Avetisyan H, Monken C H
Opt Lett. 2017 Jan 1;42(1):101-104. doi: 10.1364/OL.42.000101.
Due to the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric downconversion, the generated twin photons are entangled in their spatial degrees of freedom. This spatial entanglement can be observed through correlation measurements in any set of modes in which one may choose to perform measurements. Choosing, e.g., a Hermite-Gaussian (HG) set of spatial modes as a basis, one can observe correlations present in their spatial degrees of freedom. In addition, these modes can be used as alphabets for quantum communication. For global quantum communication purposes, we derive an analytic expression for two-photon detection probability in terms of HG modes, taking into account the effects of the turbulent atmosphere. Our result is more general as it accounts for the propagation of both signal and idler photons through the atmosphere, as opposed to other works considering one photon's propagation in vacuum. We show that while the restrictions on both the parity and order of the downconverted HG fields no longer hold, due to the crosstalk between modes when propagating in the atmosphere, the crosstalk is not uniform: there are more robust modes that tend to keep the photons in them. These modes can be employed in order to increase the fidelity of quantum communication.
由于在自发参量下转换过程中泵浦光束的角谱转移到双光子态，所产生的孪生光子在其空间自由度上是纠缠的。这种空间纠缠可以通过在任何一组可选择进行测量的模式中的关联测量来观察。例如，选择一组厄米 - 高斯（HG）空间模式作为基，就可以观察到其空间自由度中存在的关联。此外，这些模式可以用作量子通信的字母表。出于全球量子通信的目的，考虑到湍流大气的影响，我们推导了一个关于HG模式的双光子探测概率的解析表达式。我们的结果更具一般性，因为它考虑了信号光子和闲频光子在大气中的传播，这与其他只考虑一个光子在真空中传播的工作不同。我们表明，虽然由于在大气中传播时模式之间的串扰，下转换HG场的奇偶性和阶数的限制不再成立，但串扰并不均匀：存在更稳健的模式，倾向于使光子保持在其中。可以利用这些模式来提高量子通信的保真度。
