Can A White Photon Exist?not so easy to Answer

[Cthugha]

It is not a popular misconception, it is a fact. The Poisson distribution simply means that photons arrive at purely random times. They are detected singly because they are just that, single photons.

This is pure nonsense. If you claim to have single photons you need to demonstrate antibunching. The Poisson distribution means that detection events are distributed statistically independent of each other. However, whether these belong to just a single field originating from a single emitter (single photon) or from many fields originating from different emitters possibly including contributions from more than one field (coherent or thermal light for example) cannot be distinguished just by knowing that "single clicks" were the origin of the detection events. Do you have any peer-reviewed publication that shares your opinion that even in Poisson distributed light there are always single photons? Kimble et al. say otherwise (Phys. Rev. Lett. 39, 691–695 (1977)). Also, showing antibunching is THE tool to identify single photon sources today, see e.g. Science 290, 2282-2285 (2000) by Peter Michler et. al.

The randomness is in the arrival times between successive photons. The physical meaning of this randomness is that the electric field always contains some uncertainty in its value. You can modify this distribution of arrival times by quantum mechanical technology, such as non-linear optical systems that produce phase effects such as quadrature squeezing. What that achieves is that either the times between photon arrivals are a bit closer together than you expect classically, or conversely they can be a bit less closer together - commonly known as bunching or anti-bunching and is quantum mechanical, not classical.

Sure, but you can have each of these for any amount of intensity. Only antibunching corresponds to single photons.

Photons tend to bunch slightly anyway

Thermal light tends to bunch, coherent light does not. The emission from single photon sources of course also does not bunch.

Photon number is simply a conjugate property of the phase, these things are how we describe the wave as a quantum mechanical wave function, so none of this changes the fact that these are photons, pure and simple, quanta of energy with a characteristic frequency, or if you prefer - colour.

That basically means that you have the opinion that Glauber's theory of coherence is not necessary and nonsense.

So yes you can reduce the intensity down to a single photon (a gedankenexperiment) and you will detect a red photon and then a blue photon etc coming out of your prism with plenty of random time lag between them to convince yourself that there are no white photons. Case closed.

You can reduce it to a single photon detection per time unit ON AVERAGE. Still, most of the work of Mandel and part of the Nobel prize winning work of Glauber was devoted to showing that you need a hierarchy of correlation functions to describe a light field most precisely and that you need at least second order correlations to identify single photons.

 

[kaonyx]

In between bunching and antibunching is neither. So if we start with bunched statistics, or neither, you are suggesting that reducing the intensity must alter the shape of the distribution?

 

[Antiphon]

It's a basic fact of Fourier decomposition that a finite (in time) entity does not have a single frequency, it has a spectrum.

If the line width of a single quantum is sharp, it has a definite energy. And it must therefore persist for an indefinite time.

The math is not forgiving on this topic. A photon that has N cycles in it's wavetrain can only have a definite energy (zero linewidth) as N approaches infinity.

 

[bcrowell]

It was amusing to me to see this pop up as a necro-thread, and also to see how many posts and how much sophisticated argumentation had gone into it. I'm the person who wrote the discussion question: http://www.lightandmatter.com/html_books/lm/ch34/ch34.html The book is targeted at biology majors who haven't had calculus. Although I included the discussion question in my book, I think I have never actually used it with any of my classes over the years. My intention was simply that the answer would be "yes, of course, because photons are waves, and waves can superpose, so you can superpose a bunch of different wavelengths."

 

[kaonyx]

But surely photons are not waves, they are photons., particles, they can collide with other particles e.g. xrays with electrons and impart momentum to the electron. The properties of the photons themselves are subject to the uncertainty principle so you have to be a bit guarded when imagining you can have two of then localised in a radiation field, so that you can create a superposition in the way that you might be able to do by bringing two relatively massive bodies like electrons together into a chemical bond. Photons can all share the same state anyway so is that really a valid way to create a new superposition state?

As far as the Fourier analysis of the wave goes, are we not talking about two different kinds of wave here? The electromagnetic wave (Maxwell) is not exactly the same thing as the quantum wave (Schrödinger) is it? I mean the electric field can be uncertain but these quantum waves have a kind of platonic form? I think you can use the maxwell wave to compute the quantum wave, (that's handy!) but one is a field equation and the other is a probability wave. The Fourier breakdown of quantum wave packet gives probability amplitudes, not energies?

 

[Cthugha]

In between bunching and antibunching is neither. So if we start with bunched statistics, or neither, you are suggesting that reducing the intensity must alter the shape of the distribution?

No, of course not. It is exactly my argument that you do not get single photons by reducing the intensity of a coherent/thermal beam because you do not change the statistics, only the mean photon number.

But surely photons are not waves, they are photons., particles, they can collide with other particles e.g. xrays with electrons and impart momentum to the electron. The properties of the photons themselves are subject to the uncertainty principle so you have to be a bit guarded when imagining you can have two of then localised in a radiation field, so that you can create a superposition in the way that you might be able to do by bringing two relatively massive bodies like electrons together into a chemical bond. Photons can all share the same state anyway so is that really a valid way to create a new superposition state?

Well, at least all photons inside a coherence volume are indistinguishable and you have to treat them that way which means that they behave very differently from independent single photons in that case. You will also only see a thermal photon number distribution if you consider indistinguishable photons in a coherence volume. Outside of it, they are usually never distributed thermally. QED and quantum optics are still field theories after all.