What happens when you try to chop a photon in half?
What happens when you try to chop a photon in half?
当你试图把一个光子劈成两半时会发生什么？
A photon is a single particle of light, and under normal circumstances, it can’t be divided. But a photon is also not a particle, in the sense that it does not have a specific location. Instead, it is an extended object. So if a photon is only partway through the process of reflecting from a perfect mirror and you yank the mirror away, what happens? The answer, from a trio of Norwegian physicists, turns out to be more complex than I expected.
光子是光的单个粒子，在正常情况下，它无法被分割。但从某种意义上说，光子也不是一个粒子，因为它没有特定的位置。相反，它是一个延展的对象。那么，如果一个光子在从完美镜面反射的过程中只进行了一半，而你突然把镜子移走，会发生什么呢？三位挪威物理学家给出的答案，比我预期的要复杂得多。
A photon divided? Let’s first talk briefly about dividing and combining photons. If this were a common experience in our lives, then shining a single color of light through a piece of glass or reflecting it from a surface might cause photons to divide or combine. This would lead to an amazing array of colors: Our universe would be the most fantastic and legal LSD trip you could imagine. But this doesn’t generally happen, hence LSD.
光子被分割了？让我们先简单谈谈光子的分割与合并。如果这是我们生活中常见的现象，那么让单色光穿过玻璃或从表面反射时，可能会导致光子分裂或合并。这将产生令人惊叹的色彩阵列：我们的宇宙将是你所能想象到的最奇妙且合法的迷幻药（LSD）之旅。但这通常不会发生，所以才会有 LSD。
What does happen is that photons can divide and combine under the right circumstances—essentially, the medium through which the light travels has to change in response to the light. This can lead to a rainbow of colors from a single color source. Technically, we would say that the light interactions we see around us are linear, and the combination/division of photons is a nonlinear process. Typically, to overcome that nonlinearity, you need either a very sensitive medium or a very high-intensity light source, like a laser.
实际发生的情况是，光子可以在特定条件下分裂和合并——本质上，光传播的介质必须对光做出反应而发生改变。这可以使单一颜色的光源产生彩虹般的色彩。从技术上讲，我们称周围看到的光相互作用为线性的，而光子的合并/分裂是一个非线性过程。通常，要克服这种非线性，你需要一种非常敏感的介质或高强度的光源，比如激光。
The sudden removal of the mirror while a photon is reflecting is not nonlinear in the way that I would normally think about it. But if you give it more than a moment’s thought, it’s clearly a nonlinear event. This line of thinking is obscured by how we think about single photons at mirrors, though, as I will illustrate below.
在光子反射时突然移走镜子，这与我通常理解的非线性方式不同。但如果你多思考一下，这显然是一个非线性事件。然而，正如我将在下面阐述的那样，这种思考方式被我们看待镜面上单个光子的方式所掩盖了。
A single photon goes through the looking glass. Or does it? Let’s start with the example of a partially reflective mirror. When a single photon hits that mirror, it will either go through the mirror or reflect from the mirror. The photon is considered to enter a superposition state of having both reflected and passed through (the probabilities of each path depending on how reflective the mirror is). If we place detectors in the path of the reflected and transmitted photons, when one clicks, it collapses the superposition, and the other potential path disappears. There are no circumstances in which both detectors will click at the same time. We do not record half a photon each way.
单个光子穿过镜子。真的是这样吗？让我们从半透镜的例子开始。当单个光子撞击镜子时，它要么穿过镜子，要么从镜子反射。光子被认为进入了一种既反射又穿过的叠加态（每条路径的概率取决于镜子的反射率）。如果我们在这两条路径上放置探测器，当其中一个发出信号时，叠加态就会坍缩，另一个潜在路径就会消失。在任何情况下，两个探测器都不会同时发出信号。我们不会记录到两边各半个光子。
Naively, we could make the same argument for a fully reflective mirror that is removed midway through reflection. In this argument, the photon enters a superposition state of transmitted and reflected, with the probability determined by when the mirror was removed compared to the “size” of the photon. Again, when we try to measure which way the photon went, we’d expect the superposition to collapse, and only one detector would click. But that is not what happens. When I stopped to think about it, it was obvious that this was wrong. But to understand why, we need some extra theoretical baggage.
天真地想，我们也可以对一个在反射中途被移走的完全反射镜提出同样的论点。按照这个逻辑，光子进入了透射和反射的叠加态，概率取决于镜子移走的时间点与光子“大小”的对比。同样，当我们试图测量光子去了哪里时，我们预期叠加态会坍缩，只有一个探测器会响。但事实并非如此。当我停下来思考时，很明显这是错误的。但要理解原因，我们需要一些额外的理论知识。
A photonic thunderclap. Time and frequency are two sides of the same coin. If we play a note on a piano, there is a time-domain picture: a regular variation in pressure with time that continues for quite a while. This note can be described by a single frequency with a single amplitude (how loud it is). More complicated sounds (chords, staccato notes) have a complicated structure in time and are described by more complicated combinations of frequencies, each with its own amplitude (phase also matters, but we will ignore that). This picture is universal and applies to all time-varying signals—and far more than those, too.
光子雷鸣。时间和频率是同一枚硬币的两面。如果我们弹奏钢琴上的一个音符，就会有一个时域图像：压力随时间规律变化，并持续一段时间。这个音符可以用单一频率和单一振幅（音量）来描述。更复杂的声音（和弦、断奏）在时间上有复杂的结构，由更复杂的频率组合来描述，每个频率都有自己的振幅（相位也很重要，但我们暂且忽略）。这种图像是普遍的，适用于所有随时间变化的信号，甚至更多。
The shorter an event in time, the more frequency spectrum is required to support it. On the flipside, a single tone that does not change for a very long time requires very little spectrum (only the tone itself). This rule also applies to photons reflecting from mirrors. The photon is reflecting from the mirror, and the electromagnetic field is varying regularly and smoothly changing from the incoming to the reflected wave. The transmitted wave doesn’t exist, so the amplitude is a happy zero. Then the mirror is yanked away. The reflected wave’s amplitude abruptly drops to zero, and the transmitted wave suddenly jumps from zero. Those are two sharp transitions that require a lot more bandwidth than the original photon had.
一个事件在时间上越短，支持它所需的频谱就越宽。反之，一个长时间不变的单音只需要很少的频谱（仅音符本身）。这个规则也适用于从镜面反射的光子。光子从镜面反射，电磁场规律且平滑地从入射波变为反射波。透射波不存在，所以振幅为零。然后镜子被移走。反射波的振幅突然降为零，透射波突然从零跳变。这两个剧烈的转变需要比原始光子更多的带宽。
Our photon that has been cut off is still in a superposition of reflected and transmitted. But it also has a sharp edge, which requires a multitude of photons at different frequencies. Cutting a photon in half generates a rainbow. And as far as I can tell, the generated photons are in a superposition of both reflected and transmitted light. But since there are potentially many photons, both transmitted and reflected light could be measured simultaneously.
我们被切断的光子仍然处于反射和透射的叠加态中。但它也有一个尖锐的边缘，这需要大量不同频率的光子来支撑。把一个光子切成两半会产生一道彩虹。据我所知，产生的光子处于反射光和透射光的叠加态中。但由于可能存在许多光子，透射光和反射光可以同时被测量。
Can we do it for real? This will be a complex experiment to perform. Researchers will need a source that generates single photons on demand with a very narrow spectral bandwidth. This will spread them out in time so that any additional photons that come from cutting it off are observable. They then need to be able to trigger the mirror at the right time. This won’t be done with something like a bathroom mirror. The authors calculate that the transition from reflective to transmission needs to take…
我们能真正做到吗？这将是一个复杂的实验。研究人员需要一个能够按需产生极窄光谱带宽的单光子源。这将使它们在时间上分散开来，以便观察到因切断而产生的任何额外光子。然后，他们需要在正确的时间触发镜子。这不可能用浴室镜子之类的东西来完成。作者计算出，从反射到透射的转变需要花费……