# How would I transmit 1 photon?

1. Sep 12, 2014

### mrspeedybob

I'm thinking about photons of low frequency as would be produced by a radio transmitter. How would a transmitter have to be set up to transmit just one photon? The smallest transmission I can think of would be to move 1 electron from one end of the antenna to the other. I would think that would produce at least 2, one as the electron accelerated and another as it decelerated to a stop. Am I thinking about this correctly at all?

2. Sep 12, 2014

### DrChinese

The frequency of a photon is inversely proportional to its wavelength. This is completely different than the rate at which a radio transmitter emits light.

Creating a known number of photons is not normally done via radio transmitter, but rather other processes. Is there anything more you can add?

3. Sep 12, 2014

### mrspeedybob

Radio transmitters are familiar territory to me. I understand (in a classical way) how wiggling some charges in one place can make some other charges somewhere else wiggle in response. I think if understood this in terms of photons as well as electromagnetic waves I might have a better intuition about the nature and behavior of photons, and by extension, other quantum particles.

4. Sep 13, 2014

### exponent137

I think that Feynman's "QED: The Strange Theory of Light and Matter" will give you answers. It is more oriented on intuition than on mathematics.

5. Sep 15, 2014

### f95toli

Low frequency (i.e R/MW) photons can be transmitted using a suitable waveguide, and presumably also an antenna (although that experiment has -to the best of my knowledge- not been done yet.
There is no fundamental difference between RF photons and optical photons, you just have to use a different waveguide: optical fiber for optical photons and RF waveguides (e.g. a coaxial cable or coplanar waveguide) or RF/MW photons.

The main difference would be in how you generate the photon in the first place, and also that you have to worry about your photon being swamped by room temperature radiation; which is one of several reasons why RF/MW experiments have to be done at cryogenic temperatures.

6. Sep 28, 2014

### mrspeedybob

That's kind of the crux of my question.
My classical understanding of electromagnetic waves comes mostly from this...
http://physics.weber.edu/schroeder/mrr/MRRtalk.html
My quantum understanding of photons comes mostly from 4 Feynman lectures which Wikipedia states are the basis for the book that exponent137 suggested.
I'm struggling to find a way to unify these 2 ideas in my mind.

I can think of accelerating charges causing waves in the electric field, but in what way would an electron have to accelerate to transmit 1 and only 1 photon?

Photons are generally thought of (by me anyway) as resulting from and electron changing it's orbital from a high energy state to a lower one. How can I relate this back to accelerating a charge? Acceleration is change in velocity / time. Velocity in change in position / time. So when position is in constant superposition shouldn't acceleration be in constant superposition? What would that even mean?

7. Sep 28, 2014

Staff Emeritus
mrspeedybob, do you want exactly one photon or approximately/on average one photon? It makes a big difference.

If you want exactly one, radios are not a good model. Radios are designed to operate at a particular frequency, and if you have a system in an eigenstate of photon number, it is not in an eigenstate of frequency. If you take an ordinary radiation source (like an antenna) and reduce its intensity, you won't end up with a single photon source.

8. Sep 28, 2014

### mrspeedybob

What will you end up with?

9. Sep 28, 2014

### vanhees71

The problem is that the word "photon" is the most abused concept in historty ;-)). Not only popular-science books but also (otherwise very good) introductory textbooks on quantum mechanics start with a chapter on the "historical development" introducing the subject with a notion of "photon" that's outdated, namely the "old quantum mechanics". Ironically Einstein got the Nobel prize not for his long-lasting achievements in our fundamental understanding of space and time, the theory of relativity (both the general and the special, where as the name says the special theory is a special case of the general in circumstances where gravity is negligible), but for his ideas on photons, mostly the photoelectric effect. That's ironic, because these ideas where already obsolete during his lifetime with the development of modern quantum theory (Heisenberg, Born, Jordan 1925; Schrödinger 1926; Dirac 1925). The correct notion of photons was introduced by Jordan and independently by Dirac when the quantum-field theoretical formulation of many-body quantum theory has been discovered.

The point is that nearly anything, advocated as the proof of the existence of photons is explainable as well in terms of the semiclassical theory, where only the matter particles (mostly electrons if we consider the detection of light with everyday-matter) are described quantum theoretically while the electromagnetic field is treated as classical. From this picture you get precisely the formula describing the energy bilance of the photoelectric effect a la Einstein, ironically showing that the photoelectric effect does not prove the existence of photons at all. On the other hand it shows the necessity for a quantum-mechanical description of matter. In this respect Planck was correct with his scepticism against Einstein's idea of "light particles".

Another statement, often made, is that you can procuce single photons by just diming a laser to very low intensity. The same holds also true for antenna sending out radio waves, as stressed by Vanadium already. At high intensity these devices send out classical electromagnetic waves (light being just the electromagnetic waves with typical frequencies in the range our eyes are sensitive too and which we thus realize as light). If you ask, how to understand such classical waves in a quantum-theoretical way, you come to the idea of coherent states. These are quantum states of the photon field which are a superposition of states containing all numbers of photons. It's hard to explain without the mathematical machinery of quantum field theory (quantum electrodynamics in this case). The point is that, if you have such a state of the electromagnetic field and you ask, "how many photons are there?", you'll get a different answer in any measurement you make on a such prepared state. Quantum theory only tells you the probability distribution to find 0, 1, 2,... photons. What you get is a Poisson distribution,
$$P(n)=\frac{\lambda^n}{n!} \exp(-\lambda),$$
with an average photon number
$$\langle n \rangle=\lambda.$$
So you can make $\lambda$ as small as you like (even less then 1). If you plot the distribution in such a case, you'll see that the most probable photon number to find is 0, i.e., no photons present!

So the answer is: If you dim down a laser or a radio antenna to very low intensity you don't get a single photon source but a coherent state of very low average photon number, but the photon number is indetermined. You can find with some probability 1 but also with some (lower) probability 2 or more photons.

It's not so easy to really get a single-photon source. Nowadays the quantum opticians employ birefringent crystals. Shooting with a laser on it, under certain circumstances you get out polarization-entangled photon pairs. Besides the fact that you have this entanglement which gives rise to the weirdest quantum phenomena (weird of course only in the sense that we are not used to the quantum behavior in our macroscopic every-day experience) you can also have true one-photon states: By detecting and absorbing one of the entangled photons, you are sure that there must be the other photon, and it's indeed really exactly one photon.

10. Sep 28, 2014

### DrChinese

1. mrspeedybob, the above from vanhees71 is an excellent answer and I hope you will read it carefully. The number N of photons present, either known or indeterminate or a Poisson distribution, makes a substantial difference in expected behavior. This is why answering your original question accurately is difficult, because it is not clear which direction you are going.

2. Surprisingly, rigorous experiments demonstrating the existence of photons and ruling out semi-classical explanations were not performed until relatively recently (circa 1974). Here is one such using, as vanhees71 suggested, entangled photons:

http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf

11. Sep 28, 2014

### mrspeedybob

Let me run with this idea for a minute and see if I get any closer to the truth...

Suppose I have transmitter at very low intensity (or great distance). In order to detect the transmission I have a second antenna connected to a receiver. In order for the receiver to detect anything at least one electron must move in the antenna. The electrons are bound to their atoms by a certain force. The electrons already have an indeterminate amount of energy related to the temperature of the antenna/receiver. No detection is possible until an electron has enough energy to break free and move. Energy received electromagnetically from the transmitter may occasionally bump an electron over that threshold resulting in a detection event and the registering of a "photon".

In this experiment the receiver will appear to register discrete individual photons, but the number of detection events per unit time is determined by the intensity of radiation incident on the antenna which would be a continuous and non-discrete function of the amplitude of the transmission and distance between transmitter and receiver.

Am I getting any closer?

Last edited: Sep 28, 2014
12. Sep 28, 2014

### KL7AJ

I wrote a tongue-in-cheek essay a while back, "Walking the Planck" which demonstrated the futility of such an exercise. Being essentially a low frequency "R.F. Guy" Planck's Constant all but guarantees that photons are irrelevant in our particular career. :)

13. Sep 28, 2014

### DrChinese

Now you are talking about detecting a single photon. You could do that with a suitable photomultiplier unit and filters.

So that is the deal with antennae? It might help if you explained more about the source of your question.

14. Sep 28, 2014

### mrspeedybob

I can't think off the top of my head about any better way to describe the source of my question then what I already have. Quantum mechanics treats EM radiation as a barrage of quantum objects, Percells explanation of electromagnetism treats it as variations in the electric field, and it seriously bothers me that I do not understand the phenomena well enough to see how those 2 descriptions describe the same thing.

As far as shifting focus to detecting single photons...
Transmission, propagation, and detection are all different parts of any actual experiment that could be performed. If understanding the whole process requires refocusing my attention to a different part then I'll try it.