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Hong-Ou-Mandel干涉可以更好地抵抗相位噪声的干扰. 近年来基于双光子干涉的量子全息提出, 通过待测量子态和标准量子态的二阶干涉, 可以将待测光子的波函数信息解译出来. 为了更好地理解和发展该方法, 本文建立了量子全息的理论框架. 根据不同的待测态和参考态, 分别研究了利用单光子态或相干态作参考, 测量待测的单光子态和相干态. 本文讨论的所有情况下, 待测态的波函数信息以相似的数学形式反映在归一化的二阶关联函数中. 通过简洁算法便可提取待测态波函数的信息. 该量子全息也保持了Hong-Ou-Mandel干涉的鲁棒性, 相位噪声并不影响测量结果.
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关键词:
- 量子全息/
- Hong-Ou-Mandel干涉/
- 归一化二阶关联函数/
- 鲁棒性
As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Because of this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In the quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are used at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state by using standard single photon state or coherent state and measuring the wave function of coherent state through using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is made and analysed.-
Keywords:
- quantum holography/
- Hong-Ou-Mandel interference/
- normalized second-order correlation function/
- robustness
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待测态 参考态 归一化的二阶关联函数 $\left| {\psi}_{\text{test}} \right > =\displaystyle\int{{\psi}_{\text{test}}(q)}\left|{1}_{q}\right > {\rm{d}}q $ $\left| { \psi}_{ \text{ref} } \right > =\displaystyle\int { { \psi }_{ \text{ref} }(q) } \left| { 1 }_{ q } \right > \text{d}q $ $\dfrac{T^2\left(q_1\right)+T^2\left(q_2\right)-2 T\left(q_1\right) T\left(q_2\right) \cos \left[\phi\left(q_1\right)-\phi\left(q_2\right)\right]}{\left[T^2\left(q_1\right)+1\right]\left[T^2\left(q_2\right)+1\right]} $ $\left| {\psi}_{\text{test}} \right > =\displaystyle\int{{\psi}_{\text{test}}(q)}\left|{1}_{q}\right > {\rm{d}}q $ $\left| { \psi }_{ \text{ref} } \right > = \displaystyle\prod\nolimits_{ q }^{ }{ \left| { \alpha_ \text{ref} (q) } \right > } $ $1-\dfrac { T^{2}(q_{1})T^{2}(q_{2})+2 T(q_{1})T(q_{2})\cos \left[\phi\left(q_1\right)-\phi\left(q_2\right)\right]}{ ({T^{2}(q_{1})+1})(T^{2}(q_{2})+1)} $ $\left| { \psi }_{ \text{test} } \right > = \displaystyle\prod\nolimits _{ q }^{ }{ \left| { \beta_ \text{test} (q) } \right > } $ $\left| { \psi}_{ \text{ref} } \right > =\displaystyle\int { { \psi }_{ \text{ref} }(q) } \left| { 1 }_{ q } \right > \text{d}q $ $1-\dfrac { 2 T(q_{1})T(q_{2})\cos \left[\phi\left(q_1\right)-\phi\left(q_2\right)\right]+1}{ ({T^{2}(q_{1})+1})(T^{2}(q_{2})+1)} $ $\left| { \psi }_{ \text{test} } \right > = \displaystyle\prod\nolimits_{ q }^{ }{ \left| { \beta_ \text{test} (q) } \right > } $ $\left| { \psi }_{ \text{ref} } \right > =\displaystyle\prod\nolimits _{q }^{ }{ \left| { \alpha_ \text{ref} (q) } \right > } $ $1-\dfrac { 2 T({ q }_{ 1 })T({ q }_{ 2 }) \text{cos}[\phi ({ q }_{ 1 })-\phi ({ q }_{ 2 })]}{ ({ { T }^{ 2 }({ q }_{ 1 }) }+1)({ { T }^{ 2 }({ q }_{ 2 }) }+1) } $ 
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