I Why don't we ever hear about low-frequency photons?

[Rob Lewis]

We're told that all electromagnetic radiation consists of photons. But you never hear them mentioned when discussing low-frequency radio waves. Why not? I get that, due to the low frequencies, the energy of each individual photon would be very small, so there must be lots and lots of them flying around, no? Are they launched in vast waves from transmitting antennas? Is it possible to detect individual photons from, say, a broadcast FM transmitter? Any discussion/clarification/illumination (pun intended) would be appreciated.

 

[Mentz114]

We're told that all electromagnetic radiation consists of photons. But you never hear them mentioned when discussing low-frequency radio waves. Why not? I get that, due to the low frequencies, the energy of each individual photon would be very small, so there must be lots and lots of them flying around, no? Are they launched in vast waves from transmitting antennas? Is it possible to detect individual photons from, say, a broadcast FM transmitter? Any discussion/clarification/illumination (pun intended) would be appreciated.

Microwave photons are often used in cavity experiments where the resonant frequency is in the WiFi range. Each photon has an energy of (roughly) 10^-30 J.

I have got a paper describing such an experiment but I can't find it. I'll post it when I do.

 

[slow]

Is it possible to detect individual photons from, say, a broadcast FM transmitter? Any discussion/clarification/illumination (pun intended) would be appreciated.

To answer your question, we would need to answer other questions beforehand. Does discrete photons appear from the source in the transmitter, or appear when wave front reaches a minimum distance from the emitter? If the photons are formed at a distance from the emitter: 1) Is that distance independent or dependent on the frequency? 2) Is it dependent or independent of the power emitted? If the formation of photons happens at a distance dependent on the frequency and power emitted then it could happen, for radio frequencies and the powers usually emitted, too far from the emitter, perhaps far from the planet.

 

[PeterDonis]

We're told that all electromagnetic radiation consists of photons.

Pop science sources often say that, yes. But it might not mean what you think it means. See below.

Does discrete photons appear from the source in the transmitter, or appear when wave front reaches a minimum distance from the emitter?

Neither. "Discrete photons" might not appear at all. It depends on what kind of measurement you are making and what state the EM field is in. But if discrete photons are measured, it isn't because they "form" at some distance from the transmitter. That's not what photons are.

The term "photon" actually has several meanings, some of which are vague and imprecise and should be avoided if you actually want to understand the physics involved. For example, when pop science sources say things like "the energy in the EM field comes in little packets called photons", that is a vague and imprecise statement and doesn't have any simple relationship to the actual physics.

Even if we stick to precise meanings, there are at least two possible ones for the term "photon":

(1) An eigenstate of the photon number operator. For example, in cavity experiments such as the ones referred to by @Mentz114 , the EM field inside the cavity is in this type of state. In this case it makes sense to talk about the field containing a definite number of photons, each one having a definite energy equal to $\hbar \omega$, where $\omega$ is the "frequency" of the field. However, this type of field state is nothing like the usual "EM radiation"; that type of EM field is a quite different kind of state (see item #2 below). A key property of this kind of state that makes it useful in cavity experiments is that, when it exchanges energy with something else (like a qubit), it does so in whole photon increments, so it's simple to model the interaction involved.

(2) A coherent state of the quantum EM field. For example, the EM field describing the radio waves emitted by an antenna is in this type of state. This type of state is useful because it has the same kinds of properties as a classical EM wave, so your intuitions about how classical EM waves work basically carry over to coherent states with no problem. However, a coherent state is not an eigenstate of the photon number operator and in most situations it cannot usefully be viewed as containing photons; for example, a coherent state also does not have a definite frequency (it's not an eigenstate of the frequency operator), so there's no way to "count" the photons using the formula $E = \hbar \omega$. A key property of this kind of state that makes it act like a classical EM wave is that "measuring a photon" from this state (mathematically this corresponds to acting on it with the photon annihilation operator) does not change the state (a coherent state is defined as an eigenstate of the annihilation operator); so, heuristically, you can make measurements on it without affecting its behavior (as you would expect for a classical system).

 

[Demystifier]

(2) A coherent state of the quantum EM field.

Maybe it is wrong to say that coherent state is made of photons, but it is certainly true that coherent state can be written as a superposition of photon states (with different numbers $n$ of photons, including $n=0$). And if you measure the number of photons in a coherent state, there is a finite probability that you will find exactly one photon.

 

[f95toli]

Is it possible to detect individual photons from, say, a broadcast FM transmitter? Any discussion/clarification/illumination (pun intended) would be appreciated.

Not from FM (yet); but certainly in the GHz range where WiFI and cell phones operate.
For a "popular" description see e.g.
Lindstrom et al. "Controlling Single Microwave Photons: A New Frontier in Microwave Engineering." Microwave Journal 60.5 (2017): 118-130.
(available on the web)

For a "proper" articles see e.g.

Peng, Z. H., et al. "Tuneable on-demand single-photon source in the microwave range." Nature communications 7 (2016): 12588.

 

[A. Neumaier]

coherent state can be written as a superposition of photon states (with different numbers nnn of photons, including n=0).

Yes. But it doesn't imply what you then claim:

if you measure the number of photons in a coherent state, there is a finite probability that you will find exactly one photon.

As detailed in any textbook on quantum optics, measuring the number of photons in a fixed coherent state (in the most natural way to makes sense of this) will give you arbitrarily many detection events if you wait long enough, following a Poisson distribution whose mean is proportional to the intensity of the coherent state. This is loosely related to the fact mentioned by PeterDonis that coherent states are eigenstates of the annihilation operator.

But perhaps you had in mind a different meaning for your phrase. In this case, please indicate the kind of experiment that would carry out your measurement and gives a meaning to the word ''exactly one photon'' in your statement!

 

[f95toli]

But perhaps you had in mind a different meaning for your phrase. In this case, please indicate the kind of experiment that would carry out your measurement and gives a meaning to the word ''exactly one photon'' in your statement!

I believe this to large extent comes down to terminology. Heavily attenuated coherent radiation is used both in the optical regime (where e.g. nearly all QKD protocols operate with attenuated lasers) and for lower frequencies (MW) and most people (at least the experimentalists) will still talk about single photons in these cases.
In both cases you will indeed get a Poisson distribution. However, I guess the point is that the detection events themselves are still quantised (the energy you observe will be a multiple of hf); the fact that you sometimes get more than one photon and is not in a "proper" Fock state does not change the fact that the "particle nature" (for lack of a better word) is fairly obvious in these experiments.

 

[A. Neumaier]

the fact that you sometimes get more than one photon

How can you detect more than one photon in a coherent state?

You get clicks and spots at random times, with a Poisson statistics depending on the intensity (mean photon number), and that's all quantum mechanics predicts. The number of clicks depends on the observation time, and there is no way to associate these to single-time photon numbers.

Except by the customary convention that one click is one photon - which excludes multiple photons.
(Note that this is a pure convention, nothing derived from more basic theory or postulates!)

This is independent of attenuation mechanisms, and independent of whether you do experiments in the microwave of infrared or optical regime.

 

[jeremyfiennes]

So what is the lowest frequency photon that a photon detector can at present detect?

 

[f95toli]

So what is the lowest frequency photon that a photon detector can at present detect?

That is a bit of a difficult question. There are bolometric detectors that could -at least in principle- detect photons frequencies of a few hundred MHz. However, in order to show that you are really detecting single photons you need to do what is known as a g(2) correlation measurements (basically a Hanburry-Brown and Twiss setup). Experimentally, I believe this has been demonstrated for photons of frequencies of around 5 GHz.

 

[Derek P]

Microwave photons are often used in cavity experiments where the resonant frequency is in the WiFi range. Each photon has an energy of (roughly) 10^-30 J.

h=6.626* 10^-34 J.s. Your WiFi must run at 1.5 kilohertz :)

 

[jeremyfiennes]

That is a bit of a difficult question. There are bolometric detectors that could -at least in principle- detect photons frequencies of a few hundred MHz. However, in order to show that you are really detecting single photons you need to do what is known as a g(2) correlation measurements (basically a Hanburry-Brown and Twiss setup). Experimentally, I believe this has been demonstrated for photons of frequencies of around 5 GHz.

Thanks.