Questions tagged [coherent-states]
The specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It obeys the minimal uncertainty relation in Heisenberg's uncertainty relationship.
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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 ...
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"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 $$\lim_{\hbar \to 0}\frac{i}{\hbar}[A,B](p,q)=\{a(p,q),...
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Free evolution of coherent states
Is there a closed formula to express the time evolution of coherent states in absence of the potential term (only kinetic energy)?
The coherent state $|\alpha \rangle$ is defined by
$$\hat a|\alpha \...
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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 ...
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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(\...
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Majorana Boson Coherent States
Consider $a$ be a bosonic operator, and we define $\Phi = a+a^{\dagger}$ and it is clear that $\Phi^{\dagger}=\Phi$ that implies "Majorana Boson". Now, i want to find the coherent states for ...
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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 ...
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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). ...
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Question about coherent population trapping
In coherent population trapping, if we denote the ground states in a $\Lambda$-like system as $|0\rangle$ and $|1 \rangle$ and the excited state $|2 \rangle$, there is a linear combination $|d \...
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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 ...
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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}|...
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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
$$
|\theta, \phi\rangle = \bigotimes\limits_{k=1}^{N} \left[ \cos\frac{\theta}{2} |0\rangle_k + e^{...
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Paradox when expressing an operator in terms of creation/annihilation operators [duplicate]
I'm trying to expand an arbitrary operator using creation/annihilation operators following this post, where $|m\rangle \langle n|$ is expressed as
$$
|n\rangle \langle m|~=~\sum_{k\in\mathbb{N}_0} c^{...
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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 $\...
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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\...
