Coherent state of photons in a laser

[zincshow]

Do photons used to produce the Sagnac effect (interference) have to have their phase in a coherent state or will a collection of random photons have the same property.

Along the same lines, if you purchase a simple laser pointer are the photon produced here in a coherent state?

Finally, is there an easy way to check if photons coming out of a laser are in a coherent state?

 

[Cthugha]

Do photons used to produce the Sagnac effect (interference) have to have their phase in a coherent state or will a collection of random photons have the same property.

The two beams used in a Sagnac interferometer will travel slightly different lengths. The coherence length of the light used should be longer than this distance in order for interference to occur. Therefore, random photons will not do the trick.

Along the same lines, if you purchase a simple laser pointer are the photon produced here in a coherent state?

For most laser pointers: yes, but the coherence time may be rather short. Some cheap laser pointers may suffer from mode competition and youo may get a rather unstable emission consisting of several modes which is not really coherent.

Finally, is there an easy way to check if photons coming out of a laser are in a coherent state?

First, get to know the coherence time of your light field. As soon as you know that, place the laser emission on a beam splitter and place one photo diode at each exit port. Attach these diodes to a TAC (time to amplitude converter) and use one diode for the start and the other for the stop signal. Perform a histogram of the distribution of the time delay between two consecutive photon detections and plot it. If the distribution is more or less constant, you have coherent light (in the sense of second-order coherence). If time delays shorter than the coherence time occur more or less often than longer delays, you do not have coherent light. If they occur more often, the light is typically thermal. If they appear less often, you have non-classical light, maybe a Fock state or amplitude-squeezed light.

However, I am not sure, whether you consider this an easy way. All I can tell you is that there are ways that are way more complicated.

 

[zincshow]

Very clear and concise, thanks a bunch. I am doing an experiment with a laser pointer and a pin where diffraction around the pin causes interference and you play with polarizers on each side of the pin. Did not think this kind of stuff could be done at home with simple equipment, but it really can. Raises lots of questions, but fun stuff for sure.

 

[DrDu]

Do photons used to produce the Sagnac effect (interference) have to have their phase in a coherent state or will a collection of random photons have the same property.

I think that any sufficiently monochromatic light source will do as only first order coherence is required. Coherent states differ from random light sources only in terms of higher order coherence.

 

[zincshow]

Ug, one yes one no...

The assumption is a monochromatic light source (532 nm green laser pointer).

Regarding the coherence of the phase, how would you get interference unless one set of photons is different from the other set of photons by a multiple of 266nm (ie. travels a path 266nm longer then the other set of photons)? If the phase of the photons is essentially random, how can they interfere with each other in an organized fashion to either produce a peak or a valley that persists at a particular point over a long period?

 

[DrDu]

Each photon interferes with itself after passing through a beam splitter, taking different paths and recombining in a second splitter. No need for a phase relation between different photons.

 

[Cthugha]

If the phase of the photons is essentially random, how can they interfere with each other in an organized fashion to either produce a peak or a valley that persists at a particular point over a long period?

Two points:
1) All photons inside one coherence volume are indistinguishable anyway. So if you can tell different photons apart, you are talking about some incoherent situation. As has already been stated by DrDu, standard first-order interference phenomena rely on single-photon interference and no fixed phase relationship between distinguishable photons is necessary.

2) If you have a state where the phase is essentially random at each instant, you have very incoherent light, but you will certainly not have monochromatic light. Rapid phase fluctuations cause a broadened spectrum.

If all you really care about is simple interference, you do not need a coherent state, just a reasonable coherence length/time (these are also possible without having a coherent state, in case that was unclear before). Take any light source you want and shine the light through a narrow spectral filter. The light that passes the filter will have a reasonably long coherence time, no matter what light you started with. You will of course also lose a lot of intensity that way.