自发参量下转换产生单光子对的应用及其统计特性研究
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摘要
自发参量下转换过程利用非线性晶体的二阶非线性效应实现：一个频率较高的光子(泵浦光)在满足相位匹配的条件下,在非线性晶体内同时(时间差不超过10-15秒)产生两个频率较低的光子(下转换光),这两个光子在时间、空间以及能量方面有着高度关联的特性。到目前为止,自发参量下转换过程被认为是能够最有效地产生高度关联的单光子对的方法之一,而单光子态作为一种非经典光场,在基础量子光学实验研究、量子保密通讯、量子计算以及量子高精度测量等领域有着重要的应用。
自从自发参量下转换过程首次在实验被观察到以来,这个过程所产生的高度关联的孪生光子对的特性就被人们进行了广泛的研究,尤其是人们可以只探测其中一个单光子,用以判定另一单光子的存在,也即在不破坏(探测)单光子的情况下预言单光子的存在,进而可以将此单光子提供给后续研究。由于自发参量下转换过程有着这一独特的优点,使得对这个过程特性的研究成为国际上各个小组的研究热点之一。本文的主要内容均是围绕自发参量下转换过程所展开,结合单光子的探测、计数统计、以及符合计数测量等手段详细地研究了下转换产生的关联光子对的分布范围,计数统计分布特性以及其在一些量子过程中的应用。
本文的主要工作有以下几个方面：
1.详细地回顾了目前可以在实验上产生单光子的各种方法,并给出自发参量下转换过程产生单光子所具有的独特的优点。进而介绍了自发参量下转换过程在基础物理研究,及其在量子计算、量子度量衡等方面的应用。
2.从相位匹配条件出发,理论上分析了当泵浦源为单色平面波和飞秒脉冲时对Ⅰ类相位匹配的自发参量下转换产生的信号(闲置)光分布范围以及符合范围所造成的不同的影响。结果表明由于飞秒脉冲具有较宽的光谱分布,使得其作为泵浦源时,下转换产生的信号(闲置)光的角分布范围明显要比单色波泵浦时的范围要大。而且,泵浦脉冲的谱越宽,下转换产生的信号(闲置)光的角分布范围越大。最后,在实验上测量了当泵浦为飞秒脉冲时下转换光的角分布,结果与理论分析基本一致。
3.研究了利用飞秒脉冲泵浦的Ⅰ类非共线相位匹配的自发参量下转换过程实现的量子鬼成像,并分析了测量带宽对量子鬼成像实验的成像范围和分辨率所造成的影响。结果表明,有限的测量带宽将会缩减所能成像的范围,但会使成像的分辨率有所提高。同时,探测时所选用的滤波片的透射线型将会影响到量子鬼成像的实验结果,通过归一化过程处理,可以消除这种影响。
4.利用自发参量下转换过程以及一个单光子探测器,提出一个实现受激发射型探测器的理论方案,并研究了利用此类型探测器实现的反常规排列的二阶关联函数和Fano因子的测量结果,比较了其与常规探测器测量所得结果的不同,给出此类型探测器的优点。最后,在现有的实验条件下对提出的理论模型进行了测量研究,实验结果与理论分析定性一致。
5.利用光子计数技术对自发参量下转换产生的信号光以及一个弱赝光场的光子计数统计分布进行了研究。研究发现当热光场的强度足够低时,光子计数统计分布依然满足负二项分布,但是传统理论给出的对应分布中简并因子的表达式不能与实验结果相符,传统理论具有一定的局限性。在此基础之上,用量子理论重新推导了简并因子的表达式,并给出了一个新的、通用的关于简并因子的量子力学表达式。实验结果与量子理论推出的表达式相符,证明了量子噪声在光子计数统计中的重要性。
在这些研究工作中,属于创新性的工作有以下几点：
1.详细地研究了利用飞秒脉冲作为自发参量下转换的泵浦源时,泵浦谱宽和探测带宽对下转换产生的信号(闲置)光分布范围和符合范围造成的影响,并与实验进行了对比,二者基本一致。
2.研究了利用自发参量下转换过程实现的量子鬼成像中,测量带宽对量子鬼成像所造成的影响,并给出消除这种影响的方法。
3.提出了自发参量下转换过程实现受激发射型探测器的一个理论方案,并给利用出此探测器在测量光场反常规排列函数,例如二阶关联函数以及Fano因子等中的应用。
4.给出了热光场光子计数统计分布-负二项分布中关于简并因子的一个新的、通用的量子力学表达式。并在实验上对其进行了验证,实验结果和新的量子力学表达式相符。
Spontaneous Parametric Down Conversion (SPDC) process was realized using the second-ordered nonlinear effect of the crystal. In the condition of phase matching, a pump photon with high frequency was divided into two photons with lower frequency, and these twin photons have high correlations in time, space and energy. Up to now, SPDC was considered as one of the most effective ways to generate the single photon pair with high correlations, and the single photon state was used widely in basic quantum optics experimental researches, quantum key distribution and quantum calculating as a nonclassical field.
Since SPDC was observed in the experiments, the photon pairs generated by it were widely investigated. Particularly, we could obtain a single photon by detecting the one of the twin photon, that's to say, we can predict the existence of a single photon without destroying it. Due to the special advantages of the SPDC, the researches in this paper are based on SPDC processes, combining the technology of single photon detecting, coincidence counting and photocounting statistics technology.
The main research points of this paper are as follows:
1.Parts of the ways to generate the single photon were reviewed and the advantages of SPDC were given. Then the applications of SPDC in the region of basic quantum theory researching, quantum calculating, and the quantum metrology were given.
2.Based on the phase matching conditions, the distribution range and coincidence range of the signal and idler generated by SPDC were theoretically analyzed, when a CW wave and a femto-second pulse was used as the pump source of SPDC.The results showed that the angel distribution range of signal is wider when the femto-second pulse used as the pump because it has wide spectrum, and wider the spectrum, wider the distribution range of signal.Finally, the experimental results confirmed the analyses about the angel distribution of the signal, when femto-second pulse was used as the pump source of SPDC.
3.The influences of detection bandwidth on the quantum ghost imaging were analyzed when a femto-second pulse was used as the pump of a type-I SPDC.The results showed that the detection bandwidth would limit the range of imaging, but would improve the visibility of ghost image.And, the line shape of the filter would influence the ghost imaging. Finally, a normalization process was shown to eliminate these influences.
4. A theoretical scheme about a stimulated emission-based detector was proposed using the SPDC processes.And the antinormally ordered second order correlation and Fano factor were analyzed using such detector. The results were compared with the normal detector and the advantages of stimulated emission based detector were given.Finally, the theoretical scheme is confirmed in the experiments and the results matched with theoretic qualitatively.
5.The photocounting statistic distribution of SPDC and a weak pseudo-thermal field was investigated. We found that the statistical distribution continues to be well described by the negative binomial function. However, the degeneracy factor in the distribution is observed to be markedly different from the conventional value. The Mandel theory is reexamined, and quantum fluctuation of light intensity is determined to be the source of this discrepancy. Finally, the theoretic was confirmed by the experiments.
The creative works are as follows:
1.The influence of femto-second pulse as the pump source of SPDC to the distribution range and coincidence range of signal and idler is analyzed, and the experimental results matched with the theoretical results.
2.The influence of detection bandwidth to the ghost imaging process was investigated, and the ways to eliminate such influences were given.
3.A theoretical scheme about the stimulated emission-based detector was proposed using the SPDC processes, and the applications of such detector in antinormally ordered second order correlations and Fano factor were investigated.
4.The Mandel theory was reexamined, and a new quantum expression for the degeneracy parameter in photocounting statistics distribution for thermal field was given. And it was confirmed a correct expression by the experiments.
自从自发参量下转换过程首次在实验被观察到以来,这个过程所产生的高度关联的孪生光子对的特性就被人们进行了广泛的研究,尤其是人们可以只探测其中一个单光子,用以判定另一单光子的存在,也即在不破坏(探测)单光子的情况下预言单光子的存在,进而可以将此单光子提供给后续研究。由于自发参量下转换过程有着这一独特的优点,使得对这个过程特性的研究成为国际上各个小组的研究热点之一。本文的主要内容均是围绕自发参量下转换过程所展开,结合单光子的探测、计数统计、以及符合计数测量等手段详细地研究了下转换产生的关联光子对的分布范围,计数统计分布特性以及其在一些量子过程中的应用。
本文的主要工作有以下几个方面：
1.详细地回顾了目前可以在实验上产生单光子的各种方法,并给出自发参量下转换过程产生单光子所具有的独特的优点。进而介绍了自发参量下转换过程在基础物理研究,及其在量子计算、量子度量衡等方面的应用。
2.从相位匹配条件出发,理论上分析了当泵浦源为单色平面波和飞秒脉冲时对Ⅰ类相位匹配的自发参量下转换产生的信号(闲置)光分布范围以及符合范围所造成的不同的影响。结果表明由于飞秒脉冲具有较宽的光谱分布,使得其作为泵浦源时,下转换产生的信号(闲置)光的角分布范围明显要比单色波泵浦时的范围要大。而且,泵浦脉冲的谱越宽,下转换产生的信号(闲置)光的角分布范围越大。最后,在实验上测量了当泵浦为飞秒脉冲时下转换光的角分布,结果与理论分析基本一致。
3.研究了利用飞秒脉冲泵浦的Ⅰ类非共线相位匹配的自发参量下转换过程实现的量子鬼成像,并分析了测量带宽对量子鬼成像实验的成像范围和分辨率所造成的影响。结果表明,有限的测量带宽将会缩减所能成像的范围,但会使成像的分辨率有所提高。同时,探测时所选用的滤波片的透射线型将会影响到量子鬼成像的实验结果,通过归一化过程处理,可以消除这种影响。
4.利用自发参量下转换过程以及一个单光子探测器,提出一个实现受激发射型探测器的理论方案,并研究了利用此类型探测器实现的反常规排列的二阶关联函数和Fano因子的测量结果,比较了其与常规探测器测量所得结果的不同,给出此类型探测器的优点。最后,在现有的实验条件下对提出的理论模型进行了测量研究,实验结果与理论分析定性一致。
5.利用光子计数技术对自发参量下转换产生的信号光以及一个弱赝光场的光子计数统计分布进行了研究。研究发现当热光场的强度足够低时,光子计数统计分布依然满足负二项分布,但是传统理论给出的对应分布中简并因子的表达式不能与实验结果相符,传统理论具有一定的局限性。在此基础之上,用量子理论重新推导了简并因子的表达式,并给出了一个新的、通用的关于简并因子的量子力学表达式。实验结果与量子理论推出的表达式相符,证明了量子噪声在光子计数统计中的重要性。
在这些研究工作中,属于创新性的工作有以下几点：
1.详细地研究了利用飞秒脉冲作为自发参量下转换的泵浦源时,泵浦谱宽和探测带宽对下转换产生的信号(闲置)光分布范围和符合范围造成的影响,并与实验进行了对比,二者基本一致。
2.研究了利用自发参量下转换过程实现的量子鬼成像中,测量带宽对量子鬼成像所造成的影响,并给出消除这种影响的方法。
3.提出了自发参量下转换过程实现受激发射型探测器的一个理论方案,并给利用出此探测器在测量光场反常规排列函数,例如二阶关联函数以及Fano因子等中的应用。
4.给出了热光场光子计数统计分布-负二项分布中关于简并因子的一个新的、通用的量子力学表达式。并在实验上对其进行了验证,实验结果和新的量子力学表达式相符。
Spontaneous Parametric Down Conversion (SPDC) process was realized using the second-ordered nonlinear effect of the crystal. In the condition of phase matching, a pump photon with high frequency was divided into two photons with lower frequency, and these twin photons have high correlations in time, space and energy. Up to now, SPDC was considered as one of the most effective ways to generate the single photon pair with high correlations, and the single photon state was used widely in basic quantum optics experimental researches, quantum key distribution and quantum calculating as a nonclassical field.
Since SPDC was observed in the experiments, the photon pairs generated by it were widely investigated. Particularly, we could obtain a single photon by detecting the one of the twin photon, that's to say, we can predict the existence of a single photon without destroying it. Due to the special advantages of the SPDC, the researches in this paper are based on SPDC processes, combining the technology of single photon detecting, coincidence counting and photocounting statistics technology.
The main research points of this paper are as follows:
1.Parts of the ways to generate the single photon were reviewed and the advantages of SPDC were given. Then the applications of SPDC in the region of basic quantum theory researching, quantum calculating, and the quantum metrology were given.
2.Based on the phase matching conditions, the distribution range and coincidence range of the signal and idler generated by SPDC were theoretically analyzed, when a CW wave and a femto-second pulse was used as the pump source of SPDC.The results showed that the angel distribution range of signal is wider when the femto-second pulse used as the pump because it has wide spectrum, and wider the spectrum, wider the distribution range of signal.Finally, the experimental results confirmed the analyses about the angel distribution of the signal, when femto-second pulse was used as the pump source of SPDC.
3.The influences of detection bandwidth on the quantum ghost imaging were analyzed when a femto-second pulse was used as the pump of a type-I SPDC.The results showed that the detection bandwidth would limit the range of imaging, but would improve the visibility of ghost image.And, the line shape of the filter would influence the ghost imaging. Finally, a normalization process was shown to eliminate these influences.
4. A theoretical scheme about a stimulated emission-based detector was proposed using the SPDC processes.And the antinormally ordered second order correlation and Fano factor were analyzed using such detector. The results were compared with the normal detector and the advantages of stimulated emission based detector were given.Finally, the theoretical scheme is confirmed in the experiments and the results matched with theoretic qualitatively.
5.The photocounting statistic distribution of SPDC and a weak pseudo-thermal field was investigated. We found that the statistical distribution continues to be well described by the negative binomial function. However, the degeneracy factor in the distribution is observed to be markedly different from the conventional value. The Mandel theory is reexamined, and quantum fluctuation of light intensity is determined to be the source of this discrepancy. Finally, the theoretic was confirmed by the experiments.
The creative works are as follows:
1.The influence of femto-second pulse as the pump source of SPDC to the distribution range and coincidence range of signal and idler is analyzed, and the experimental results matched with the theoretical results.
2.The influence of detection bandwidth to the ghost imaging process was investigated, and the ways to eliminate such influences were given.
3.A theoretical scheme about the stimulated emission-based detector was proposed using the SPDC processes, and the applications of such detector in antinormally ordered second order correlations and Fano factor were investigated.
4.The Mandel theory was reexamined, and a new quantum expression for the degeneracy parameter in photocounting statistics distribution for thermal field was given. And it was confirmed a correct expression by the experiments.
引文
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[23]Pulse Check,德国APE公司生产。
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