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Light Plus Light = Darkness: No Energy Problem, but Quantum Weirdness

Posted on 2007-09-27 as a part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2007_09_27.html

Author: , RP Photonics Consulting GmbH

Abstract: The article begins with discussing energy conservation for cases with destructive interference, and also mentions issues of quantum weirdness as can be found particularly on the single photon level.

Dr. Rüdiger Paschotta

Ref.: encyclopedia articles on interference, photons, quantum optics

We don't know it from experience in our everyday life, but still believe it: the superposition of two light beams with equal intensities, equal frequencies and a proper relative phase shift can result in zero optical intensity. We call this destructive interference, and one may describe this with the equation “light + light = darkness”.

Checking the energy balance, one may at first be a bit irritated: light comes in through two beams, carrying some optical power, and no light comes out. So does energy of the light beams disappear? Well, we tend to strongly believe in energy conservation, but how to resolve this puzzle?

The key is to look at concrete situations:

So far, that's all classical wave optics, and once you have swallowed that light behaves like waves, you will no longer find destructive interference so puzzling. Things get really weird, however, in experiments with single photons. Consider an interferometer, set up for destructive interference in one output port, and a single photon being sent into the device. One might think that destructive interference can not happen in that case, since the photon can go only through one of the two interferometer ports, but experiments tell the opposite. That shows quite clearly that photons should not be naively identified with wave packets. (Also don't do that with electrons or atoms, please!) To calculate what happens, we always have to assume that a beam splitter sends some wave stuff into each output, even when it receives a single photon only. This holds, even though we have never seen half a photon in a light beam (or half an electron, if you use those). There is a significant number of interesting quantum optics experiments in that area, and Google presents you with interesting reading when fed e.g. with “single photon interferometer”. Such experiments often involve photon pairs, and quantum entanglement is often essential to understand them.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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