用“湮灭”算符创造量子
Creating quanta with "annihilation" operator
摘要：
玻色子“破坏”算符$\hat{a}$和它的“创造”伙伴$\hat{a}^{\dagger}$的不对称性质通过将它们应用于不同于Fock态$|n>$的量子态$|ψ>$而变得明显。我们表明，它是可能的{ \em增加}（许多倍或任何数量）的量子在新的“光子减去”状态$\hat{a}|ψ>$的平均数。此外，对于某些“超泊松”态$|ψ>$，（归一化）态$\hat{a}|ψ>$中的量子平均数可以比“光子添加”态$\hat{a}^{\dagger}|ψ> $中的量子平均数大得多。给出了这个“悖论”的解释，并考虑了阐明Mandel的$q$参数和指数相位算子的意义的一些例子。
英文摘要：
An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner $\hat{a}^{\dagger}$ is made apparent by applying them to a quantum state $|ψ>$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|ψ>$. Moreover, for certain `hyper-Poissonian' states $|ψ>$ the mean number of quanta in the (normalized) state $\hat{a}|ψ>$ can be much greater than in the `photon-added' state $\hat{a}^{\dagger}|ψ> $. The explanation of this `paradox' is given and some examples elucidating the meaning of Mandel's $q$-parameter and the exponential phase operators are considered.
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