Coherent Definition and 167 Threads

I came across the following formula (2.68) in di Francesco's CFT book for a fermionic coherent state: $$\ket{\xi} = e^{\psi^{\dagger}T\xi}\ket{0}$$ where##\ket{\xi} = \ket{\xi_{1},...,\xi_{n}}##, ##\xi_{i}## is a Grassman number, ##T## is some invertible matrix, and ##\psi^{\dagger}## is the...

(Attempted answer:) Question 1: Yes, the detection events follow a Poisson distribution. Question 2: Yes, interference phenomena are clearly observed across all time bins even in the regime of much less than one photon per bin (N2 per bin << 1), which implies that the detection of supposedly...

I am trying to find the expected value of the variance of energy in coherent states. But since the lowering and raising operators are non-hermitian and non-commutative, I am not sure if I am doing it right. I'm pretty sure my <H>2 calculation is right, but I'm not sure about <H2> calculation...

By considering the power series for ##e^x##, I assert that ##N=e^{-\lambda^2/2}## and that ##a\Psi_\lambda = \lambda \Psi_\lambda##. Because the Hamiltonian may be written ##\hbar \omega(a^\dagger a + 1/2)##, ##\langle E \rangle = \hbar \omega(\langle a \Psi_\lambda, a \Psi_\lambda \rangle +...

What I have done is the following: \begin{equation} \braket{\eta_k | \eta_k}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\bra{0}(A^{\dagger})^nA^n\ket{0}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\int...

This is a question specifically for @A. Neumaier ! At Peter Woit's blog, Arnold commented about his formalism for quantum mechanics, coherent quantization. I left a question but Peter Woit doesn't always let comments through, so, here is the question: Why aren’t you restricted to unitary...

It is commonly said that the phase of coherent states can't be measured, just the relative phase between two coherent states. A qubit example: define the states $$|\phi\rangle=[|0\rangle+\exp (\mathrm{i} \phi)|1\rangle] / \sqrt{2}$$ and the measurement operators...

Answer:

Given the usual raising & lowering operators ##A^{\dagger}## & ##A## for a quantum harmonic oscillator, consider a coherent state ##|\alpha\rangle \equiv e^{\alpha A^{\dagger} - \bar{\alpha} A} |0\rangle##. I first check that ##|\alpha\rangle## is an eigenvector of ##A##. I already proved that...

I have attached my work here. I don't know how to proceed further?

Hi, I was reading through some online notes and was wondering: when dealing with coherent FSK, what is the minimum tone spacing and why? I know that for non-coherent FSK, we can show that the minimum is: ## f_1 - f_0 = \frac{1}{T} ## where ## T ## is the symbol period. However, if we are now...

Hello all. I have a question about building the coherent transfer function and specifically how I would go about deriving the pupil function for this figure. I have not come across this in my class yet and am a bit stumped. Any help would be appreciated.

I began this solution by assuming a = x+iy since a is a complex number. So I wrote expressions of <a| and |a> in which |n><n| = I. I got the following integral: Σ 1/πn! ∫∫ dx dy exp[-(x^2 + y^2)] (x^2 + y^2)^n I I tried solving it using Integration by Parts but got stuck in the (x^2 + y^2)^n...

Given the hamiltonian: \hat{H} = \hbar \omega_{0} \hat{a}^{+}\hat{a} + \chi (\hat{a}^{+}\hat{a})^2, where ##\hat{a}^{+}##, ##\hat{a}## are creation and annihilation operators. Find evolution of the state ##|\psi(t) \rangle##, knowing that initial state ##|\psi(0)\rangle = |\alpha\rangle##...

I just want to know if Black Holes would be quantumly coherent.

I've tried to square and compare ##\Delta X## and ##\Delta P## but they are not equal I have to say I am pretty lost here and a hint would be appreciated. I have studied coherent states and I know how to proof some properties related to it. For instance, I see how to proof that the state is...

So, should i write All of these as accodring to wiki pedia maxwell applied coherence concept to FPS, CGS, and SI is already coherent so answer will be All of these ?? Am i right or MKS because question is restricted to mechanics only ?

For two different coherent states \langle \alpha|\beta \rangle=e^{-\frac{|\alpha|^2+|\beta|^2}{2}}e^{\alpha^* \beta} In wikipedia is stated https://en.wikipedia.org/wiki/Coherent_state"Thus, if the oscillator is in the quantum state | α ⟩ {\displaystyle |\alpha \rangle } |\alpha \rangle it is...

Is coherence the medium in which quantum waves propagate? Does coherence also exist in the future to flag decoherence events?

Hey there, the task I'm working on is written below. Find the quadrature distribution ρ(q), for an optical mode being in the coherent state |α>. Hint: use ∑Hn(x)*(t^n)/(n!) I really am struggling with this type of tasks :D I tried to follow a solved example that I found in my workbook, but...

i am reading this paper . in the definition 19 we have |z><z| = :exp(a-z)^\dagger (a-z): in the extansion the first term is the identity son it is not hart to find an eigenvector for the value 1. it is ok if the vector is annihilated by a. if is the case for the coherent grouns state. how to...

Hello, I would like to understand as well as possible what (quantum) coherent states are. Can anyone advise on what books (or other materials) I should read? Please assume I have an introductory level in Quantum Physics (where by "introductory" I mean the material introduced in books like, for...

Hello! I am not sure I understand how neutron coherent scattering takes place. The case I am particularly talking about is neutron scattering off a hydrogen molecule. When thinking of Coulomb interaction, I would imagine this as if the incident particle (not a neutron, as the neutron doesn't...

Coherent Quantum Physics: A Reinterpretation of the Tradition by @A. Neumaier https://www.amazon.com/dp/3110667290/?tag=pfamazon01-20

Hi All, When I teach the basic structure of a laser setup, stimulated emission appears as a fundamental phenomenon. But in no reference I found a description that could account for the increase of coherent length of the EM laser field. According to my knowledge, one photon typically doesn't...

As far as I know we can express the position and momentum operators in terms of ladder operators in the following way $${\begin{aligned}{ {x}}&={\sqrt {{\frac {\hbar }{2}}{\frac {1}{m\omega }}}}(a^{\dagger }+a)\\{{p}}&=i{\sqrt {{\frac {\hbar }{2}}m\omega }}(a^{\dagger }-a)~.\end{aligned}}.$$...

Homework Statement: In the attached image. Homework Equations: formulas of fringe width and phase differences I think. It has been a long time since I have dealt with these kinds of interference/fringewidth problem, I can't figure out a way to start solving this problem. I was thinking about...

Hi Michael, Is it fair to say that whether system A is coherent or decoherent, it is always with respect to another system B? Of course the environment is another system (E), and an observer yet another system (O). So when we specify coherence or decoherence of system A, it is in respect to...

No evidence for globally coherent warm and cold periods over the preindustrial Common Era This is being reported in the popular news, here's a link to the Nature abstract. https://www.nature.com/articles/s41586-019-1401-2

Can anybody explain why the bright and dark fringes exist during the the interference phenomenon from two coherent sources.. I wanted to know why that specific pattern occurs

Coherent states are eigen state of lowering operator ##a## |\alpha\rangle=e ^{-\frac{|\alpha|^2}{2}}\sum^{\infty}_{n=0}\frac{\alpha^n}{\sqrt{n!}}|n \rangle , where ##\{|n \rangle\}## are eigenstates of energy operator. What is the case of state ##|0 \rangle##? a|0 \rangle=0|0 \rangle=0. So...

The definition of coherent state $$|\phi\rangle =exp(\sum_{i}\phi_i \hat{a}^\dagger_i)|0\rangle $$ How can I show that the state is eigenstate of annihilation operator a? i.e. $$\hat{a}_i|\phi\rangle=\phi_i|\phi\rangle$$

Dear all, I am aware that a weakly driven dipole can be modeled as a damped driven simple harmonic oscillator. If I have to model the dipole as being driven by a classical monochromatic electromagnetic wave, would the corresponding simple harmonic oscillator then be in coherent state ? In...

Homework Statement Which of the following statements is correct? a. coherent sources are not needed to produce interference fringes b. two coherent light sources do not always produce bright and totally dark fringes on a screen c. the atoms in a tungsten filament lamp produce coherent light...

Homework Statement Show that the coherent state ##|c\rangle=exp(\int \frac{d^3p}{(2\pi)^3}c(\vec{p})a^{\dagger}_{\vec{p}})|0\rangle## is an eigenstate of the anhiquilation operator ##a_{\vec{p}}##. Express it in terms of the states of type ##|\vec{p}_1...\vec{p}_N\rangle## Homework Equations...

I do not want to get into a religious discussion. The question is an abstract one, not directed at any belief system. With that prologue: is it theoretically possible to give a rigorous and coherent definition of "supernatural" that would allow an observable event to be supernatural, independent...

Hello. I've been struggling for a day with the following problem on Quantum coherent states, so I was wondering if you could tell me if I'm going in the right direction (I've read the books of Sakurai and Weinberg but can't seem to find an answer) 1. Homework Statement *Suppose a Schrödinger...

Can someone explain the meaning of the k vector and the general meaning of this equation?

I am studying Quantum Cryptography and I am quite new in Quantum area. I have read an article and I found this confusing statement: My questions: 1. The three stage protocol implementing multiphoton. What is the meaning of coherent states of mean photon number? 2. How to describe the quantum...

If you have two similar coherent sources which are separated from each other by a barrier. Now one source sends particles one by one into one slit and the other sends particles into the other in a double slit interference experiment. Now, the photons are always undistinguishable, so they should...

In an old fashioned electron microscope (the type I was meant to understand at university 50 years ago), are the electrons coherent, or do we just consider an electron interfering with itself? If they are coherent, how are they made coherent?

Is there a notion of “coherent” operations on Jacobian matrices? By this I mean, an operation on a Jacobian matrix A that yields a new matrix A' that is itself a Jacobian matrix of some (other) system of functions. You can ascertain whether A' is coherent by integrating its partials of one...

I've read that using a pinhole aperture and a wavelength filter can turn a "white" incoherent light source like a light bulb into a temporally and spatially coherent light source (albeit at low efficiency). Can a temporally and spatially coherent light source be made with a monoenergetic (or...

Hi! We will make a lab analogous to the stern gerlach experiments but with polarized light. How can we get only one single photon in experiment with a coherent light source? I'm going to make a lab where we need to get in only one single photo at a time. I have read that you can use some...

Edit: I'm pretty sure I have answered my own question. I think I need to sandwich the integral between a bra and ket to pick out one term from the sum. 1. Homework Statement Show that a Fock state ##|n\rangle## can be represented by the integral $$|n\rangle = \frac{\sqrt{n!}}{2 \pi r^n}...

I am curious about Ultrafast multi-dimensional coherent spectroscopy and want to get a bit of in-depth knowledge on this topic. I've always been very interested in spectroscopy, much like my passion in quantum mechanics, though I don't get a lot of time after daily routine to study either...

What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix} 0.5 \\ -\frac{i}{\sqrt{2}} \\ -0.5...

In a coherent state defined by |\alpha\rangle = \exp{\left(-\frac{|\alpha|^2}{2}\right)}\exp{\left(\alpha \hat{a}^\dagger\right)} |0\rangle there is a definite phase associated with the state by \alpha = |\alpha| \exp{\left(i\theta\right)} where the number operator and phase operator are...

Homework Statement Homework EquationsThe Attempt at a Solution These are what i solved except (e), I have no idea how to solve (e).

I understand that laser is based on the phenomenon of coherence. But I wonder how, say, two photons could be said to be located at the exact same spot when their locations could not be precisely defined due to the principle of uncertainty. To specify, which between the following two would be...