All Questions
Tagged with phase-space quantum-optics
27
questions
0
votes
1
answer
79
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Phase space formulation: "Representation" vs "function" vs "quasi-probability distribution"
In the phase space formulation, the terms "representation", "function, and "quasi-probability distribution" (as in Glauber–Sudarshan P representation, $P$-function) seem to be used interchangeably.
I ...
- 387
5
votes
2
answers
2k
views
What is the Wigner function of a thermal state?
I am wondering how you would compute the Wigner Function of a Thermal State with
average phonon number $\bar{n}_{\mathrm{th}}$.
I know the result should be a Gaussian with variance in position $\...
- 141
1
vote
1
answer
124
views
Wigner phase space operator correspondence: how to order?
According to Gardiner-Zoller (Quantum Noise), operators acting on the density matrix can be mapped via e.g. (I'm taking Wigner space as an example, but the same holds for P and Q)
$$a\rho\...
- 1,620
1
vote
1
answer
347
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Wigner map of the product of two operators
Does anyone know how to prove that for the product of two operators $\hat{A}\hat{B}$ the Weyl-Wigner correspondence reads
$$
(AB)(x,p) = A\left (x-\frac{\hbar}{2i}\frac{\partial}{\partial p}, p+\frac{\...
- 793
1
vote
1
answer
163
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Fourier transform of cross-spectral density space matrix elements
In order to derive phase space like equation of motion (e.g. the equation of motion for the Wigner function of a single particle in one-dimension), it is an advantage to work with the Fourier ...
- 793
0
votes
1
answer
476
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Plotting quadrature uncertainties in phase space
In most books like in the picture given below, the uncertainties regarding quantum states like coherent and squeezed states are represented in phase space plot by some area enclosed within a circle or ...
- 119
4
votes
1
answer
916
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Why exactly is the Husimi-Q distribution not a real probability distribution?
From this question I understood that the uncertainty principle is causing a problem because two points $x,p$ and $x',p'$ in phase space can be confused. Why exactly is this a problem? I don't grasp ...
user164828
1
vote
1
answer
281
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Pegg-Barnett phase implementation does not seem to work
I attempt to monitor the phase of a wavevector $|\psi\rangle$.
As I found (e.g. here ), a matrix representation for the Pegg-Barnett phase operator in Fock base can be obtained as
$$\Phi=\sum_{m,n,...
- 1,620
5
votes
1
answer
596
views
Proof of "non-existence" of marginals of the Husimi $Q$-function
There are many ways to consider the Husimi ($Q$) quasi-probability distribution function, e.g. as the expectation of the density operator in a coherent state or as the Weirstrass transform of the ...
- 266
15
votes
1
answer
3k
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Understanding the relationship between Phase Space Distributions (Wigner vs Glauber-Sudarshan P vs Husimi Q)
I am moving into a new field and after thorough literature research need help appreciating what is out there.
In the continuos variable formulation of optical state space.
(Quantum mechanical/Optical) ...
- 630
2
votes
1
answer
574
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Wigner functions, symmetry
I'm trying to get more insight into quasiprobability distributions, as for example the Wigner function.
There are some Wigner functions, which are symmetric.
Symmetric:
Fock state
Thermal states
...
- 560
4
votes
1
answer
497
views
Are the Wigner and Husimi transforms injective?
I am wondering if the Wigner function is injective. By injective I mean, that, for every density matrix $\rho$, there is a different Wigner distribution. The same question applies to the Husimi ...
- 2,090