# Can the wavelength of a single photon be measured?

Jeff Root
Is there any way to accurately measure the wavelength of a single,
individual photon? How precise could such a measurement be?

I will be satisfied if the "measurement" consists only of confirmation
that a photon from a monochromatic source has the expected value,
as long as it has sufficient precision to provide useful information
about the photon. But it would be better if the wavelength could
actually be measured without knowing beforehand exactly what
the wavelength should be.

If the former is possible but the latter is not, I would like to know
anything you can tell me about what makes the difference.

-- Jeff, in Minneapolis

Mentor
You could measure its frequency and divide by c. Since measurements of time are so precise that would be more accurate.

Jeff Root
Can the frequency of a single photon be measured?

Just replace the word "wavelength" in my original post with
the word "frequency".

-- Jeff, in Minneapolis

Gold Member
Theoretically; the same way you can measure lots of photons. For example, bounce it off of a grating and see which of several detectors it hits.
Practically; there are a whole lot of issues to address with each part of the experiment that will effect the accuracy (i.e. how good is your grating) and the chance of not seeing anything (the sensitivity of your detector, etc.).

Jeff Root
A single photon of a given wavelength and frequency might bounce
off a grating at any angle, even if the grating is perfect. A statistically
large number of photons all having that same given wavelength and
frequency will cluster around a specific angle. Measuring a single
photon gives a good chance that the angle is appropriate to the
wavelength and frequency, but there is also a good chance that it is
wildly different.

-- Jeff, in Minneapolis

Gold Member
A single photon of a given wavelength and frequency might bounce
off a grating at any angle, even if the grating is perfect. A statistically
large number of photons all having that same given wavelength and
frequency will cluster around a specific angle. Measuring a single
photon gives a good chance that the angle is appropriate to the
wavelength and frequency, but there is also a good chance that it is
wildly different.

-- Jeff, in Minneapolis
Yes, not a good example.
But now I understand your question better. It is definitely "above my pay grade". You may get better answers from google than here. For example, this was the first hit I got:
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-23-28898
(I didn't read it, but I suspect that measuring a "single photon source" isn't the same as measuring a single photon)

Jeff Root
Thanks. I think a "single photon source" IS what I'm asking about.
But it also looks like that article goes into a lot of deep technical
areas that are only distantly related to what I'm interested in.
It might answer my question, but I doubt I could understand.

-- Jeff, in Minneapolis

Gold Member
Can the frequency of a single photon be measured?

-- Jeff, in Minneapolis

Yes. How accurately will depend on the frequency.
Single photon calorimeters are -I believe- routinely used in e.g. X-Ray radio astronomy,

Mentor
Can the frequency of a single photon be measured?
Yes. Just use a very specific atomic transition.

Gold Member
The idea of the spatial nature of photons needs to be treated with care. There is the risk of a picture in the mind of a 'short sperm-like squiggle'. That's really not much better than the 'little bullet' picture. You can only talk about the properties of any photon after the event, when it has been deleted. We can't know where they are or the effective path taken until we see where they turn up.
One thing that is fairly reasonable, however, would be the Energy (AKA frequency).
With my RF Engineer's hat on, I have a problem, even with that idea. A photon that's emitted by an atom with one energy transition doesn't need (by logic) to be absorbed / detected at its destination by a precisely identical (tautology on purpose) atom; there has to be a Bandwidth involved - as with your familiar transmitter and receiver set up. That will presumably show itself as a probability distribution of the interaction of the incident photon and the receptor. If, as we believe, all photons are identical except for their Energy then how does that translate to things like coherence length of a photon beam? I find that confusing.

Gold Member
Is there any way to accurately measure the wavelength of a single,
individual photon?

Once you measure the energy you calculate from that what the wavelength would be for a very large collection of such photons. But you cannot observe the wave effects unless you have a very large number of particles. So the very concept of a wavelength for a single particle makes no sense to me.

sophiecentaur
Thanks. I think a "single photon source" IS what I'm asking about.

Let me ask one question in return to clarify: Are you interested in a single photon state, which you can prepare several times and then measure an ensemble of identically prepared photons or are you interested in a single individual photon that cannot be prepared repeatedly? And if you are interested in the second case, do you know roughly when and where to expect the photon? If so, Dale's idea to use a narrow transition and check for absorption will work well.

If you do not have any prior information, a technique from the attosecond community might work in principle (Goulielmakis et al., Direct Measurement of Light Waves, Science 305, 1267 (2004), https://www.attoworld.de/fileadmin/...ns/paper_Science_Y2004_M08_D27_V305_P1267.pdf ).
The details are probably too technical, but the basic idea is as follows: You fire a strong ultraviolet light field at a gas, which knocks some electrons loose, so they are removed from their atoms. The light field to be measured then passes this gas at the same time. As light is an electromagnetic field, the loose electrons feel the field and their momentum changes slightly due to the presence of the light field. Measuring the spatially resolved momentum distribution of the electrons reproduces the spatially resolved electromagnetic field of the light field of interest, which also allows one to deduce the wavelength. Of course the sensitivity achieved is usually far from the single photon level, but the principle should work as well.

Gold Member
Thanks. I think a "single photon source" IS what I'm asking about.
But it also looks like that article goes into a lot of deep technical
areas that are only distantly related to what I'm interested in.
It might answer my question, but I doubt I could understand.

-- Jeff, in Minneapolis
OK, another suggestion:
Find out who makes commercial single photon sources. Plus I'll toss in my former employer Coherent and other scientific laser manufacturers. Then call and ask to talk with an applications engineer. You won't get a PHD but you probably will get some useful free advice about what is out there and how people do this in practice. Big laser companies like Coherent, Newport, etc. will have a staff of people that do this. Smaller companies will probably refer you to their R&D staff which might be better, if you can get them to talk with you. These companies sell scientific instruments by networking with their customers, so you will get some information, how useful it will be depends on who you get on the phone. Sound like somebody who might buy one of their instruments. Or just ask who you should call next.

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But you cannot observe the wave effects unless you have a very large number of particles. So the very concept of a wavelength for a single particle makes no sense to me.
Are you suggesting that individual particles (photons,electrons, helium atoms) are not diffracted according to their wavelength by an appropriate grating?

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I will be satisfied if the "measurement" consists only of confirmation
that a photon from a monochromatic source has the expected value,
as long as it has sufficient precision to provide useful information
about the photon. But it would be better if the wavelength could
actually be measured without knowing beforehand exactly what
the wavelength should be.

I am late to this conversation but has anyone recommended a "filter"?. There are interference filters for light with passband widths of ~1 Angstrom and transmittance of >90% midband. They are multiple layer interference devices and are remarkably effective.

Gold Member
Are you suggesting that individual particles (photons,electrons, helium atoms) are not diffracted according to their wavelength by an appropriate grating?
If you have enough of those individual particles, then you can see a display of a diffraction.pattern.

One particle is not anywhere near enough to make such a pattern.

Jeff Root
f95toli said:
Jeff Root said:
Can the frequency of a single photon be measured?
Yes. How accurately will depend on the frequency.
All else being equal, I would expect the precision to be
directly proportional to the frequency, so that-- making
up some play values-- a measurement of 500 nm might be
precise to +/- 1 nm, while a measurement of 500 cm might
be precise to +/- 1 cm. I wouldn't expect the *accuracy*
to be frequency-dependant.
f95toli said:
Single photon calorimeters are -I believe- routinely used in
Interesting. I'll look that up, but the idea of a calorimeter
seems inappropriate for answering my question. Measurement of
heat energy resulting from a photon-particle interaction is a
roundabout way of determining the wavelength or frequency.
Heat is essentially a property of large numbers of particles,
and I'd expect any measurement of heat energy to have a large
uncertainty. I think I need something more direct.

-- Jeff, in Minneapolis

Jeff Root
Dale said:
Jeff Root said:
Can the frequency of a single photon be measured?
Yes. Just use a very specific atomic transition.
That must be what was meant by others I talked with.

My belief has been that the wavelength or frequency of
light can only be measured with a statistically large
population of photons, due mainly to the argument I gave
above that a single photon might bounce off a grating at
any angle. It is most likely to be close to a specific
angle, but a largish number of photons are required to
define that angle precisely, whether each photon hit is
measured separately or the effect of the whole beam is
observed.

I didn't think of the possibility of detecting the effect
of photons inducing a very specific atomic transition.
So my question may be: How precise is such a measurement?
More precise than the position of a spectrograph line?

-- Jeff, in Minneapolis

Jeff Root
Mister T said:
Once you measure the energy you calculate from that what the
wavelength would be for a very large collection of such photons.
But you cannot observe the wave effects unless you have a very
large number of particles. So the very concept of a wavelength
for a single particle makes no sense to me.
An interference pattern can be made on a screen by passing a
beam of monochromatic light through a barrier with two parallel
slits of appropriate size and spacing for the wavelength of the
light. This works even if the beam is so sparse that only one
photon hits the screen at a time. I find this a convincing
argument that each individual photon has a wavelength.

Although the interference pattern only emerges from a large
number of photons hitting the screen, each photon must have a
wavelength that contributes to the pattern. Although each
photon in a monochromatic beam has the same wavelength, the
path of any individual photon to the screen is unpredictable,
untraceable, and unknowable, but the wavelength is inferred
from the angle between fringes.

-- Jeff, in Minneapolis

Jeff Root
sophiecentaur said:
The idea of the spatial nature of photons needs to be treated
with care. There is the risk of a picture in the mind of a
'short sperm-like squiggle'. That's really not much better
than the 'little bullet' picture.
I think of photons as short sperm-like squiggles.

Although the squiggles are electromagnetic, not spatial in the
transverse direction. But ultimately I'm trying to find out
whether photons have length. I know they are often treated as
pointlike. I'm going to use an analogy with the sperm-like
squiggle to describe my mental picture. I'm not asking whether
this picture is correct or not. If it has problems I will be
happy to hear them. But at the moment I'm just trying to find
out whether the wavelength and frequency of individual photons
can be measured, because it was previously my belief that they
cannot. I am surprised to learn that they may be measurable.
That would be awesome!

A photon cannot change over time. Time does not exist in the
photon's reference frame. That means the wave nature of the
photon cannot be caused by the photon changing, such as pulsing
or moving up and down. Instead, the wave must be a fixed form
which moves as a whole, unchanging unit.

Here's the analogy. Draw a waveform on a scrap of paper, then
move the paper past you. You see the point on the wave that is
directly in front of you move up and down, while the wave itself
is unchanging. With light, made of photons, the changes in the
electromagnetic field represented by this up and down motion
cannot be observed. Even if the light comes straight at you,
and reaches your eye, you can't see the changes because a photon
can only be detected as a single interaction at a single point
in time, at a single point in space. The entire photon must reach
and be absorbed by the detector, or it is not detected. There is no
such thing as a part of a photon. But since we know the photon
must have a wavelength, I argue that this wavelength can only be
a property of the photon if the waveform has length.

That definite length is relative to the observer. Depending on
the relative motion of the light source and the observer, the
photon's wavelength will be longer or shorter, and so the photon
itself must be longer or shorter.

That's the idea I'm ultimately exploring, but again, at the
moment, I'm just trying to find out whether the wavelength can
be measured.

sophiecentaur said:
You can only talk about the properties of any photon after
the event, when it has been deleted.
I think we can talk about the properties at any time, but
we can only know what they are after they have been observed.

Did you mean "detected" rather than "deleted"?
A photon is deleted when it is detected, so both are true.

sophiecentaur said:
We can't know where they are or the effective path taken
until we see where they turn up.
Can we know the path even then? I thought that was also
unknowable at the level of individual photons.

sophiecentaur said:
One thing that is fairly reasonable, however, would be the
Energy (AKA frequency).

With my RF Engineer's hat on, I have a problem, even with
that idea. A photon that's emitted by an atom with one energy
transition doesn't need (by logic) to be absorbed / detected
at its destination by a precisely identical (tautology on
purpose) atom; there has to be a Bandwidth involved - as with
presumably show itself as a probability distribution of the
interaction of the incident photon and the receptor. If, as
we believe, all photons are identical except for their Energy
then how does that translate to things like coherence length
of a photon beam? I find that confusing.
Saying "all photons are identical" raises another question:

Can the polarization of a single photon be measured?

-- Jeff, in Minneapolis

Last edited:
Jeff Root
Cthugha said:
Are you interested in a single photon state, which you
can prepare several times and then measure an ensemble of
identically prepared photons or are you interested in a single
individual photon that cannot be prepared repeatedly?
I don't know. Those concepts are beyond my understanding.

Cthugha said:
And if you are interested in the second case, do you know
roughly when and where to expect the photon?
I think the setup can be whatever will reveal the wavelength
or frequency of individual photons. I imagine a light source
filtered to be monochromatic and almost always allow only one
photon to reach the detector at a time. Any means of doing
that should be OK as far as I know.

Cthugha said:
If so, Dale's idea to use a narrow transition and check for
absorption will work well.
Is the probability of absorption at exactly the transition
frequency greater than the probability that the photon
diffracts from a grating at exactly the characteristic angle?
Even if the grating is perfectly ideal? Does the absorber
need to be at absolute zero temperature to avoid relative
motion of the source and absorber?

-- Jeff, in Minneapolis

If you have enough of those individual particles, then you can see a display of a diffraction.pattern.

One particle is not anywhere near enough to make such a pattern.
I don't think that's true. Of course you will not see a pattern. But with a good grating, photons will only be scattered in directions fulfilling the Bragg condition.
So although you cannot predict the refraction order you will observe for a single photon, you can obtain its wavelength.

I also want to point out that photons normally don't have a well defined frequency or wavelength. This is only the case for monochromatic light sources but not e.g. for the photons making up, say, a femtosecond laser light pulse.

Gold Member
Are you suggesting that individual particles (photons,electrons, helium atoms) are not diffracted according to their wavelength by an appropriate grating?
A diffraction pattern is a statistical phenomenon. One value doesn't make a statistical distribution. A single photon could arrive literally anywhere but the probability would be to do with the energy and the geometry.
Can the polarization of a single photon be measured?
This is also a difficult one. If one photon can only be detected once then, if it passes through a polariser, there must be a probability distribution of whether it will be detected or not by a polarised detector. So Any Photon 'may' be detected, irrespective of the way the equipment has been set up.
IMO it's all a bit Zen and you need to ignore some of the 'obvious' things that apply in the macroscopic world.

Gold Member
I don't think that's true. Of course you will not see a pattern. But with a good grating, photons will only be scattered in directions fulfilling the Bragg condition.
So although you cannot predict the refraction order you will observe for a single photon, you can obtain its wavelength.
That gets us somewhere - it means that we can at least be fairly certain about what photon energies are very unlikely when we have detected one.

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The diffraction pattern gives the relative probability for detection of a photon from the grating. Each photon detection is a measurement event. The predictive validity (confidence level) of resulting data will scale roughly with the square root of number of photons detected as with any sampling test.

Is the probability of absorption at exactly the transition
frequency greater than the probability that the photon
diffracts from a grating at exactly the characteristic angle?
Even if the grating is perfectly ideal? Does the absorber
need to be at absolute zero temperature to avoid relative
motion of the source and absorber?

I am not sure what you mean. Assuming a perfectly ideal grating that shows no absorption and only first order diffraction with perfect efficiency, the angle at which a photon gets diffracted always corresponds to the wavelength/frequency of that photon. The width of the peak is caused by uncertainty, which means that one is in principle unable to prepare an ensemble of photons so perfectly, that they will all have the same frequency (also at some point the diffraction limit wll come into play), even under ideal conditions, but what you measure directly yields the frequency of that very photon you measured.

Gold Member
The width of the peak is caused by uncertainty,
Just the same as any diffraction pattern. As it happens, this particular diffraction pattern has one very narrow peak with a width that's calculable using wave calculations. Nothing different in principle. With the sort of apertures available, would we not be talking in terms of several arc minutes of resolution? That's actually pretty poor when you think of the possible accuracy of macroscopic frequency measurements.

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Folks I have lost track of what question we are trying to answer.

The determination off wavelength is what a spectrometer does. Their design is a very mature art. How precise they can be is affected by many factors including optical "leverage" and wavelength range of the grating. Detectors have finite size. In the end these will "collide" with the diffraction pattern from the entrance slit. So the answer to that question is complicated and specific.
Interference filters can select wavelengths to fractions of Angstroms.
There are a host of other clever interference techniques .
The question of polarization measurement has been looked at in exhaustive detail in the context of Bell's Theorem and the Einstein Rosen Podolsky arguments as well as quantum computing.
So I would ask the OP to reiterate his question keeping in mind that no measurement is perfect. There are many ways to measure the wavelength of a single photon. None is exact.

Gold Member
There are many ways to measure the wavelength of a single photon
I think the point has already been made that the wavelength of a photon is not a very meaningful value. Waves have wavelength and a photon is not a wave; it is a particle (which, of course, can have Energy.)

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I think the point has already been made that the wavelength of a photon is not a very meaningful value. Waves have wavelength and a photon is not a wave; it is a particle (which, of course, can have Energy.)
I apologize but I haven't a clue what you are talking about. Can you be a little more specific as to where this is shown to be true? Is there an external reference?

Gold Member
Can you be a little more specific as to where this is shown to be true?
If you want to assign a particular frequency for a photon then it would have to exist for long enough for the frequency to be definable (ideally an infinite length of time) and if you want to assign a wavelength, the same applies. Can you define the lifetime and extent of a photon? A photon is a particle with completely undefined extent so how can you give it meaningful wave properties? An external reference could be any book on the basics of time varying functions and the frequency spectrum. (Fourier analysis)
PS You implied that "a fraction of an Angstrom" corresponds to great accuracy. That's a little better than 0.1% accuracy. Frequency of a continuous wave is quite easily measured to within one part in 1010. That's what I would call accurate.

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A photon is a particle with completely undefined extent so how can you give it meaningful wave properties?
This will be a great surprise to astronomers using spectrophotometers with (cooled) cameras that count photons one at a time and characterize their wavelength spectrum. I myself have counted individual photons from faint fluoroscopic emissions filtered and selected by their wavelength to enable counting. So I simply do not know what you are talking about.
PS A measurement of one second duration (hardly the age of the universe!) gives a frequency uncertainty of roughly 1 Hz. according to Fourier (and information theory and Heisenberg etc) That's not very much energy spread...
What am Ii missing here?

Just the same as any diffraction pattern. As it happens, this particular diffraction pattern has one very narrow peak with a width that's calculable using wave calculations. Nothing different in principle. With the sort of apertures available, would we not be talking in terms of several arc minutes of resolution? That's actually pretty poor when you think of the possible accuracy of macroscopic frequency measurements.

Well, that is a question of how much loss in intensity you consider acceptable. One may increase resolution, while sacrificing efficiency. However, the resolution using a spectrometer will not be ideal in practice. I agree.

If you want to assign a particular frequency for a photon then it would have to exist for long enough for the frequency to be definable (ideally an infinite length of time) and if you want to assign a wavelength, the same applies. Can you define the lifetime and extent of a photon? A photon is a particle with completely undefined extent so how can you give it meaningful wave properties?

I partially disagree on this. Lifetime and extent of a single photon are unknown, if you do not know anything about the emission process. However, from a fundamental point of view, a photon emission event from a simple system (imagine a single atom) consists of the emitter being in a superposition of the excited state and the ground state and the light field being in a superposition of having 0 and 1 excitation. The duration of how long this superposition can be kept alive defines the extent (which usually means coherence length) of a single photon. If you place a single photon emitter inside a cavity, considering the single photon (with the meaning of fixed photon number and not of fixed frequency) lifetime and extent is quite a common thing to do.