# Photon Pairs - Can photons travel in pairs?

Buckeye
Light can be left or right polarized (circularly or elliptically). This is achieved by passing unpolarized light through various polarizing crystals which are optically active (ie chiral).

My paired questions are:
1. When we consider the photons before they strike the polarizers, can we think of those unpolarized photons as traveling in pairs or a pair-like fashion?
2. If they can not travel as pairs, then what evidence contradicts this possibility?

Staff Emeritus
Gold Member
Light can be left or right polarized (circularly or elliptically). This is achieved by passing unpolarized light through various polarizing crystals which are optically active (ie chiral).

My paired questions are:
1. When we consider the photons before they strike the polarizers, can we think of those unpolarized photons as traveling in pairs or a pair-like fashion?

Why would you consider that ? Imagine that I have a bag with red balls and green balls, and then I pass them through a machine that let's the red balls pass, and takes away the green balls. Do we consider that balls come in "red-green" pairs ?

At first sight, quantum systems are different, but because you talk about *unpolarized* photons, we have to assume that they appear in a 50-50 statistical mixture, in which case the red-green ball analogy is applicable.

That said, they CAN travel in pairs: in 2-photon states. But usual light has only a very small amount of those.

2. If they can not travel as pairs, then what evidence contradicts this possibility?

If you would use a polarizing beam splitter, then you should find high coincidence rates if they came in pairs, which is not observed with usual unpolarized light (but IS observed in special situations when 2-photon states are produced).

Buckeye
Why would you consider that ? Imagine that I have a bag with red balls and green balls, and then I pass them through a machine that let's the red balls pass, and takes away the green balls. Do we consider that balls come in "red-green" pairs ?

At first sight, quantum systems are different, but because you talk about *unpolarized* photons, we have to assume that they appear in a 50-50 statistical mixture, in which case the red-green ball analogy is applicable.

That said, they CAN travel in pairs: in 2-photon states. But usual light has only a very small amount of those.

If you would use a polarizing beam splitter, then you should find high coincidence rates if they came in pairs, which is not observed with usual unpolarized light (but IS observed in special situations when 2-photon states are produced).

I'm not sure the red-green filter system applies when we deal with symmetry based on chirality, which is, if memory serves me right, identical with parity and helicity. Am I thinking wrong?

Am fussy on 2-photo states. Is that entanglement?

Please point me toward a book or paper on the results of polarizing beam splitter results. Thanks!

Staff Emeritus
Gold Member
I'm not sure the red-green filter system applies when we deal with symmetry based on chirality, which is, if memory serves me right, identical with parity and helicity. Am I thinking wrong?

Am fussy on 2-photo states. Is that entanglement?

Please point me toward a book or paper on the results of polarizing beam splitter results. Thanks!

Concerning polarizing beam splitters:
http://en.wikipedia.org/wiki/Polarizer

Just a random article concerning the observation of 2-photon states and the use of beam splitters (I just did a search and came up with this one, there are many):

http://prola.aps.org/abstract/PRA/v64/i4/e041803
or
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000070000003000260000001&idtype=cvips&gifs=yes [Broken]

A 2-photon state is something else than two entangled photons. In fact, two entangled photons is rather the superposition of at least 2 different 2-photon states.

You should see a 2-photon state rather as similar to a 2-particle state: there are two particles present. In most classical optics, things happen "one photon at a time". That's why one can consider the "quantum wave function" of a single photon to be equivalent to the classical electromagnetic field (it's not the *same* though).
That's why, if you analyse classical light, you will get few coincidences: you will normally detect "one photon at a time", and the only reason why you sometimes get two of them is due to the dead-time of your detectors and the Poissonian distribution of the "single photons". In fact, this is not entirely correct: the full quantum-mechanical description of an intense classical beam is best described not by single-photon states, but by coherent states, which are superpositions of 1-photon, 2-photon, 3-photon ... states. But for not-too-intense beams, the 1-photon state is dominant.

However, by some interactions, like parametric down conversion, it is possible to turn 1-photon states into 2-photon states, and this light doesn't behave classically at all - or at least, has the potential of showing non-classical correlations and effects. They are at the core of the entire business of quantum optics.

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That's why, if you analyse classical light, you will get few coincidences: you will normally detect "one photon at a time", and the only reason why you sometimes get two of them is due to the dead-time of your detectors and the Poissonian distribution of the "single photons". In fact, this is not entirely correct: the full quantum-mechanical description of an intense classical beam is best described not by single-photon states, but by coherent states, which are superpositions of 1-photon, 2-photon, 3-photon ... states. But for not-too-intense beams, the 1-photon state is dominant.

You have to be very careful here. These statements are wrong for most cases. The photon number distribution is only Poissonian for laser light. Usual light from a bulb or from the sun is thermal light and the photon number distribution follows Bose-Einstein statistics. The distribution only gets Poissonian again if you sample time intervals, which are large compared to the coherence time of the light source. From a QM point of view, the 0-photon state is dominant for thermal light.

If you do coincidence counting with thermal light, you will also notice, that there are more coincidences than expected. Thermal light has a certain tendency for photons to arrive in pairs, called photon bunching, which was first demonstrated in the famous papers of Hanbury Brown and Twiss (R. Hanbury Brown and R. Q. Twiss (1956). "A Test of a New Type of Stellar Interferometer on Sirius". Nature 178: 1046-1048 or R. Hanbury Brown and R. Q. Twiss (1957). "Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation". Proc of the Royal Society of London A 242: 300-324).

However, it should be emphasized, that there is no connection between photon bunching and linearly or unpolarized light. Unpolarized light does not require photons to travel in pairs.

Staff Emeritus
Gold Member
You have to be very careful here. These statements are wrong for most cases. The photon number distribution is only Poissonian for laser light. Usual light from a bulb or from the sun is thermal light and the photon number distribution follows Bose-Einstein statistics. The distribution only gets Poissonian again if you sample time intervals, which are large compared to the coherence time of the light source. From a QM point of view, the 0-photon state is dominant for thermal light.

If you do coincidence counting with thermal light, you will also notice, that there are more coincidences than expected. Thermal light has a certain tendency for photons to arrive in pairs, called photon bunching, which was first demonstrated in the famous papers of Hanbury Brown and Twiss (R. Hanbury Brown and R. Q. Twiss (1956). "A Test of a New Type of Stellar Interferometer on Sirius". Nature 178: 1046-1048 or R. Hanbury Brown and R. Q. Twiss (1957). "Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation". Proc of the Royal Society of London A 242: 300-324).

Correct. I over-simplified too much.

Buckeye
You have to be very careful here. These statements are wrong for most cases. The photon number distribution is only Poissonian for laser light. Usual light from a bulb or from the sun is thermal light and the photon number distribution follows Bose-Einstein statistics. The distribution only gets Poissonian again if you sample time intervals, which are large compared to the coherence time of the light source. From a QM point of view, the 0-photon state is dominant for thermal light.

If you do coincidence counting with thermal light, you will also notice, that there are more coincidences than expected. Thermal light has a certain tendency for photons to arrive in pairs, called photon bunching, which was first demonstrated in the famous papers of Hanbury Brown and Twiss (R. Hanbury Brown and R. Q. Twiss (1956). "A Test of a New Type of Stellar Interferometer on Sirius". Nature 178: 1046-1048 or R. Hanbury Brown and R. Q. Twiss (1957). "Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation". Proc of the Royal Society of London A 242: 300-324).

However, it should be emphasized, that there is no connection between photon bunching and linearly or unpolarized light. Unpolarized light does not require photons to travel in pairs.

Thanks!
How can we be sure that our detectors have truly detected individual photons if the photons used to calibrate the detectors have actually measured bunched pairs?