所以采用将压缩光注入接收端的量子增强手段和将量子压缩态光场和微弱回波信号进行高效耦合才能实现量子资源有效利用。
采用自零拍探测方案进行量子压缩光高效耦合,耦合方案如图2所示,将正交振幅压缩态光场代替传统相干态光场作为本振光,利用正交振幅压缩态光场具有更低的强度噪声来降低探测系统的噪声基底,从而提高测量灵敏度。其中偏振互相垂直的雷达回波信号和压缩态光场在偏振分束棱镜PBS1上耦合,再通过半波片和偏振分束棱镜PBS2进行干涉耦合,其输出光场可以表示为:
图 2 量子增强自零拍探测原理图(PBS:偏振分束棱镜;PD:光电探测器;SA:频谱分析仪)
Figure 2. Theoretical diagram of the quantum enhanced self-homodyne detection (PBS: polarization beam splitter; PD: photodetector; SA: spectrum analyzer)
$${\hat d_1} = \frac{1}{{\sqrt 2 }}(\hat a - \hat b{{\rm{e}}^{i\theta }})$$ (2) $${\hat d_2} = \frac{1}{{\sqrt 2 }}(\hat a + \hat b{{\rm{e}}^{i\theta }})$$ (3) 式中:
$\hat a$ 为从分束器耦合进的真空场;$\hat b$ 为雷达回波的信号场;$\theta $ 为两束光场之间的相对位相,此时$\theta = 0$ 。之后分别由探测器PD1和PD2进行自零拍联合探测,探测器输出的光电流表示为:$${i_{{d_1}}} = \hat d_1^\dagger {\hat d_1} = \frac{1}{2}({\hat a^\dagger }\hat a - {\hat a^\dagger }\hat b{{\rm{e}}^{i\theta }} - {\hat b^\dagger }\hat a{{\rm{e}}^{ - i\theta }} + {\hat b^\dagger }\hat b)$$ (4) $${i_{{d_2}}} = \hat d_2^\dagger {\hat d_2} = \frac{1}{2}({\hat a^\dagger }\hat a + {\hat a^\dagger }\hat b{e^{i\theta }} + {\hat b^\dagger }\hat a{e^{ - i\theta }} + {\hat b^\dagger }\hat b)$$ (5) 利用线性化算符关系,明亮光场的产生和湮灭算符可表示为光场幅度的平均值和量子涨落之和,即
$\hat a = \alpha + \delta \hat a,{\rm{ }}\hat b = \beta + \delta \hat b$ ,将此式代入公式(4)和公式(5)得两探测器输出光电流的和与差分别为:$$ \begin{split} {i_ + } =& {i_{{d_2}}} + {i_{{d_1}}} = {{\hat a}^\dagger }\hat a + {{\hat b}^\dagger }\hat b =\\ & {\left| \alpha \right|^2} + \alpha \delta {{\hat a}^\dagger } + {\alpha ^ * }\delta \hat a + {\left| \beta \right|^2} +\\ & \beta \delta {{\hat b}^\dagger } + {\beta ^ * }\delta \hat b\\ \end{split} $$ (6) $$ \begin{split} {i_ - } = &{i_{{d_2}}} - {i_{{d_1}}} = {{\hat a}^\dagger }\hat b{{\rm{e}}^{i\theta }} + {{\hat b}^\dagger }\hat a{{\rm{e}}^{ - i\theta }} = \\ & {\alpha ^ * }\beta {{\rm{e}}^{i\theta }} + {\beta ^ * }\alpha {{\rm{e}}^{ - i\theta }} + {\alpha ^ * }\delta \hat b{{\rm{e}}^{i\theta }} + \\ & \alpha \delta {{\hat b}^\dagger }{{\rm{e}}^{ - i\theta }} + \beta \delta {{\hat a}^\dagger }{{\rm{e}}^{i\theta }} + {\beta ^ * }\delta \hat a{{\rm{e}}^{ - i\theta }} \\ \end{split} $$ (7) 由于在自零拍探测中,
$\hat b$ 近似为真空场,其平均值$\beta = 0$ ,所以有:$${i_ + } = {\left| \alpha \right|^2} + \alpha \delta {\hat a^\dagger } + {\alpha ^ * }\delta \hat a$$ (8) $${i_ - } = {\alpha ^ * }\delta \hat b + \alpha \delta {\hat b^\dagger }$$ (9) 所以,光电流和与差的起伏分别为:
$$\left\langle {{\delta ^2}{i_ + }} \right\rangle = \alpha (\delta {\hat a^\dagger } + \delta \hat a) = \alpha {X_a}$$ (10) $$\left\langle {{\delta ^2}{i_ - }} \right\rangle = \alpha (\delta \hat b + \delta {\hat b^\dagger }) = \alpha {X_b}$$ (11) 由公式(10)和公式(11)可以看出,光电流差的起伏可作为散粒噪声基准,而光电流和的起伏为信号光场正交振幅分量的量子起伏,所以在接收端利用低噪声压缩态光场代替相干态光场可以降低信号噪声基底,从而提高信号信噪比,实现量子增强探测,并且量子压缩态光场压缩度越大增强效果越显著。
Quantum enhanced Doppler LiDAR based on integrated quantum squeezed light source(Invited)
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摘要: 传统激光雷达探测灵敏度不断提高,但仍然受激光光源的量子噪声以及探测端引入的额外噪声等因素限制。为了进一步提高激光雷达的探测性能,提出利用量子压缩态光场作为激光雷达的本振信号提高激光雷达探测精度的新方案,分析了所提出方案提高激光雷达探测精度的关键因素。制备了集成化低噪声压缩态光场并进行了激光雷达多普勒信息测量实验。实验结果表明,相较于传统相干多普勒激光雷达探测方案,所提方案实现了多普勒信息探测灵敏度3 dB的提升,为量子激光雷达中多普勒信息等微弱信号的探测提供研究途径。Abstract: Though the measurement precision of the traditional LiDAR is gradually increased, it is still limited by the quantum noise of the optical field and the extra noise introduced by the detection process. To improve the detection performance of LiDAR, a new scheme using quantum squeezed state light field as local oscillator of LiDAR was proposed and the key factors for improving the detection precision of LiDAR was analyzed. Then an integrated low-noise squeezed light field was prepared, and the experiment of LiDAR Doppler information measurement was carried out. The results show that the Doppler information detection sensitivity by using quantum squeezed state is 3 dB higher than the traditional scheme of the coherent state light field as the local oscillator, which paves a research path for the detection of weak signals such as Doppler information.
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Key words:
- squeezed state /
- quantum enhancement /
- LiDAR /
- quantum radar
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图 3 基于压缩态光场的量子增强激光雷达探测方案装置图。HR:高反镜,AOM:声光调制器,BS:分束器,DBS:双色分束器,OPA:光学参量放大器,PBS1-2:偏振分束棱镜,PD:光电探测器,SA:频谱分析仪
Figure 3. Experimental setup of quantum enhanced LiDAR detection based on the squeezed state light field. HR: high reflectivity mirror; AOM: audio-optical modulator; BS: beam splitter; DBS: dichromatic beam splitter; OPA: optical parameter amplifier; PBS1-2: polarization beam splitter; PD: photodetector; SA: spectrum analyzer
图 4 集成压缩态光场压缩度测量结果((a) 量子噪声极限;(b) 压缩态光场噪声谱;(c) 压缩态光场噪声谱最低压缩度)
Figure 4. Measurement results of squeezing level of the integrated squeezed light field ((a) Quantum noise limit; (b) Noise spectrum of squeezed state light field; (c) Minimum squeezed degree of noise spectrum of squeezed state light field)
图 5 利用自零拍探测系统进行量子增强多普勒信息探测结果((a) 压缩光注入的回波信号噪声谱;(b) 散粒噪声基准噪声谱;(c) 相干光注入的回波信号噪声谱)
Figure 5. Measured results of quantum enhanced Dopplor information detection by self-homodyne detection system ((a) Noise spectrum of squeezed light injection echo signal; (b) Noise spectrum of shot noise datum; (c) Noise spectrum of coherent light injection echo signal)
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