半经典光子态的操纵
Manipulation of Semiclassical Photon States
摘要：
加布里埃尔F。卡尔沃和安东尼奥·皮康定义了一类用于量子通信的算子，允许任意操纵三个最低的二维厄米-高斯模式。|0，0>，|1，0>，|0，1>}。我们的论文继续这些算子的研究，我们的结果分为两类。首先，我们证明了算子的生成元具有无穷的亏指数，并且我们明确地描述了所有的自伴实现。其次，我们研究了传播子的半经典近似。其基本方法是从一个半经典的Fourier积分算子出发，构造相应的发展方程的近似解。在这样做时，我们给出了一个完整的描述的汉密尔顿流，这在大多数情况下是由椭圆函数。我们发现，半经典近似行为良好时，充分本地化的初始条件，例如，半经典厄米-高斯模式的有限和，因为在原点附近的Hamilton轨迹跟踪出有界分量的椭圆曲线。
英文摘要：
Gabriel F. Calvo and Antonio Picon defined a class of operators, for use in quantum communication, that allows arbitrary manipulations of the three lowest two-dimensional Hermite-Gaussian modes {|0,0>,|1,0>,|0,1>}. Our paper continues the study of those operators, and our results fall into two categories. For one, we show that the generators of the operators have infinite deficiency indices, and we explicitly describe all self-adjoint realizations. And secondly we investigate semiclassical approximations of the propagators. The basic method is to start from a semiclassical Fourier integral operator ansatz and then construct approximate solutions of the corresponding evolution equations. In doing so, we give a complete description of the Hamilton flow, which in most cases is given by elliptic functions. We find that the semiclassical approximation behaves well when acting on sufficiently localized initial conditions, for example, finite sums of semiclassical Hermite-Gaussian modes, since near the origin the Hamilton trajectories trace out the bounded components of elliptic curves.
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