The Photon Wave Function in Principle and in Practice
The Photon Wave Function in Principle and in Practice
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光子波函数的原理和实践
DOI：
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发表时间：
2015
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通讯作者：
V. Debierre
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作者：
V. Debierre
在这三年里，我们专注于量子光学和量子电动力学的几个主题。我们研究的中心主题是光子波函数。能否借助描述实验中光子的波函数在位置空间中简单地描述量子光学和量子电动力学实验？这个问题的答案并不十分明显：通常对光子的描述发生在波矢的倒易空间中。但这些实验需要在位置表示中进行波力学描述，就像量子力学教科书中在大质量粒子的情况下所做的那样。此外，在最近的一项实验中 [1]，观察到了通过杨氏双缝装置的单光子轨迹。为了尝试并形式化地描述这些轨迹，很自然地为光子建立波力学形式主义。因此，我们详细研究了光子波函数的形式结构，直到 20 世纪 90 年代才对其进行了很少的研究。我们还研究了存在源的情况下光子波函数的性质。为此，我们考虑了几个开放（相互作用）的量子系统。我们看到，在定义光子波函数时，原则上存在无限多种可能性。我们强调了几个标准，根据这些标准，波函数只有三种选择是有趣的。其中之一与 Glauber [2] 引入并使用的一个物体相吻合，用于研究光探测和量子领域中电磁场的相关性。我们还看到，在没有源的情况下，单个光子的传播方程在形式上等价于麦克斯韦方程组。在低光子数下，波函数形式非常有用。我们将其应用于交互系统，首先是空腔量子电动力学 (QED) [3]，特别是 Serge Haroche 小组进行的实验 [4]。我们提出了一个简单的模型来描述 QED 腔中的光子。通过这个模型，并借助光子波函数，我们研究了从腔中逸出的光子的传播。我们还构建了 Lindblad 主方程，而没有引入非酉量子跃迁（另见 [5]）。我们最终研究了原子电子衰变过程中发射的光子的时空演化。在仔细研究了电子衰变的动力学，特别是在非常短的时间内[6, 7]，我们开始尽可能严格地描述发射的电磁场。令人惊讶的是，这个发射场并没有因果演化。尽管考虑到黑格费尔特定理，这并不完全出乎意料，该定理指出[8]对于由哈密顿量描述的量子系统来说，因果关系是不可能的，其光谱如下所示，但我们确定了[9]另外两个非因果关系的来源。其中一个是 Shirokov [10] 定性预测的，而另一个据我们所知是全新的，仍有待更好地理解
During these three years we focused on several topics in quantum otpics and quantum electrodynamics. A central theme in our investigations is that of the photon wave function. Can quantum optics and quantum electrodynamics experiments be described simply, in position space, with the help of a wave function describing the photon(s) featured in the experiment ? The answer to that question is not quite obvious: the usual description of photons takes place in the reciprocal space of wave vectors. But these experiments call for a wave mechanical description in the position representation, as is done in quantum mechanics textbooks in situations featuring massive particles. Moreover, in a recent experiment [1], single photon trajectories through a Young two-slit setup have been observed. In order to try and describe these trajectories formally, it is natural to build a wave mechanical formalism for photons. We therefore studied in detail the formal construction of the photon wave function, an object which was little studied until the 1990s. We also studied the properties of the photon wave function in the presence of sources.To do that, we considered several open (interacting) quantum systems. We saw that there exists in principle an infinite number of possibilities when defining the photon wave function. We emphasised several criteria on the basis of which it appears that only three choices for the wave function are interesting. One of them coincides with an object introduced and used by Glauber [2] to study light detection andthe correlations of the electromagnetic field in the quantum regime. We also saw that, in the absence of sources, the propagation equation for a single photon is formally equivalent to Maxwell’s equations. At low photon numbers, the wave function formalism can be very useful. We adapted it to interacting systems,first, to cavity quantum electrodynamics (QED) [3], in particular to the experiments carried out by Serge Haroche’s group [4]. We proposed a simple model to describe photons in QED cavities. With this model, and with the helpof the photon wave function, we studied the propagation of photons escaping a cavity. We also constructed the Lindblad master equation without introducing nonunitary quantum jumps (also see [5]). We finally investigated the spacetime evolution of a photon which is emitted during the decay of an atomic electron. After having carefully studied the dynamics of the electronic decay, especially at very short times [6, 7], we set out to describe the emitted electromagnetic field as rigorously as possible. This emitted field, surprisingly, does not evolve causally. Though this is not entirely unexpected in view of Hegerfeldt’s theorem, which states [8] that causality is impossible for quantum systems which are described by a Hamiltonian with a spectrum which is bounded by below, we identified [9] two other sources of non causality. One of them was predicted qualitatively by Shirokov [10], while the other one, which is completely new as far as we can tell, is still to be better understood