What Does a Photon Waveform Look Like?

[mermeladeK]

Firstly let me say that I am a telecommunications engineer so I am not an expert in physics and I hope this question doesn't bother you.

In radiofrequency or microwaves metallic antennas are used for receiving a signal or waveform. The field induces a current on the metal and the wave signal becomes an electrical signal. There's no reason why you cannot in principle apply this for example to optic signals. However, the signal would be so low that other methods are use.

But imagine we could sense an optic or even a x-ray signal with a regular antenna. You could then measure the electronic signal which would be a replica of the waveform. Now imagine a source which emits single photons very slowly. In the antenna you would measure the waveform... of a single photon every time one is sent. Am I wrong?

My question is, what would this waveform look like?

In theory a photon has a discrete frequency associated, but this is just impossible, because in Fourier theory a single frequency is a pure sinusoidal signal that last infinitely (I guess this is not the photon case because it would also imply it has infinite energy). So here is were I guess it is the central frequency what is called the frequency of the photon.

Then the bandwidth of a single photon has a translation as a waveform in the time domain. I heard some people say a photon has an inherent noise. Does this noise have a relation with this bandwidth?

Is a photon waveform like an AM signal were the modulating signal is like a Gaussian pulse and the carrier has the so called frequency of the photon?

Is this waveform always the same?

Is a waveform in low frequencies the sum of all the waveforms of the single photons?

Well, I think you have enough of my questions. :)

 

[f95toli]

First of all, you CAN use antennas to detect single photons. There are single photon detectors that work down to a few hundred GHz. They generally use planar on-chip antennas to couple the radiation (which is often coming from a larger antenna) to the detector. Hence, this is not just a theoretical question.

However, photons do NOT have a waveform as such; photons have a discrete frequency which as you points out, in classical physics would imply that they are "infinitly long". However, this problem tend to "disappear" when you do the actual calculations in QM. Remember that we have given the name "photon" to a mathematical construct which can't be interpreted using a classical picture; most of the conceptual problems with photons come from trying to understand them using ideas such as waves, particles etc which have very limited applicability in QM. Hence, the idea of a photon as a spatially distributed "classical wave" (or a classical particle) is not correct.

That said, I think you are missing an imporant point. A destructive detector will at a given time either detect a photon or it will not. You can't detect a photon "slowly"; it is a discrete process. Single photon detection actually follows a poisson distribution (which is discrete).

 

[Cthugha]

However, photons do NOT have a waveform as such;

One could argue about that. Walther gave an example of what could be interpreted as a single photon waveform in one of his last papers (http://www.nature.com/nature/journal/v431/n7012/abs/nature02961.html, Nature 431, 1075 - 1078 (28 Oct 2004)).

However this definition is of course pretty meaningless, if you just have a look at a single photon. It does just make sense, if you talk about an ensemble of single photons generated by several pump pulses.

 

[pervect]

First of all, you CAN use antennas to detect single photons. There are single photon detectors that work down to a few hundred GHz.

Can you give us a reference for this?

 

[f95toli]

For single photon detection in general or just THz photons?
For the THz regime (a few hundred GHz up to far-infrared)

See e.g. Komiyama et al Nature 403, 405-407

For 1.3 um range and upwards you can find lots of information just using google (but they are not using antennas since this is in the optical regime). I might be wrong, but I think superconducting nanowire NbN single-photon counters are the best detectors available in the IR range

see e.g the work done at MIT

http://www.rle.mit.edu/qnn/

Berggren gave a nice talk at a conference I attended a couple of week ago.

 

[Claude Bile]

But imagine we could sense an optic or even a x-ray signal with a regular antenna. You could then measure the electronic signal which would be a replica of the waveform. Now imagine a source which emits single photons very slowly. In the antenna you would measure the waveform... of a single photon every time one is sent. Am I wrong?

What you would see is the classical signal, plus shot noise which is due to the discrete nature of the photons. At low light levels, shot noise has the potential to overwhelm analog signals to the point of forcing one to switch to a digital, photon-counting regime.

In theory a photon has a discrete frequency associated, but this is just impossible, because in Fourier theory a single frequency is a pure sinusoidal signal that last infinitely (I guess this is not the photon case because it would also imply it has infinite energy). So here is were I guess it is the central frequency what is called the frequency of the photon.

The Fourier relationship between frequency and time for a photon is embodied in the Heisenberg Uncertainty principle - the product of the uncertainties in frequency and time (time being the "time of arrival" so to speak at some observation point). As we become more certain of the frequency of the photon, we become less certain about when it will actually arrive at our detector. For a photon with a precisely known frequency, the time of arrival will be completely unknown.

Essentially Fourier theory tells us about the photon's wavefunction, but reveals precious little detail about the photon itself.

Claude.

 

[mermeladeK]

Hi all,

Hehehe. Your answers were... uncertain. Some of you helped a little more thought.

My question doesn't require a complex answer: What would be the waveform observed in an antenna when a single photon is sent?

It is a must that you observe something there. My question only asks for the result as it must be a result. As you say you can tell all you know about the theory but if you really know the theory you'll be able to tell what is observed in the antenna.
:)

Possible answers: we don't know, it is a random waveform, it is a pulse, nothing appears and so on. But something WILL happen as an electrical signal from the reception of this photon. I look forward to receiveing an answer. ;)

F95toli: What you say about discrete photons is not exactly true. The reason a "photon detector" detects discrete photons is because it is designed to do so. But a photon is not totally discrete from a wavepoint of view, otherwise there would no waveform for a radiofrequency signal since EVERY electromagnetic wave is composed of photons.
If you want I can expand this. In a photon detector the physical principle is not the same than in an antenna. What they do is that they detect the electrical charge excited by the interaction of the photon with the semiconductor material. For instance if are doing spectroscopy the signal processing chain is designed to just tell you about the photon energy and nothing else. But this DOESN'T mean a photon doesn't produce any waveform in an antenna.

My question is not a practical/engineering issue, the antenna example is just to make easier to understand my theoretical question.

Cthugha: thanks, I'll check the paper.

Claudie Bile: What do you mean by the classical signal? As far as I know shot noise is theoretically defined to last infinitely. I don't think a single photon produces and infinite electrical shot noise. My question is not about the uncertainty of the photon frequency either. It can be uncertain but this doesn't mean it hasn't a specific frequency. When you it is spoken about the frequency of a photon, frequency is referring to a waveform property. If there was no relation with a waveform it wouldn't make sense to speak about frequency. Or maybe frequency means something else here but I don't think it is the case.

Nil

 

[f95toli]

Hi all,
F95toli: What you say about discrete photons is not exactly true. The reason a "photon detector" detects discrete photons is because it is designed to do so. But a photon is not totally discrete from a wavepoint of view, otherwise there would no waveform for a radiofrequency signal since EVERY electromagnetic wave is composed of photons.
If you want I can expand this. In a photon detector the physical principle is not the same than in an antenna. What they do is that they detect the electrical charge excited by the interaction of the photon with the semiconductor material. For instance if are doing spectroscopy the signal processing chain is designed to just tell you about the photon energy and nothing else. But this DOESN'T mean a photon doesn't produce any waveform in an antenna.

You are still thinking in terms of classical physics. I should perhaps point out that I am quite familiar with how single photons behave in terms of "ordinary" EM transmission theory since I work in the field of circuit-QED. (in my case a system comprising an on-chip superconducting coplanar waveguide resonator strongly coupled to a flux-qubit, it is the basically the circuit analogue to cavity-QED fn quantum optics, but I use microwave electronics instead of mirrors etc).
I am also somewhat involved (some antenna design) in a project on single-photon detection in the THz regime.

Anyway, the main problem here is that we obviously have to use QM to answer your question; there is no such thing as a photon in classical EM theory.
BUT, if you try to use QM on a "few" photons you run into the next problem: There is no exact analogue to a classical E-field (or B-field); a coherent field is actually as close as we can come (which is what we usually mean when we talk about "classical" fields in QM).

Now, most fields we come across in the classical world can be described as an large ensemble of independent harmonic oscillators (i.e. modes of the field) which toghether form the kinds of fields (and waveforms) we come across in classical EM theory (this is why the unquantized Maxwell's equations work in the limit of many photons)

But this will obviously not work for a single photon which can ONLY be described in terms (sums) of creation $$a$$ and annhilation $$a^\dag$$ operators; these operators create of destroy a single photon of the field. Hence, there is no such thing as a "waveform" for a single photon; we can only add or subtract discrete quanta to a given field. Thus, any form of detection is a discrete (but probabilistic) process which is why single photon detection follows a Poisson distribution regardless of how it is implemented. Furthermore, a single photon (or any number state with zero variance) does not have a defined phase (or, to be more specic, the uncertainty in phase is infinite) which again is a very "non-classical" property.


Now, when we model a real system this is handled "automatically" by the formalism since we are always writing the Hamiltonian of the light-part in terms of the abovementioned annilation and creation operators.
Fortunately we can (usually) get away with using classical EM theory to design our systems (I am mainly using ordinary transmission line theory to design circuits); i.e. if the "classical" field has an anti-node at a certain point this also means that this is where a photon is also most likely to couple to the environment (which can also be shown by a more rigorous theory where the transmission line equations are quantized).
However, we can NOT use classical theory to predict the response of the system in the limit of a few photons since their "discrete" nature then becomes important (this is the regime I am interested in).

I should perhaps also point out that the fact that photons are discrete does NOT imply that you will see zero linewidth in an experiment; due to the fact that they are interacting with the environment the linewidth is non-zero. In the case of a simple LC-oscillator it can actually be shown that the linewidth is just given by the classical Q-value even when the mean photon number $$<n>=<a^\dag a>$$ in the resonator is much smaller than one.

 

[fleem]

My question doesn't require a complex answer: What would be the waveform observed in an antenna when a single photon is sent?

When a device is designed to "detect single photons", it must amplify a single instance of shot noise so that we can hear it in a speaker or see it on a scope. The amplifier causes decoherence, wavefunction collapse, multiverse merging--whatever you like to call it--making the pulse we hear classical so that our classical brain can know there was a single photon. Before this shot noise is amplified, however, we cannot think of that shot noise as a pulse, unit function, monocycle, wavelet, differentiated monocycle, or anything like that. We know it is none of these, but frankly we don't really know what it is. Oh, we can describe how to predict the classical result (unfortunately, we can only observe the classical result because we are classical beings), but we don't yet know what really happened, or what physics more fundamental (than QM) is at play. QM predicts the classical observation, but it does not explain why. Its like how QM explains classical mechanics, and is a more fundamental theory. We don't have anything more fundamental than QM to explain QM yet.

The classical result, after amplification, would be a unit function, I suppose. But understand that that is NOT what the photon was.

 

[Claude Bile]

What do you mean by the classical signal?

The shape of the output waveform one would get if there where many photons (i.e. when the discrete nature of the photons can be neglected).

As far as I know shot noise is theoretically defined to last infinitely. I don't think a single photon produces and infinite electrical shot noise.

Sorry about the misconception here, I should have specified that I was referring to optical shot noise, not electronic shot noise.

My question is not about the uncertainty of the photon frequency either. It can be uncertain but this doesn't mean it hasn't a specific frequency. When you it is spoken about the frequency of a photon, frequency is referring to a waveform property. If there was no relation with a waveform it wouldn't make sense to speak about frequency. Or maybe frequency means something else here but I don't think it is the case.

Okay, it sounds like the concern here is my previous use of the term "frequency". The frequency I referred to is the frequency (or frequency uncertainty) of the photon's wavefunction. We can measure the frequency of a photon, and it doing so, the photon will take on a frequency - the probability of the photon taking on a specific frequency is governed by the wavefunction of the photon - this is the probabilistic nature of Quantum Mechanics.

Photons are packets of energy, they don't have (insofar as we know) an internal waveform, the only waveform one could consider applying to a photon is the photons wavefunction.

Back to the single-photon detection - you would get a current spike. The duration of the spike will depend on the characteristics of the detector. In practice, these spikes are converted to TTL pulses that can then be counted with the proper electronics. This is what I alluded to in my previous post, at very low light levels, you need to count photons, analog detection simply doesn't cut the mustard.

Claude.

 

[mermeladeK]

Hi f95toli, fleem and Claude Bile,

Let me apologize if I sounded a little pedantic when I posted my second post.
You guys definitely know what you're talking about.

It's hard for me, just an engineer to deal with your explanations even though they were probably very good. Perhaps I should study physics.

Right now the idea I have in my mind is that whatever happens there after the antenna it cannot be explained in regular language. It is not a continuous pulse as I understood from fleem's explanation. It is something we don't know and that we wouldn't know how to define with regular words. I am just trying to write this in a way I can understand.

Thanks.

 

[fleem]

Keep asking questions like that. Those that answer such questions often learn more in getting their thoughts straight than do those that ask the question.

 

[Claude Bile]

I agree with fleem, there's no need to apologise, ask whatever questions it takes to clarify things in your own mind.

Claude.

 

[mermeladeK]

The funny thing is that if you google photon waveform this is the first result. :D

 

[yoron]

Very interesting f95toli. Thanks for your descriptions. Photons never stop to confuse me :) And if you have something more to add about how to describe them, do not hesitate to add it. I'll keep this thread under observation.
==

Ouch, an old one is it? But qualitatively as good as new to me :)
Got referred to it by Google.

And yep, everything that makes me see a photon will be of interest.