All Questions
Tagged with coherent-states hilbert-space
62
questions
6
votes
2
answers
639
views
When is a state entangled?
I have read from What's the difference between an entangled state, a superposed state and a cat state? that an entangled state is one that cannot be expressed as product state. Suppose we have the ...
1
vote
2
answers
66
views
Coherent creation operator: unitary or not?
In Quantum Mechanics, for coherent states $|z\rangle$ it can be prooved that if $|0\rangle$ is the vacuum state for an harmonic oscillator, therefore:
\begin{equation}
|z\rangle=e^{za^{\dagger}-z^*a}|...
0
votes
1
answer
96
views
Identity of bosonic coherent states
I have a short question about the meaning of the identity of the bosonic coherent states.
Before I ask the question I will explain some background.
The eigenstate of the bosonic annihilation operator $...
- 237
1
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0
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22
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Can we treat Gazeau-Klauder coherent states for infinite potential well as a superposition of Fock states?
If we define coherent states of infinite potential well based on Gazeau-Klauder coherent states. Can we use ladder operators and bosonic algebra for them which we use for Glauber coherent states?
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4
votes
1
answer
161
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Application of Schur's lemma to proving the completeness of coherent states
I am studying many-body path integral through Altland & Simons's textbook called "Condensed Matter Field Theory," and the book states the completeness of the coherent states as below:
$$\...
- 340
1
vote
0
answers
199
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Overcompleteness of coherent states
I am trying to show that the basis of coherent states,
$$ |\phi\rangle =e^{-\sum_{\alpha'}\phi_{\alpha'}a^\dagger_{\alpha'}}|0\rangle, \quad\text{ where }\quad a_\alpha|\phi\rangle=\phi_\alpha|\phi\...
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2
votes
0
answers
57
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Could one call eigenstates of $ \hat{a} = \hat{x} + i\hat{p}$ coherent states for other potentials than the harmonic oscillator?
Let's say I look at the quantum system of a particle in one dimension, subject to any other potential than the one of the harmonic oscillator, and I define $\hat{a}$ as stated above. I would find the ...
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1
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1
answer
171
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Decomposing a coherent state? [closed]
Can you decompose a coherent state $|\alpha\rangle$ into $p|p\rangle+q|q\rangle$, where $|p\rangle$ and $|q\rangle$ are eigenstates of the $P$ and $Q$ operators respectively with eigenvalues p and q?
...
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1
vote
1
answer
128
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Confusion with two-mode bra-ket notation [closed]
Let us consider some abstract two-mode bosonic model with a conserved total number of quanta (i.e. eigenvalue $N$ of the operator $\hat{N} = a^\dagger a + b^\dagger b$ remains constant with ...
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1
vote
1
answer
106
views
Equation of motion for space and momentum of a $\textbf{coherent state}$ [closed]
Given the coherent states
$$| \alpha \rangle\, e^{\textstyle -|\alpha|^2/2}\,\sum_{n = 0}^\infty \dfrac{\alpha^n}{\sqrt{n!}}\,|n\rangle$$
that satisfy the eigenvalue-equation: $A|\alpha\rangle=\alpha\,...
- 462
2
votes
1
answer
722
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Fock Space and Coherent state
Can a coherent photon state also belong to the Fock space? If yes, under what conditions? For example I read that
$$\exp\bigg\{-\frac{1}{2}\sum_i|\alpha_i|^2\bigg\}\exp\bigg\{-\sum_i\alpha_ia_i^{\...
- 3,992
0
votes
2
answers
393
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Does the number of photons in a displaced coherent state is same as the original coherent state? [closed]
Lets say I receive a quantum state $|\alpha\rangle$ with number of photons $N$ and I displace this state by $\alpha$ $\hat D(\alpha)$ so the resultant state is $|2\alpha\rangle$ with same number of ...
0
votes
1
answer
85
views
Why can we arbitrarily set the expectation value of a field operator by representing the field state as a product of coherent states?
In the paper "Unusual Transitions Made Possible by Superoscillations", the author begins by solving for a coherent state \begin{equation}|\alpha\rangle\end{equation} such that
\begin{...
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0
votes
1
answer
332
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Is $SU(2)$ coherent state normalized?
I know Glauber coherent state are normalized such that the inner product of < α|α > =1 where |α > is Glauber coherent state.
My question is (is SU(2) COHERENT STATE NORMALIZED)?
I MEAN IF |Z&...
- 11
3
votes
1
answer
424
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What does "coherent evolution" of an $N$-body quantum system mean?
In classical physics we know of coherence of waves and in quantum physics we identify coherent states.
While those are clearly defined concepts/terms, in literature we regularly encouter also that a $...
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