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...
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
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 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...
So, I am doing my undergraduate research project in Quantum Cryptography, and I have some confusion in a few areas, especially in the topic of continuous variable quantum key distribution.
From what I understand,
Discrete Variable - Single photon. That is, for example, the BB84 protocol. Bob...
I’m confused about how you find the vector |s;s⟩ to use in the general equation
|θ,ϕ⟩=exp(−iϕS3) * exp(−iθS2) |s;s⟩
For spin Coherent states (From http://www.scholarpedia.org/article/Coherent_state_(Quantum_mechanics)#4._Spin_Coherent_States
Eq 12)
Or
how you find the vector |j,m=j⟩ to use...
I've found online that the coherent state of the harmonic oscillator is
|\alpha \rangle = c \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}} | n\rangle
where
|n\rangle = \frac{(a^\dagger)^n}{\sqrt{n!}} |0\rangle
and |0> is called the initial state.
I've some code where I need to have this...
How does one write a Lagrangian of a coherent state of vector fields (of differing energy levels) in terms of the the individual Lagrangians?
I desperately need to know how to know to do this, for a theory of mine to make any progress.
Please stick with me, if I didn't make sense just ask...
My question is, how does one get a wave function for a 'combined' spin-1 and a spin-0 field? How is this possible? I have only been able to find combined states for equal spin identical particles.
If you don't understand my question, I'll be glad to reword it.
Hi, I am trying to find the wavefunction of a coherent state of the harmonic oscillator ( potential mw2x2/2 ) with eigenvalue of the lowering operator: b.
I know you can do this is many ways, but I cannot figure out why this particular method does not work.
It can be shown (and you can find...