二阶非线性光学频率转换两模量子场耦合系统的时间演化与量子起伏
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摘要
二阶非线性光学频率转换系统(即二阶参量过程)是产生可调谐相干辐射、压缩真空态、压缩相干态、压缩数态以及其它非经典态的一种强有力的工具。它主要由二次谐波产生、和频产生、差频产生、光参量振荡等构成。一般来说,在同一块晶体中至多有一种参量过程能产生出足以察觉得到的非线性光学效应。产生这种现象的原因是:只有参与相互作用的耦合光波满足能量守恒和相位匹配的条件,才能有效地实现非线性相互作用;而通常在一块晶体中不会有多于一种的参量过程满足这样苛刻的限制条件。所以,过去人们主要仅需面对单个独立的参量过程。随着准相位匹配技术的发展,今天人们可以通过合理设计准周期极化序列使晶格具有合适的倒格矢,可同时满足耦合参量过程中的各参量过程的准相位匹配条件,在一块光学超晶格中可同时实现多个参量过程。这就使得我们在理论上进一步研究由多个参量过程组成的一般二阶非线性参量过程具有一定的实际意义。本文首先对非线性光学频率转换技术的发展以及光的压缩态的研究进展进行了一个简短的回顾,接着对电磁场的量子化,光的几个基本量子态、单光子装置和双光子装置的主要性质,以及一般二阶非线性参量过程的哈密顿算符的推导过程进行了简要的概述。为了求解复杂的含时系统,对Lewis–Riesenfeld量子不变量理论进行了深入的讨论。在此基础上,我们运用Lewis–Riesenfeld量子不变量理论,重点研究了几个较复杂的二阶非线性光学频率转换两模量子场耦合系统的时间演化规律与量子起伏性质;并获得如下主要结论:
1.采用Lewis–Riesenfeld量子不变量理论,研究了(哈密顿量包含任意含时驱动
Second-order nonlinear optical frequency conversion system (i.e. second-order parametric process) is a powerful tool for generating tunable coherent radiation, squeezed vacuum state, squeezed coherent state, squeezed Fock state and other kinds of nonclassical states of light. It mainly consists of harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric oscillation and etc. In general, typically no more than one of these nonlinear optical processes will be present with any appreciable intensity in a nonlinear crystal. The reason for this behavior is that the nonlinear interaction can efficiently implemented only if the photon energy conservation and phase matching conditions are satisfied, and usually these conditions cannot be satisfied for more than one parametric process. So in the past, one mainly needs to treat single parametric process. With the development of the Quasi-phase matching technology, today we can realize efficiently several parametric processes in a quasiperiodic optical superlattice. It is valuable to study further the general second-order parametric processes.
In this paper the development of nonlinear optical frequency conversion technique and the advances in researches for squeezed states are reviewed at first, then the quantization of the electromagnetic field, the properties of the basis quantum states, a one-photon device and a two- photon device, the effect of some simple nonlinear processes as well as the Hamiltonians describing the general second-order parametric processes are also described. In order to solve the complex time-dependent system, the Lewis–Riesenfeld invariant theory is discussed. Depending on these bases, we place the emphasis on exploration of the time evolution and quantum fluctuation for the complex second-order nonlinear optical frequency conversion
1.采用Lewis–Riesenfeld量子不变量理论,研究了(哈密顿量包含任意含时驱动
Second-order nonlinear optical frequency conversion system (i.e. second-order parametric process) is a powerful tool for generating tunable coherent radiation, squeezed vacuum state, squeezed coherent state, squeezed Fock state and other kinds of nonclassical states of light. It mainly consists of harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric oscillation and etc. In general, typically no more than one of these nonlinear optical processes will be present with any appreciable intensity in a nonlinear crystal. The reason for this behavior is that the nonlinear interaction can efficiently implemented only if the photon energy conservation and phase matching conditions are satisfied, and usually these conditions cannot be satisfied for more than one parametric process. So in the past, one mainly needs to treat single parametric process. With the development of the Quasi-phase matching technology, today we can realize efficiently several parametric processes in a quasiperiodic optical superlattice. It is valuable to study further the general second-order parametric processes.
In this paper the development of nonlinear optical frequency conversion technique and the advances in researches for squeezed states are reviewed at first, then the quantization of the electromagnetic field, the properties of the basis quantum states, a one-photon device and a two- photon device, the effect of some simple nonlinear processes as well as the Hamiltonians describing the general second-order parametric processes are also described. In order to solve the complex time-dependent system, the Lewis–Riesenfeld invariant theory is discussed. Depending on these bases, we place the emphasis on exploration of the time evolution and quantum fluctuation for the complex second-order nonlinear optical frequency conversion
引文
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