论文标题
向下转换场模式的光子统计数据对泵场模式的光子统计数据的依赖性
Dependence of the photon statistics of down-converted field-modes on the photon statistics of pump field-mode
论文作者
论文摘要
使用零时间延迟的二阶摩擦函数来研究光子统计，我们研究了通过参数下转换（PDC）过程产生的场模式的光子统计方法如何取决于泵场模式的光子统计。我们为多模式和单模PDC过程的下转换场模式的零时间延迟二阶相关函数得出一般表达式。我们进一步研究这些表达式在弱下转换极限中。我们表明，对于两个光子的两模式PDC过程，其中泵光子将两个光子分成两个光子分成两个单独的场模式，零时间延迟的零时间延迟二阶相关函数等于泵场模式的两倍。 Furthermore, for an $n$-photon $n$-mode down-conversion process, in which a pump photon splits into $n$ photons into $n$ separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to $2^{(n-1)}$ times that of the pump field-mode.但是，与单模PDC过程的多模式PDC过程相反，单模PDC过程将泵的光子分成两个或多个光子分为单个模式，零时间段式二阶二阶摩擦函数在弱下降偏置限制中与泵的泵不成比例。但是，我们发现它与泵场模式中的平均光子数量成反比。
Using the zero time-delay second-order correlation function for studying the photon statistics, we investigate how the photon statistics of the field-modes generated by parametric down-conversion (PDC) process depends on the photon statistics of the pump field-mode. We derive general expressions for the zero time-delay second-order correlation function of the down-converted field-modes for both multi-mode and single-mode PDC processes. We further study these expressions in the weak down-conversion limit. We show that for a two-photon two-mode PDC process, in which a pump photon splits into two photons into two separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to twice that of the pump field-mode. Furthermore, for an $n$-photon $n$-mode down-conversion process, in which a pump photon splits into $n$ photons into $n$ separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to $2^{(n-1)}$ times that of the pump field-mode. However, in contrast to the multi-mode PDC processes, for a single-mode PDC process, in which a pump photons splits into two or more photons into a single mode, the zero time-delay second-order correlation function of the down-converted field-mode is not proportional to that of the pump in the weak down-conversion limit. Nevertheless, we find it to be inversely proportional to the average number of photons in the pump field-mode.
