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Does a photon having superimposed frequencies exist?

(wrt frequency detected by prism or other detectors, not wrt human eye as only rod-cells can detect one photon falling in the detectable (visible) frequency band and the single photon is perceived by eye+brain as grey irrespective of frequency).

Also, with white here, I do not wish to restrict the question implying all VIBGYOR frequencies or only RGB as each color is also a range of frequencies and white to trichromatic-sensor human eye is just output from three frequencies RGB.

Or can it be that materials which slow light down cause a photon of some single frequency and higher energy to split into VIBGYOR? || and the entire spectrum of human eye's detection range is VIBGYOR+W (as monochromatic light of high intensity can also be perceived white by human eye and it is not related to individual color sensors of human eye at all but that above a certain energy per unit volume (referring to detector area of eye cells), we perceive it white, (somewhat but not exactly) similar to combination of red and green which human eye+brain calls yellow.

I have added the additional description to make the question more precise. If my description causes confusion, please stay with the original question and use description just to get an idea of the intent of the question.

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    $\begingroup$ In theory yes a photon can be in a superposition of many different frequencies (frequency is basically equivalent to energy $E=hf$). But on measuring it, in any way, you will always collapse the wave function into a state of well defined frequency. $\endgroup$
    – Quantum spaghettification
    Commented Nov 9, 2016 at 21:50
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    $\begingroup$ Superposition of different frequencies as a state of a photon has little in common with mixture of photons (or waves) with different frequencies that produces white color. All terms of the superposition are monochromatic, they do not "mix", and each is a complete picture of what might happen observationally. So photon may exist in a superimposed state, but it won't be white. For the same reason superposition of dead and alive Schrödinger cats is not a dead-and-alive cat, despite the popular misconceptions, it is more like two cats in ephemeral "parallel worlds". $\endgroup$
    – Conifold
    Commented Nov 9, 2016 at 23:06
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    $\begingroup$ @Quantumspaghettification frequency is frequency, how can a photon have many of them? $\endgroup$
    – Bill Alsept
    Commented Nov 10, 2016 at 4:58
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    $\begingroup$ @BillAlsept The same reason an electron can have a (superposition of) an up spin and a down spin. A photon can be in two (or more) different energy eigenstates at the same time. On measurement you will only see one frequency, like on measuring the spin of an electron you will only see up spin or down spin. $\endgroup$
    – Quantum spaghettification
    Commented Nov 10, 2016 at 13:46
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    $\begingroup$ @SPARK There is a saying, (the origin of which I cannot find) that an electron is not a wave, nor is it a particle; it is an electron. The same holds for photons. I don't think considering it as a 'quantum energy packet' would help, this seems to imply that a photon has a well defined energy (/frequency) - it may not. I think the picture of a 'quantum packet of vibration' is more helpful if you want to go down that route. I visualize in the same way I visualize an electron - i.e. as a particle (like thing). $\endgroup$
    – Quantum spaghettification
    Commented Nov 10, 2016 at 13:55

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There are a lot of contradictory answers here. The basic facts are

  • Yes, a photon by itself can be in a quantum superposition of different frequencies, which one might call "white".
  • No, such a photon probably can't be produced by a simple natural process.
  • No, such a photon would not look white, because the superposition collapses upon measurement, giving only one frequency. (Only one of your cone cells could possibly fire in response, assuming that any even fire at all.) However, a collection of many such photons would collectively look white.
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A photon is axiomatically one of the elementary particles building up the standard model of particle physics. It has energy $E=hν$ where $ν$ is the frequency a large number of photons of that energy will build up. Its mass is zero and its spin +/- 1 in its direction of motion. The axioms of the standard model have been chosen because the model fits the data, and innumerable experiments have validated it.

As a quantum mechanical entity photons can be in superposition, and three of them with appropriate frequencies might fall in the group that gives the perceptiong of white in the diagram .

There is no "white frequency", as color perception is a biological mechanism.

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A good approach to answering the question is to design an experiment that would answer it. There are lasers that emit "supercontinuum" beams, in intense pulses. A pulse is very short, on the order of a femtosecond or less. One of the pulses, passed through a diffraction grating, fans out into an array of beams of different wavelength / frequency. Downstream, the beams can be recombined coherently to form a new pulse. This is an interferometer of sorts- a temporal interferometer.

Now we need an experiment that produces a particular result if and only if (A) only one photon passes through the system at a time, and (b) the photon must have had multiple wavelengths. We know from QM that to meet condition (B), our detector needs to be completely incapable of detecting the photon's frequency, but capable of detecting its time of arrival. Assuming such a detector exists, we should be able to reduce the intensity of the laser's pulses enough to ensure that there is only one photon in the apparatus at a time. If we integrate the times of arrival of a large number of such single-photon events and find that when the paths of the beams are all unblocked the photons all arrive at the detector with precisely the same time delay, but that when any portion of the paths taken by different wavelengths is blocked, the arrival times are spread out, then we can conclude that each photon's wavefunction contains a mix of wavelengths.

I don't know if this experiment has been done, but am confident that the results would show that each photon does contain a mix of wavelengths. This is related to other discussions on SE regarding coherence length of a photon, shape of a photon wave "packet, etc.

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  • $\begingroup$ Interesting, especially as an experiment is proposed. the question is whether it effectively measures the single photon twice, or different photons on each measurement (similar to the use of two photon emission for twin slit checking). I believe there is already a similar experiment for producing super intense pulses by the reverse process with a chirped laser (FROG - en.wikipedia.org/wiki/Frequency-resolved_optical_gating) $\endgroup$
    – Philip Oakley
    Commented Nov 17, 2018 at 21:43
  • $\begingroup$ However, I'm still of the opinion that each photon has a single precise frequency defined by its energy. And that it can only have one of two polarisations, left and right circular (otherwise that aspect would not be quantum). It's likely that the rotational frequency is the constant, while the direction of travel shape is more wavelet, and it is ultimately quaternionic (as per Maxwell, Art 618/9 IIRC). $\endgroup$
    – Philip Oakley
    Commented Nov 17, 2018 at 22:10
  • $\begingroup$ Per the Heisenberg uncertainty principle, the product of energy uncertainty and time of emission (which translates to phase) is always finite. Every laser has a finite linewidth, and that line width is a characteristic of the photons comprising the laser's emission. That is, the frequency of each photon is indeterminate within the line width of the laser. $\endgroup$
    – S. McGrew
    Commented Nov 18, 2018 at 1:24
  • $\begingroup$ For a laser we are producing a very large number of photons. There are various ensemble statistics therein. However in this case we are looking at just a single photon, so the 'statistic' aspect wouldn't be valid here. At the moment we are in a catch 22 scenario where it is [normally] claimed that we cannot in anyway measure or infer the measurement of these two apparently distinct characteristics because the theory suggests that they are bound to the same fundamental constant (which may have a systematic error, but no experimental error...) $\endgroup$
    – Philip Oakley
    Commented Nov 19, 2018 at 23:56
  • $\begingroup$ That argument could be used to say that no photon exists in a mixed state of any sort at all. In practice, we produce a lot of photons under identical conditions and measure the state of each photon individually, as in the single-photon double slit experiment. Even though the individual measurements yield definite results, the measurements all together are taken as proof that the photons are all in the same mixed state. $\endgroup$
    – S. McGrew
    Commented Nov 20, 2018 at 0:07
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I think there is nothing in principle to prevent such a photon from existing. In practice, I am not aware that such a photon exists.

All real photons have a finite homogeneous bandwidth inversely proportional to the lifetime of the transition that produces them. If this bandwidth is so large that it covers the optical spectrum you can call such a photon white. It would be a very short light pulse, of the order of one wavelength.

Note that ordinary white light is an, incoherent, superposition of multiple photons. A wide bandwidth photon has to be a coherent phenomenon.

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I don't believe this is possible. Light travelling through a medium travels at slightly different speeds depending on its wavelength. If a single photon had superimposed frequencies, each frequency would travel at a different speed, causing the photon to smudge, i.e. one frequency would be travelling ahead of another frequency, although due to quantum entanglement this might be possible.

This sentence on Wikipedia's photon article:

a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation.

implies that a single photon can only have a single wavelength/frequency, since a wave vector only describes a single wavelength/frequency.

I believe that if you had three frequencies of light travelling in a vacuum along exactly the same path and they entered a prism at the same time, you would find that they were in fact three separate photons superimposed. The Pauli exclusion principle does not apply to photons, so they can coexist at the same point in space/time, if such a concept makes sense for a wave/particle that only exists at the speed of light.

Something you would have to consider is how would a photon be created with a superposition of frequencies in the first place? What reaction could cause it? What repeatable experiment could you set up that proves that certain photons have multiple frequencies, when you can only measure one per photon? How would you distinguish between photons randomly created at different frequencies and superimposed photons detected at different frequencies?

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