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Definition: quanta of light energy

German: Photonen

Categories: general opticsgeneral optics, quantum opticsquantum optics, physical foundationsphysical foundations


Cite the article using its DOI: https://doi.org/10.61835/9qt

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When a weak light beam hits a sensitive photodetector, energy is found to be delivered in the form of small bunches, rather than continuously. This can be interpreted such that the light beam consists of small bunches of energy, called photons or light quanta (German 'Lichtquanten' = portions of light). The photon energy is <$h \nu = h c / \lambda$>, i.e. the product of Planck's constant <$h$> and the optical frequency <$\nu$>, and is also related to the vacuum wavelength <$\lambda$>.

The idea that light consists of such energy bunches had already been used early in the 20th century by Max Planck in the context of thermal radiation, and by Albert Einstein when investigating the photoelectric effect. The term photon, however, was coined only in 1926 by the physical chemist Gilbert N. Lewis [1].

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Although a 'naïve' interpretation of photons as particles of light gives a useful picture for the intuitive understanding of many quantum phenomena, it can be seriously misleading to apply it without understanding its limitations. A consistent and very powerful, but certainly not simple description of the nature of light is achieved by modern quantum optics. Here, photons are seen as the elementary excitations of the electromagnetic quantum field. This theory attributes fairly strange properties to photons, which cannot be reconciled either with a simple particle picture or with a pure wave picture, but accurately match a wide range of observations.

Some Key Properties of Photons

  • When light interacts with atoms or other particles, only amounts of energy which are integer multiples of the photon energy <$h \nu$> can be transferred to or from the light field. This can be easily interpreted as absorption or emission of some number of photons, and would thus so far be compatible with a simple particle picture of photons. Such processes are possible only if the involved atoms, ions or molecules are able to accept such amounts of energy, i.e., only if they have quantum-mechanical energy levels with an energy difference corresponding to the photon energy, or in some cases some integer multiple of it (→ two-photon absorption). A pure wave picture could explain these energy constraints as resonance effects, but can not explain the quantization of exchanged energy.
  • The energy quantization is also apparent in the interaction with sensitive photodetectors, which allow for photon counting, i.e. to register single photon absorption events. This finds applications in various areas of science and technology.
  • The propagation of light (e.g. in free space or in a waveguide) is that of a wave field. The quantum-mechanical field amplitude arising at some point in space and time is the superposition of contributions which correspond to different possible paths for light. These contributions can constructively or destructively interfere with each other, and this is the basis of the well-known optical interference effects. The likelihood or rate of photon detection at a certain location is proportional to the modulus squared of the quantum-mechanical field amplitude, and may thus suppressed if different field contributions cancel each other, leading to a weak overall field. A pure particle picture is hard to reconcile with such phenomena. For example, in the classical double-slit experiment an ordinary particle would have to go through one of the two slits, and the other slit would be irrelevant; it could not be explained why particles can reach certain locations behind the double slit only when one of the slits is blocked, but not when both are open (destructive interference).
  • Photons have zero rest mass, and can therefore not be slowed or brought to rest. There are phenomena of “slow light”, but these occur only for light in media, where the electromagnetic field strongly interacts with matter.
  • Photons can carry angular momentum of two different forms: resulting from their spin (<$s = 1$>) and also as an orbital angular momentum related to the corresponding electric field profile.
  • Due to their boson nature, photons obey Bose–Einstein statistics (in contrast to Fermi–Dirac statistics for electrons). Multiple photons “like” to populate the same mode of the radiation field. This can be seen e.g. in the process of stimulated emission (and is thus also very important for lasers), but also in the energy spectrum of thermally excited radiation (black body radiation).
  • Photons can occur in entangled states, where certain properties (e.g. polarization) are correlated between different photons, even though these properties acquire definite values only when a measurement is performed. As measurements on the different photons can occur at different places, this seemed to imply the possibility of superluminal transmission of information (Einstein–Podolsky–Rosen paradox), but a closer inspection shows that in reality this is not the case.

Of course, quantum theory can be applied to any kind of electromagnetic wave phenomena, not only to visible light. However, quantum effects are not as important e.g. in the field of radio technology, as in optics and laser technology. This is because the photon energy of radio waves is very tiny compared with the thermal energy <$k_\textrm{B} T$> at room temperature, whereas the opposite is true for optical phenomena.

Photons in Laser Physics

Various phenomena in laser physics, such as stimulated emission as the basis for light amplification in laser gain media, are often explained based on photons. Nevertheless, much of laser physics can be described with purely classical pictures, not involving photons; for example, light amplification can be described with rate equation models involving excitation numbers and classical light wave amplitudes or intensities.

A stronger involvement of photons, however, is natural in the context of laser noise, or more generally noise in optics. For example, the high-frequency intensity noise of lasers is usually at the shot noise level, and the magnitude of that is compatible with a simple model of completely randomly arriving (uncorrelated) photons. Lower (sub-shot noise) intensity noise may be observed for squeezed states of light, as can be interpreted as photons becoming correlated, such that they arrive in a more regular fashion. The calculation of squeezing and many other phenomena is again usually based not on a simple particle picture, but either on full-blown quantum mechanics or on a simplified semiclassical model involving amplitude and phase fluctuations which have to obey certain rules.

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[1]G. N. Lewis, “The conservation of photons”, Nature 118, 874 (1926); https://doi.org/10.1038/118874a0
[2]R. A. Beth, “Mechanical detection and measurement of the angular momentum of light”, Phys. Rev. 50 (2), 115 (1936); https://doi.org/10.1103/PhysRev.50.115
[3]R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light”, Nature 177, 27 (1956); https://doi.org/10.1038/177027a0
[4]C. K. Hong, Z. Y. Ou and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference”, Phys. Rev. Lett. 59, 2044 (1987); https://doi.org/10.1103/PhysRevLett.59.2044
[5]G. Molina-Terriza, J. P. Torres and L. Torner, “Twisted photons”, Nat. Phys. 3, 3050 (2007); https://doi.org/10.1038/nphys607
[6]K. E. Ballantine, J. F. Donegan and P. R. Eastham, “There are many ways to spin a photon: Half-quantization of a total optical angular momentum”, Science Advances 2 (4), e15ß1849 (2016); https://doi.org/10.1126/sciadv.1501748
[7]K. Tschernig et al., “Direct observation of the particle exchange phase of photons”, Nature Photonics 15, 671 (2021); https://doi.org/10.1038/s41566-021-00818-7
[8]C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics, Wiley, New York (1997)
[9]C. Roychoudhuri, A. F. Kracklauer, and K. Creath (eds.), The Nature of Light. What is a Photon?, CRC Press, Boca Raton, FL (2008)

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Questions and Comments from Users


Is there any actual evidence that photons “travel through space”? Doesn't that imply their existence throughout their length of travel? And if they exist throughout their length of travel then wouldn't they interact with one another occasionally?

The author's answer:

Strictly speaking, the travel through space is not based on direct observations in the sense that we cannot usually detect photons on their way. However, you may take the possibility of blocking (absorbing) photons between sender and detector as some substantial evidence that they go that way.

I don't see why you think that photons would necessarily interact with each other. Well, in some situations they do – through optical nonlinearities.

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