All Questions
Tagged with coherent-states quantum-optics
58
questions
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
1
vote
0
answers
24
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How Does Laser Light Maintain Coherence Amid Photon-Atom Entanglement?
Laser light is known to produce "coherent state light," which consists of a superposition of different photon numbers. However, wouldn't the entanglement between the atoms and the light ...
- 2,193
2
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answers
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
$$
|n\rangle \langle m|~=~\sum_{k\in\mathbb{N}_0} c^{...
- 695
1
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0
answers
31
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Existence of Glauber-Sudardhan $P$-representation of arbitrary given density operator for light field
In all textbooks on quantum optics I can reach (Scully, Leonhardt, Walls, etc), the Glauber-Sudardhan $P$-representation $P(\alpha)$ is introduced in the following two ways:
Fourier transform of $\...
- 695
2
votes
1
answer
145
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Operator acting on product of coherent states
My problem
Find $O_\phi|\psi\rangle$, where the state $|\psi\rangle$ is defined on a composite space $\mathcal H_A\otimes \mathcal H_B$ as
$$|\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
0
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1
answer
74
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Applying a phase shift to a coherent state vs a phase-space rotation (Mach-Zhender)
I'm having some trouble with the physical implementation of a phase vs rotation in phase-space for a coherent state.
Say I have a laser pulse which yields a coherent state $|\alpha\rangle$, I then put ...
- 53
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votes
0
answers
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
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0
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52
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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 ...
- 215
1
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114
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Phase distribution of coherent states
I am studying the phase distribution for coherent states, as is defined in quantum optics. (See, for example, Introductory Quantum Optics by Gerry and Knight, pages 46–48).
In this situation, we seek ...
2
votes
2
answers
168
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Non-classicality of coherent state and squeezed states
Recently I have started studying about the coherent state and squeezed states of light. But I have a question about why do we call these states non classical? What are the things that deny their ...
0
votes
0
answers
69
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Is there any way to write eigenstates of infinite square well in terms of eigenstates of harmonic oscillator?
I wanted to find Husimi Q function using expression $Q= \langle \alpha|\rho|\alpha \rangle$, where $|\alpha \rangle $ is coherent states of harmonic oscillator. I want to consider system $\rho=|u_n\...
- 781
1
vote
0
answers
117
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Finding an operator in terms of creation and annihilation operators that satisfy some conditions
I have a problem where I'm looking to find the following Hermitian operator $\hat{A}$ written in terms of the operators $\hat{a}^{\dagger}\hat{a}$, $\hat{a}^2$, $\hat{a}^{\dagger 2}$, $\hat{a}$, $\hat{...
- 21
0
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0
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73
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Homodyne Detection of Photon Number States
I'm currently trying to understand why you can detect the signal of single photons with homodyne detection. I found that the difference current $i_{34}$ is given by
$$i_{34}\sim -2 ⟨\Psi|_1⟨\alpha|_2\...
- 23
1
vote
1
answer
227
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SPDC One Arm vs Very Weak Coherent state
I know that SPDC(Spontaneous Parametric Down Conversion) is a method to generate heralded single photon source.
So If we do homodyne tomography of single photon fock state, another arm of SPDC is used ...
- 153