关于2-横模DOPO中的正则对
On canonical pairs in 2-transverse-mode DOPOs
摘要：
在文献[1]中，我们分析了在信号频率处调谐到第一横模族的简并光学参量振荡器（DOPO）的特性。在阈值以上，发射在横向平面中具有任意取向的厄米-高斯模式，并且因此系统的旋转不变性被破坏。当考虑到量子效应时，一方面发现量子噪声能够在这种经典发射模式上引起随机旋转。另一方面，平衡零差检测的分析，其中本地振荡器（LO）是正交的激发模式在任何时候，显示在正交的压缩由LO选择的这一个被发现的每一个相位，压缩是完美的π/2相位。这最后一个事实揭示了一个明显的悖论：如果所有的求积都低于散粒噪声水平，则似乎违反了不确定原理。在[1]中，我们指出，这个悖论背后的解释是，旋转正交模的求积不形成正则对，并且额外的噪声被转移到扩散方向。这些笔记是专门用来证明这一说法的。
英文摘要：
In ref. [1] we analyzed the properties of a Degenerate Optical Parametric Oscillator (DOPO) tuned to the first transverse mode family at the signal frequency. Above threshold, a Hermite-Gauss mode with an arbitrary orientation in the transverse plane is emitted, and thus the rotational invariance of the system is broken. When quantum effects were taken into account, it was found on the one hand, that quantum noise is able to induce a random rotation on this classically emitted mode. On the other hand, the analysis of a balanced homodyne detection in which the local oscillator (LO) was orthogonal to the excited mode at any time, showed that squeezing in the quadrature selected by the LO was found for every phase of this one, squeezing being perfect for a pi/2 phase. This last fact revealed an apparent paradox: If all quadratures are below shot noise level, the uncertainty principle seems to be violated. In [1] we stated that the explanation behind this paradox is that the quadratures of the rotating orthogonal mode do not form a canonical pair, and the extra noise is transferred to the diffusing orientation. Thes notes are devoted to prove this claim.
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