Talk:Coherent state

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Every quantum state is a certain superposition of eigenstates of any potential (since they are complete), so I don't think this something that should be in the first line of the article. J S Lundeen 20:42, 13 Jun 2005 (UTC)

Sure. Looks a lot better now. Thanks. --Gerd Breitenbach 19:15, 14 Jun 2005 (UTC)

Cortonin, there is a difference between a state which is coherent and a "coherent state". A "coherent state" is a specific superposition of fock states (see article). A state that is coherent has a definite phase between the terms in the superposition describing it. The opposite of this is a completely [mixed state]. J S Lundeen 22:54, 15 August 2005 (UTC)

Seems like the discussion here is limited to "canonical" coherent states, ie. those based on the Heisenberg group. Coherent states can and have been defined for any group. Also, the section on "mathematical characteristics" presents the smoothness of the coherent state overlap as a "difficulty" - but the fact is that it's precisely because of this smoothness that coherent states are mathematically "nice" to deal with.

Yes, it is limited to "canonical" coherent states. I don't know much about non-canonical definitions. If you do, feel free to add a section. However, the main part of the article should remain focused on the canonical definition since this is both the standard definition and the historical one.--J S Lundeen 16:09, 9 March 2006 (UTC)

Contents

[edit] quadratures

This article introduces dimensionless quadratures X & P in terms of x & p which are never defined or named. It would be nice if it told what these variables are. —Preceding unsigned comment added by 129.6.136.128 (talk) 19:13, 2 October 2007 (UTC)

This has been fixed in the article.--J S Lundeen (talk) 14:07, 11 January 2008 (UTC)

[edit] The first figure looks strange.

Several things seem to be wrong with the first figure.

If it shows the result of HOMODINE detection, why the amplitude is periodic?

It the leyend says "electric field", why the ordincte axis is labeled "noise current"? What is sense of negative values of the noise?

Perhaps, the figure represents variation of current at the HETERODYNE detection; then the frequency of oscillation in the figure is just difference of frequencies of two interfering lasers.

Is it possible, to put marks at the time axis (abscissas); and plot not only the noise figure, but also the pulsation of photocurrent?

dima 06:56, 19 January 2007 (UTC)

The first figure is real data from a Nature paper which measured these states. It was posted by an author of that paper. I doubt he will revise the figure. We are very lucky he added them, otherwise they would be copyrighted. The noise current would be better labelled as "difference current". It is the difference in photocurrent created in two detectors in a balanced homodyne scheme. In the theory of homodyning, this difference current is proportional to the electric field.--J S Lundeen (talk) 13:52, 11 January 2008 (UTC)

[edit] "non-correct" paragraphs.

Hello, 67.101.213.215 Let us discuss here the paragraphs you qualified as "incorrect" (13:19, 5 January 2008).

About phase of state of a single photon - very difficult question. The answer depends on the definition of phase. While we have only few photons (and perhaps no photons at all), the intuitive concept about phase fails. How about phase of a coherent state with parameter α = 0.5, the contribution of multiphoton states in this case is small. How about linear combination of states with definite number of photons: \frac{1}{\sqrt{2}} |0\rangle + \frac{1}{\sqrt{2}} |1\rangle ?

About coherent light from a conventional laser - it is not coherent state. The mathematical expectation of the field in any mode is practically zero. For this reason, the coherent combination of several lasers is not trivial. (One would be able to combine the coherent states with just beam splitter.)

Please, recover the article. I repeat, the discussion should be moved here. dima (talk) 13:43, 5 January 2008 (UTC)

Domitori, I was not 67.101.213.215 but I agree with his/her edits. I agree that it is a matter of debate whether a laser actually produces a coherent state, ala recent debates by Molmer, Terry Rudolph, Rob Speckens and Barry Sanders. However, this is still a controversial subject. Most quantum optics scientists believe that a laser does produce a coherent state and the standard textbooks also support this view. As an encyclopedia article, this should present the accepted view of the field. As such I have deleted this content. --J S Lundeen (talk) 22:40, 10 January 2008 (UTC)

Hi, Lundeen. The coherent state is destroyed in a quantum amplifier; even if the input state is coherent, the output is not. The laser output coupler releases the light after it passes through the active medium which should be considered as quantum amplifier. Linear splitting does not make the coherent state from a non-coherent state. It is very simple reason, why the laser output (even if highly coherent) is NOT a coherent state. Cold you provide an exact reference (preferably verbatim) to the claim that the coherent state can be produced with a commercial laser? We need to cite such a reference in articles laser, coherent state, quantum amplifier and quantum noise. dima (talk) 04:58, 11 January 2008 (UTC)
Domitori, I am not disagreeing with your statements about quantum amplifiers. Still, it is accepted in this field that a laser puts out a coherent state. All the books cited in the article state this. For example: Loudon, 3rd ed. p. 310: "The picture of single-mode laser light provided by the above calculations shows a field excitation that approaches the form of a coherent state as the pumping increases to values well above threshold." Of course, as with all of physics, there are approximations and limits involved with this statement. Could you please remove from other articles statements similar to the ones you added to this article? Thanks. --J S Lundeen (talk) 13:45, 11 January 2008 (UTC)
I too was shocked by the sentence "Actually the picture of one photon being in phase with another is not valid in quantum theory." Maybe you meant that "the phase of a Fock state with occupation number n relative to the phase of another Fock state with occupation number m not equal to n is not defined."
But I do not think that is true either. Consider an S matrix amplitude which is the sum of several Feynman diagrams, and in which the number of virtual photons varies from one diagram to the next. All the phases matter. Sometimes diagrams cancel each other, etc.
But you probably had something in mind when you wrote "Actually ..." Tell us the situation you had in mind or maybe give us a literature reference. James W. Overbeck Don't know how the font got messed up and I do not see how to fix it. Sorry. (talk) 22:15, 10 March 2008 (UTC)
Lundeen, other users already did that you suggest. I still do not understand: if the two identical single-mode lasers generate the coherent state, why not to compine their beams with just a beam splitter into a simgle mode beam of twiced power? Why all the analysis about coherent addition?
If a good pulsed laser emits the coherent pulses, what experiment would you suggest to verify that the state is coherent, not an entamblement of n-photonic states with thermal phonons in the gain medium? dima (talk) 08:53, 14 April 2008 (UTC)
Domitori, I agree there are no experiments which distinguish between a mixture of n-photon states (with appropriate weightings) and a coherent state. There are experiments that can measure the absolute phase of a laser pulse (e.g. relative to the peak of the pulse as in ionization experiments with ultrafast pulses (this has been done), or e.g. relative to a classical clock via a frequency comb stretching from the visible to the radiofrequency part of the spectrum (this has not been done)). These measurements collapse the state into a particular phase and thus a pure coherent state. However, this is still controversial research. The accepted thinking is that a laser creates a coherent state. This is what an encyclopedia article should say. This thinking will not lead to errors in calculations simply because there are no experiments that distinguish the difference. If you haven't already, could you remove your edits about this subject from the other articles you added them to? J S Lundeen (talk) 15:49, 17 April 2008 (UTC)

[edit] References

Inserted tag Refimprove motivated by sentence.

But the condensate fraction is less than 20% «NEEDS ACTUAL at absolute zero temperature.

Reminder to insert "actual number". JBatista 14:45, 20 March 2008 (UTC)

Sentence

(For more, see Quantum mechanical description.)

suggests this text was obtained from somewhere else. Review the text contents? JBatista 14:55, 20 March 2008 (UTC) —Preceding unsigned comment added by Jmnbatista (talk • contribs)

[edit] wave packet

Sometimes written wave-packet, sometimes wavepacket, and sometimes wave packet. Please correct this in a consistent manner. Randomblue (talk) 11:56, 23 May 2008 (UTC)