All Questions
Tagged with coherent-states quantum-mechanics
162
questions
1
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79
views
"Deriving" Poisson bracket from commutator
This Q/A shows that deriving P.B.s from commutators is subtle. Without going into deep deformation quantization stuff, Yaffe manages to show that $$\lim_{\hbar \to 0}\frac{i}{\hbar}[A,B](p,q)=\{a(p,q),...
- 785
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2
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84
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Free evolution of coherent states
Is there a closed formula to express the time evolution of coherent states in absence of the potential term (only kinetic energy)?
The coherent state $|\alpha \rangle$ is defined by
$$\hat a|\alpha \...
- 9
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0
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72
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Coherent State as Eigenvector for some Observable?
A coherent state $|\alpha\rangle$ is an eingenvector of the operator $\hat{a}$, but this is not an observable (i.e., not an hermitian operator). But every vector is eigenvector of a complete set of ...
3
votes
3
answers
186
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Prove that integrating a displacement operator with a Gaussian gives $\int d^2\gamma e^{-|\gamma|^2/2}D(\gamma)=\pi|0⟩\!⟨0|$
I'm looking for "nice" ways to prove the following identity for displacement operators:
$$\int d^2\gamma e^{-|\gamma|^2/2}D(\gamma)=\pi|0⟩\!⟨0|,$$
with $|0\rangle$ the vacuum state and $D(\...
- 14.8k
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0
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19
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Integration over the complex plane and the completeness relation of the coherent states [duplicate]
I am studying some of the properties of coherent states using the book "Introductory Quantum Optics" by C. Gerry & L. Knight. (C. Gerry & L. Knight, Chapter 3, Section 5) And when I ...
2
votes
2
answers
94
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Grassmann variables and orthogonality of coherent fermionic states
Let a coherent fermionic state
$$
\left|\phi\right> := \left|0\right> + \left|1\right> \phi,\tag{0}
$$
where $\phi$ is a Grassmann number (i.e. it anticommutes with other Grassmann numbers). ...
- 1,611
1
vote
2
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66
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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}|...
1
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0
answers
33
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Coherent spin state (CSS) for an electron with spin
Standard definition for the spin coherent state (CSS) for the system of $N$ identical particles reads
$$
|\theta, \phi\rangle = \bigotimes\limits_{k=1}^{N} \left[ \cos\frac{\theta}{2} |0\rangle_k + e^{...
- 227
2
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0
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63
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Paradox when expressing an operator in terms of creation/annihilation operators [duplicate]
I'm trying to expand an arbitrary operator using creation/annihilation operators following this post, where $|m\rangle \langle n|$ is expressed as
$$
|n\rangle \langle m|~=~\sum_{k\in\mathbb{N}_0} c^{...
- 695
2
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1
answer
145
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Operator acting on product of coherent states
My problem
Find $O_\phi|\psi\rangle$, where the state $|\psi\rangle$ is defined on a composite space $\mathcal H_A\otimes \mathcal H_B$ as
$$|\psi\rangle = \left(\bigotimes_{k=1}^N|\alpha_k'\rangle\...
1
vote
0
answers
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?
- 781
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votes
0
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45
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Prepration of a Gaussian modulated coherent state
In Continuous Variable -Quantum Key Distribution (CVQKD), usually Gaussian modulated coherent states are sent. This means both quadratures of a coherent state are chosen from two normal distribution. ...
- 1
2
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3
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245
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Finding the wavefunction of coherent state in 2D oscillator
Suppose I have a two-dimensional harmonic oscillator, $H= \hbar\omega(a_x^{\dagger}a_x+a_y^{\dagger}a_y)$. We define the operator $b=\frac{1}{\sqrt{2}}(a_x+ia_y)$.
If eigenkets of the hamiltonian are $...
- 81
1
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3
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242
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It seems that expectation value of $H$ on coherent states is independent of time? But why?
Let's say the particle is in the state $| \psi(0) \rangle = \exp(-i\alpha p/\hbar) |0 \rangle$, where $p$ is the momentum operator.
I have to show that $| \psi(0) \rangle$ is a coherent state and to ...
- 81
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0
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What is the state vector of a displaced (single-mode) squeezed vacuum state in the quadrature basis?
I've been hunting through the quantum optics literature for the displaced squeezed state written in the $q$-quadrature basis ($p$-quad would be fine too, since it's just a Fourier transform), but it ...
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