Photon-matter interactions

自量子力学早期以来，人们一直认为光子在普通粒子中是独一无二的，因为它没有带交换分量的位置操作符。直到1999年，我构造了这样一个光子位置操作符，后来与威廉·贝利斯合作，发现存在一整族依赖于光子总角动量的方向和大小的光子位置操作符。尽管实验者每天都对光子进行计数，但没有精确的方法来计算光子数密度。部分原因是人们认为，在这种意义上，没有光子位置操作符，即对于电子来说，光子位置操作符是存在的。人们通常认为光子能量密度的知识就足够了。然而，在关于非线性过程和激光理论的实用书籍中，同时考虑了光子能量密度和数密度。我目前的研究包括对光子局部化、角动量和数密度的研究，以及这些概念在超快激光脉冲和光束聚焦中的应用。与皇后大学的马克·迪格纳姆合作，我也在研究光脉冲在半导体纳米结构中产生的激发(称为激子)的描述。用激子来描述这些系统接近于实验者使用的物理图像，并且对于数值计算比基于自由电子和空穴的描述更实用。然而，当用两个光脉冲激发时，这些激子产生一个偏振光栅，它将激子散射成波矢量，从而产生四波混频，以及通常测量的n波混频信号。然而，激子基础的使用和泡利不相容原理的实施仍然存在逻辑上的困难。我在这方面正在进行的研究将是关于这些问题的解决。

Since the early days of quantum mechanics it has been thought that the photon is unique amongst common particles in having no position operator with commuting components.  In 1999 I constructed such a photon position operator and, in collaboration with William Baylis, later found that there is a whole family of photon position operators depending on the direction and magnitude of the photon's total angular momentum.   In spite of the fact that photons are "counted" every day by experimentalists, there was no precise way to calculate photon number density.  In part because of the perception that there is no photon position operator in that sense that one exists for the electron, it is commonly thought that knowledge of photon energy density is sufficient.  However, in practical books on nonlinear processes and laser theory both photon energy density and number density are considered.  My current research includes an investigation of photon localizability, angular momentum and number density and the application of these concepts to ultrafast laser pulses and focusing of optical beams. In collaboration with Marc Dignam at Queens University I am also working on the description of excitations (called excitons) created in semiconductor nanostructures by optical pulses.  The description of these systems in terms of excitons is close to the physical picture used by experimentalists, and is more practical for numerical calculations than a description based on free electrons and holes.  When excited with two optical pulses, these excitons produce a polarization grating that scatters the excitons into wave vectors that give the four-wave mixing and, in general, the n-wave mixing signals that are commonly measured.  However, there are still logical difficulties with use of the exciton basis and with implementation of the Pauli exclusion principle.  My on-going research in this area will be on the resolution of these issues.