# What is coherent light?

what is "coherent" light?

In high school, I learned that coherent light is light which has same frequency,phase and so on. In college , I learn that there is temporal coherent and spatial coherent. why we say laser is coherent source? I am confused. what is coherent? Now the new light source like free electron laser ,we all say it is coherent x ray,what does the mean coherent? what the difference between x ray which generated in x ray tube and free electron laser? Thank you all!

Simon Bridge
Homework Helper

http://www.merriam-webster.com/dictionary/coherent
http://en.wikipedia.org/wiki/Coherence_(physics [Broken])

... as you work your way through school, the concepts are taught first at their most basic and then to deeper and deeper levels as you gain understanding and skills. Many of the definitions you learned early will turn out to be incomplete.

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http://www.merriam-webster.com/dictionary/coherent
http://en.wikipedia.org/wiki/Coherence_(physics [Broken])

... as you work your way through school, the concepts are taught first at their most basic and then to deeper and deeper levels as you gain understanding and skills. Many of the definitions you learned early will turn out to be incomplete.

thank you for your answer! another question. does femtosecond laser pulses have coherence?I know monochromatic laser has coherence,but I don't think pulses does.
However, I read some books which say they have coherence. Could you please explain that?
thank you!

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Simon Bridge
Homework Helper

Think: in what sense does the author mean "coherence"?

In stimulated emmission you are going to get at least two photons - can just two photons be said to be coherent?

Cthugha

You need to distinguish several connected topics here. First, there is coherence on the field level or first-order coherence. This is what is meant by temporal or spatial coherence. This is indeed a measure of the time scale/length scale over which light fields have a predictable phase relationship. You can measure these in a Michelson interferometer or using a double slit. It is not really sensible to talk about coherent or incoherent light based on these quantities because first-order coherence is not an on-off property. You get a certain coherence time or length which may be long or short, but there is no fixed boundary where one could distinguish between coherent or incoherent.

On the other hand, there is also second-and higher order coherence, which takes place on the intensity or photon number level. This is what got Glauber his Nobel prize. Basically, this is based on joint photon number detection rates. If the average joint detection rate factorizes into the averages of the single detection rates, you have coherent light. That sounds cryptic, but only means that all photon detection events are statistically independent of each other. That sounds like the standard case, but in fact it is not. Light from the sun or from light bulbs does not have this property as these tend to emit photons in bunches of many like any thermal light source does. Single photons also do not have this property as every detection of a photon destroys it and therefore reduces the probability to detect another one.

This kind of coherence is an on-off property and allows to distinguish coherent and incoherent light. The femtosecond laser pulses are coherent in this sense. This simple factorization condition has interesting consequences. For example, the independence of detection events directly determines that the photon number distribution of a coherent light source must also be a distribution of independent events which gives you a Poisson distribution. The independence of the joint count rates also implies that the light field does not change when a photon is detected, from which you can show that coherent states are eigenstates of the photon annihilation operator.

Concerning your other question: monochromatic light implies long temporal coherence. In fact the first order temporal correlation function (its decay gives you the coherence time) is the Fourier transform of the power spectral density. In other words, the more monochromatic your light is, the longe its coherence time will be. The same applies for the angular width of your light source and spatial coherence: the more point-like your source is, the larger the spatial coherence will be. Note that this implies, that these properties are not strictly properties of your light source as you can simply increase the coherence time of some given light field just by spectrally filtering it. Femtosecond laser pulses typically have reasonable spatial coherence and are second-order coherent as discussed above.

You need to distinguish several connected topics here. First, there is coherence on the field level or first-order coherence. This is what is meant by temporal or spatial coherence. This is indeed a measure of the time scale/length scale over which light fields have a predictable phase relationship. You can measure these in a Michelson interferometer or using a double slit. It is not really sensible to talk about coherent or incoherent light based on these quantities because first-order coherence is not an on-off property. You get a certain coherence time or length which may be long or short, but there is no fixed boundary where one could distinguish between coherent or incoherent.

On the other hand, there is also second-and higher order coherence, which takes place on the intensity or photon number level. This is what got Glauber his Nobel prize. Basically, this is based on joint photon number detection rates. If the average joint detection rate factorizes into the averages of the single detection rates, you have coherent light. That sounds cryptic, but only means that all photon detection events are statistically independent of each other. That sounds like the standard case, but in fact it is not. Light from the sun or from light bulbs does not have this property as these tend to emit photons in bunches of many like any thermal light source does. Single photons also do not have this property as every detection of a photon destroys it and therefore reduces the probability to detect another one.

This kind of coherence is an on-off property and allows to distinguish coherent and incoherent light. The femtosecond laser pulses are coherent in this sense. This simple factorization condition has interesting consequences. For example, the independence of detection events directly determines that the photon number distribution of a coherent light source must also be a distribution of independent events which gives you a Poisson distribution. The independence of the joint count rates also implies that the light field does not change when a photon is detected, from which you can show that coherent states are eigenstates of the photon annihilation operator.

Concerning your other question: monochromatic light implies long temporal coherence. In fact the first order temporal correlation function (its decay gives you the coherence time) is the Fourier transform of the power spectral density. In other words, the more monochromatic your light is, the longe its coherence time will be. The same applies for the angular width of your light source and spatial coherence: the more point-like your source is, the larger the spatial coherence will be. Note that this implies, that these properties are not strictly properties of your light source as you can simply increase the coherence time of some given light field just by spectrally filtering it. Femtosecond laser pulses typically have reasonable spatial coherence and are second-order coherent as discussed above.

thank you for your informative and instructive answer! I have two questions.1.why sun tends to emit photons in bunches of many like any thermal light source does.but laser emit single independent photon.2.Single photons also do not have this property as every detection of a photon destroys it and therefore reduces the probability to detect another one.
the nobel prize in physics in 2012 seems can detection of a photon without destroys it. so single photon can have this property.am I right? Thank you!!

Cthugha

1.why sun tends to emit photons in bunches of many like any thermal light source does.but laser emit single independent photon.

These two processes tend to create very different photon number distributions. Sunlight is pretty much blackbody radiation from a system in thermal equilibrium. If one does all the math and includes that photons are bosons, one will find that the photon number distribution for any single mode will be a Bose-Einstein distribution. This distribution has the property that it is rather smooth, the most probable photon number is always zero and the distribution is very broad, still having significant probabilities far away from the mean photon number. That gives you a very noisy light field. If you have at least a photon in some mode, the probability, that there will be more photons is very high. Therefore, you get a tendency of photons to bunch. Lasers on the other hand, emit independent (but not single!) photons. You need inversion and stimulated emission and the system is therefore far from thermal equilibrium. This process gives you a much narrower photon number distribution around the mean. It turns out, that the small amount of photon number noise present cancels exactly the effect of changing the light field by destroying a photon when you detect one, so that the light field stays unaltered.

In a nutshell, the most important difference between these two emission processes is spontaneous versus stimulated emission.

the nobel prize in physics in 2012 seems can detection of a photon without destroys it. so single photon can have this property.am I right? Thank you!!

You mean the cavity QED experiments by Serge Haroche? No, he could not detect a photon without destroying it. Nobody can. He could get some information about an ensemble of identically prepared photons without destroying them by means of weak measurements. Basically, he can measure the photon number in a cavity by having atoms (far detuned from the photons - they do not absorb them) travel through that cavity. The presence of the photons introduces some phase shift in the atoms, which can be measured. However, such measurements only give you statistical information. After doing that experiment a lot of times, you can say something about the mean photon number in the cavity. However, you cannot do it just once and get a sensible result for the photon number inside the cavity during that single run.

These two processes tend to create very different photon number distributions. Sunlight is pretty much blackbody radiation from a system in thermal equilibrium. If one does all the math and includes that photons are bosons, one will find that the photon number distribution for any single mode will be a Bose-Einstein distribution. This distribution has the property that it is rather smooth, the most probable photon number is always zero and the distribution is very broad, still having significant probabilities far away from the mean photon number. That gives you a very noisy light field. If you have at least a photon in some mode, the probability, that there will be more photons is very high. Therefore, you get a tendency of photons to bunch. Lasers on the other hand, emit independent (but not single!) photons. You need inversion and stimulated emission and the system is therefore far from thermal equilibrium. This process gives you a much narrower photon number distribution around the mean. It turns out, that the small amount of photon number noise present cancels exactly the effect of changing the light field by destroying a photon when you detect one, so that the light field stays unaltered.

In a nutshell, the most important difference between these two emission processes is spontaneous versus stimulated emission.

You mean the cavity QED experiments by Serge Haroche? No, he could not detect a photon without destroying it. Nobody can. He could get some information about an ensemble of identically prepared photons without destroying them by means of weak measurements. Basically, he can measure the photon number in a cavity by having atoms (far detuned from the photons - they do not absorb them) travel through that cavity. The presence of the photons introduces some phase shift in the atoms, which can be measured. However, such measurements only give you statistical information. After doing that experiment a lot of times, you can say something about the mean photon number in the cavity. However, you cannot do it just once and get a sensible result for the photon number inside the cavity during that single run.

thank you!yes, I mean Serge Haroche's experiment!atteached are one paragraph of his paper and his paper.NOW I am totally confused!!would you please make it clear? thank you!

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Cthugha

That paper is a popular summary of Nature 446, 297-300 (2007), "Quantum jumps of light recording the birth and death of a photon in a cavity".

Have a look at the figure on the second page of the paper you linked. You can see that the result one gets is not strictly an atom in the excited state or in the ground state, but the result is very noisy and always has some atoms in the excited state when the majority is in the ground state and vice versa. Therefore you need what Haroche calls a majority vote in his paper. He has a look at the last 8 measurements and defines the photon number present as the majority result of these 8 measurements. This is a reasonable practice, but it shows the limitations of such weak or qnd measurement schemes: they only give a statistical trend, not a clear answer. Detecting an atom in the excited state does not mean that a photon is present, but that there is a certain chance, maybe 80% that a photon is present, and a 20% chance that there is no photon present. Now, by measuring again and again, you can get some good likelihoods and a good idea of what is going on. However, such an experiment does not help you for single shot measurements. If you want to know, whether a photon is present, performing such an experiment once is not very helpful. Unfortunately that is the standard situation. Haroche needed to go to cavities with very long lifetimes to have photons that live long enough to perform his kind of measurement. For a single photon in free space, that approach obviously will not work that easy.

That paper is a popular summary of Nature 446, 297-300 (2007), "Quantum jumps of light recording the birth and death of a photon in a cavity".

Have a look at the figure on the second page of the paper you linked. You can see that the result one gets is not strictly an atom in the excited state or in the ground state, but the result is very noisy and always has some atoms in the excited state when the majority is in the ground state and vice versa. Therefore you need what Haroche calls a majority vote in his paper. He has a look at the last 8 measurements and defines the photon number present as the majority result of these 8 measurements. This is a reasonable practice, but it shows the limitations of such weak or qnd measurement schemes: they only give a statistical trend, not a clear answer. Detecting an atom in the excited state does not mean that a photon is present, but that there is a certain chance, maybe 80% that a photon is present, and a 20% chance that there is no photon present. Now, by measuring again and again, you can get some good likelihoods and a good idea of what is going on. However, such an experiment does not help you for single shot measurements. If you want to know, whether a photon is present, performing such an experiment once is not very helpful. Unfortunately that is the standard situation. Haroche needed to go to cavities with very long lifetimes to have photons that live long enough to perform his kind of measurement. For a single photon in free space, that approach obviously will not work that easy.

one can't detect single photon which is because of the nature or the ability of human being?thank you!!

Cthugha

one can't detect single photon which is because of the nature or the ability of human being?

Ehm...I have not written anything even remotely similar to that.

Ehm...I have not written anything even remotely similar to that.

another question. sun emits light which is not coherent. if we filter them ,can we get coherent light? thank you!!!

Ehm...I have not written anything even remotely similar to that.

I am sorry ,my mistakes..

Cthugha

another question. sun emits light which is not coherent. if we filter them ,can we get coherent light? thank you!!!

You can increase first order coherence (=coherence time or coherence length) by filtering.

Using a narrow spectral filter will increase coherence time.

Using something like a pinhole will increase spatial coherence. This can be used to your advantage, for example if you want to perform the double slit experiment with sunlight.

You can increase first order coherence (=coherence time or coherence length) by filtering.

Using a narrow spectral filter will increase coherence time.

Using something like a pinhole will increase spatial coherence. This can be used to your advantage, for example if you want to perform the double slit experiment with sunlight.

thank you for all your answers! I think I am clear!!!thank you again!!