Talk:Coherent state

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)

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)

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)

"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 $$\alpha=0.5$$, 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)

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)

Coherent state is left unchanged by the detection (or annihilation) of a particle?
I am dubious about the sentence Physically, this formula means that a coherent state is left unchanged by the detection (or annihilation) of a particle that applies to the formula $$\hat{a}|\alpha\rangle=\alpha|\alpha\rangle$$. A state is left unchanged by detection if $$\hat{a}|\alpha\rangle=|\alpha\rangle$$, i.e. if $$\alpha=1$$. That's generally not (never?) the case for a coherent state. Arjen Dijksman (talk) 20:18, 20 September 2008 (UTC)

A state is a vector in the Hilbert space, so the factor $$\alpha$$ does not change the state ( $$|\alpha\rangle$$ and $$ \alpha|\alpha\rangle$$ are the same state). Simone De Liberato (talk) 23:17, 5 October 2008 (UTC)

The article is very confusing because the applications and examples are mixed in with the definitions. The annihilation operators in question need not be particle annihilation operators - and in the paradigmatic example involving the harmonic oscillator, they're not. --Exphysicist (talk) 15:16, 11 October 2008 (UTC)


 * I agree: the article is confusing because the definitions are mixed up with the applications and examples. I'll repeat this below. 178.38.106.251 (talk) 01:20, 27 April 2015 (UTC)

Anyway, the coherent state is NOT left unchanged by the creation of a particle, since $$[\hat{a}, \hat{a}^\dagger] \neq 0$$. I'm changing it.--Jorgealda (talk) 10:43, 28 February 2016 (UTC)

"Mathematical Characteristics" - cleanup needed?!
Why are coherent states being compared to "Fock states"? Surely the relevant point is simply the observation that they're not an orthogonal set. The first equation is confusing because \alpha and \beta are complex parameters on the left hand side, but they look like real parameters in the delta function of the right hand side.

I don't think the fact that a adjoint doesn't have an eigenket is in any way a "difficulty". Note that a not having an "eigenbra" is exactly the same statement as a adjoint not having an eigenket, not an additional piece of information. Talking of which, I would vote to replace the "right eigenstate" with just "eigenstate" further up the page - either it's an eigenstate of a, or it isn't. The whole left/right thing is really a notational game involving the Dirac notation, not a fundamental statement about the Hilbert space. --Exphysicist (talk) 15:49, 11 October 2008 (UTC)

--24.205.207.106 (talk) 23:03, 17 March 2010 (UTC)
 * I second the removal of "right" eigenstate because the information is redundant. Either a state is an eigenstate or it isn't.
 * "$$\alpha$$ is a complex number, that is not necessarily real" in the section "Quantum Mechanical Definition" is redundant. Complex numbers are by definition not necessarily real. Readers who are not aware of this, should consult http://en.wikipedia.org/wiki/Complex_number instead.
 * "Schrödinger found minimum uncertainty states for the linear harmonic oscillator to be the eigenstates of (X - iP)" in the same section does not appear to be correct because the annihilation operator is defined as $$\hat{a}=x+\imath p$$ (neglecting units) whereas $$x-\imath p$$ refers to the creation operator


 * surely right doesn't mean "proper" or anything similar, but right(handed), meaning an eigenstate when put into in operator from the right (as a ket). 91.15.138.121 (talk) 23:43, 2 November 2010 (UTC)

Translation into Chinese Wikipedia
The 23:08, 28 April 2009 Xiongfeng version of this article is translated into Chinese Wikipedia.--Wing (talk) 14:08, 2 May 2009 (UTC)

Explicit wavefunction
Shouldn't the explicit position-(and maybe momentum-)space wavefunctions be written down? Njerseyguy (talk) 13:52, 27 June 2009 (UTC)

Amazing Page
This page, especially the Applications to Quantum Mechanics section, is what I consider to be a shining example of what more Wikipedia physics-related webpages should look like. Kudos to the author and editors. —Preceding unsigned comment added by 71.53.206.125 (talk) 15:32, 9 February 2010 (UTC)

Agreed, it's an excellent article. Dratman (talk) 14:25, 15 March 2011 (UTC)

Splitting and renaming this article
I think (together with some knowledgeable colleagues) that this article is OK (except for some details to be edited), but by far too restrictive. Indeed it covers essentially only the application of coherent states in quantum optics. This is justified historically, but in the recent years, coherent states have become an important field in mathematical physics, starting with the connection with group theory introduced by Perelomov (see his textbook from 1986). For instance, coherent state quantization, Gazeau-Klauder coherent states, wavelets (which are coherent states of the affine group) are flourishing domains that deserve to be described in Wikipedia. A large part of these developments is already contained in the textbook by Ali-Antoine-Gazeau (Springer 2000) and much more has happened since then.

There fore we suggest to split the article in two. The present article (properly edited, with references updated) should become "Coherent states (Quantum Physics)" and a new article introduced, called "Coherent states (Mathematical Physics)". Both are ready for posting. CSmaker (talk) 13:23, 22 July 2011 (UTC)

Detections
The article repeated uses the word "detection". Is this synonymous with "measurement"?

I understand "measurement" to mean that you pick a Hermitian operator, apply it, and afterwards the state changes to some eigenstate of that operator. Yet the article says:


 * A Poisson distribution is a necessary and sufficient condition that all detections are statistically independent. Compare this to a single-particle state ( |1〉Fock state): once one particle is detected, there is zero probability of detecting another.

Wouldn't the rules of "measurement" mean that after a measurement, the system switches to an eigenstate of whatever you've measured? Or does "detection" mean that you apply only the specific operator a? If so, what are the possible outcomes of this, and how do you calculate probabilities? Is detection a kind of measurement?

I'm having difficulty attaching the processes suggested by the wordage to a sequence of operator applications.

178.38.106.251 (talk) — Preceding undated comment added 18:42, 26 April 2015 (UTC)

Electric field unexplained and out of place
From the article:


 * ''For an optical field,
 * $$~E_{\rm R} =

\left(\frac{\hbar\omega}{2\epsilon_0 V} \right)^{1/2} \!\!\!\cos(\theta) X \qquad \text{and} \qquad ~E_{\rm I} = \left(\frac{\hbar\omega}{2\epsilon_0 V}\right)^{1/2} \!\!\!\sin(\theta) X~$$
 * ''are the real and imaginary components of the mode of the electric field.

Here it appears that the electric field is being recast as an operator, but this has not been formally stated, explained, or linked. Also I'm puzzled by the formula since it makes it look like E is a multiple of X. That is strange. Is E supposed to be a plane wave, or an eigenmode of something? The word "mode" is used but the mode is not identified. Is θ a constant?

In any case, this equation for an electric field seems out of place here. The whole section is cast in the language of an abstract harmonic oscillator being used to record an occupancy number. I realize that photons are a main application of this, but that should be said in words, not by an orphan equation that's not otherwise connected to the text. Can it be deleted? 178.38.106.251 (talk) 19:20, 26 April 2015 (UTC)

Ordering of concepts in section entitled Quantum mechanical definition
This section uses many concepts before they are formally defined. It's confusing. Here are two examples that I fixed, I hope.

(1) ...so it is an eigenstate of the operator (X+iP). Shouldn't it be mentioned that this is the operator â? This is stated later, but it would make more sense to the reader if it were pointed out now.

(2) (If the uncertainty is minimized, but not necessarily equally balanced between X and P, the state is called a squeezed coherent state.) A coherent state was defined several paragraphs earlier as an eigenfunction of â. But it was never connected by name with the variational characterization that motivated Schroedinger. Yet we are already giving a caveat to the connection that was not made.

I fixed these, pushing the expositional strategy marginally in the direction "modern definitions" from "historical unfolding".

We now have the paragraph: ''Using the notation for multi-photon states, Glauber characterized the state of complete coherence to all orders in the electromagnetic field to be the right eigenstate of the annihilation operator—formally, in a mathematical sense, the same state. The name coherent state took hold after Glauber's work.''

Perhaps someone with knowledge could rephrase this to make Glauber's contribution not seem tautological in the present context.

Derivation of minimization condition desired
The article states: The quantum state of the harmonic oscillator that minimizes the uncertainty relation with uncertainty equally distributed between X and P satisfies the equation... How is the equation derived? At the very least there is a Lagrange multiplier missing.

178.38.106.251 (talk) 20:20, 26 April 2015 (UTC)

"Quantum mechanical definition" section is confusing
To repeat from 2008: ''"The article is confusing because the definitions are mixed up with the applications and examples."

Not just mixed up. The definitions are implicitly "glued" to the concrete examples, when in reality they are simpler and more general. And this is done without informing the reader. He finds out only because later remarks reveal the implicit assumption that we're doing a certain example. Viz. the intermittent reference to "photons" and to "Fock states" that appear throughout the section called "Quantum mechanical definition".

Here is a possible re-ordering.

(1) A coherent state can be presented first as an uncertainty-minimizing, equal-distribution state of the harmonic oscillator. This leads quickly to an eigenvalue equation using the x+ip operator. It can be solved for the Poisson distribution. (This concrete formula should be displayed early on.)

(2) Then the harmonic oscillator can be interpreted as a storage facility for someone else's bosonic quantum states -- here is where Fock states and occupancy numbers come in. The ladder operators become creation/destruction/number operators, the designation "coherent state" now fits, historically and conceptually, for what has been defined. (Or maybe it already fits in (1). Knowing this kind of nuance is why I'm reading the article instead of writing it.)

(3) As an application, the bosons can be photons. Either this should be left to the end, or it should be announced up front at the beginning and be carried out systematically. Not intermittently.

As it stands, everything is done first. Meaning all jumbled together.

The article tries to say too many overarching, philosophical things about coherent states before it has the language to do so. Also, it tries to do modern definitions and historical development at the same time. This is not so easy.

That said, the article has a lot of interesting remarks and as a test of knowledge it's first rate.

178.38.106.251 (talk) 08:09, 27 April 2015 (UTC)

Requested move 4 January 2020

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: moved as requested per the discussion below. Dekimasu よ! 17:27, 12 January 2020 (UTC)

Coherent states → Coherent state – WP:NCPLURAL. The term "coherent state" has 48 occurences in the article, "coherent states" has 51. The WP:FIRST sentence starts with the singular form. Each has about the same number of inlinks (35ish). So from internal evidence alone I think the article should be at the singular title. 94.21.10.204 (talk) 12:48, 4 January 2020 (UTC)
 * Support per nom. Surachit (talk) 01:47, 5 January 2020 (UTC)
 * Support. We have bound state. — wing   gundam  19:30, 8 January 2020 (UTC)


 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.