Talk:Coherent state

message: 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)

message: 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)
thread_title:  quadratures 

message: 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)
thread_title:  The first figure looks strange. 

message: 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)
replies: text: 'Quantum mechanical description' referred to the next section. I fixed it. Arjen Dijksman (talk) 20:06, 20 September 2008 (UTC)
thread_title:  References 

message: 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)
thread_title:  wave packet 

message: 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)
replies: text: 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)
thread_title:  Coherent state is left unchanged by the detection (or annihilation) of a particle? 

message: 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)
replies: text: 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)
thread_title:  "Mathematical Characteristics" - cleanup needed?! 

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

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

message: 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)
thread_title:  Amazing Page 

message: 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)
thread_title:  Splitting and renaming this article 

message: 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)
thread_title:  Detections 

message: 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)
thread_title:  Electric field unexplained and out of place 

message: 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)
thread_title:  Derivation of minimization condition desired 

message: 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)
thread_title:  "Quantum mechanical definition" section is confusing