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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Why can transform the $\rm SU(2)$ spin to $S^2$ space?
Spin lies in $\rm SU(2)$ space, i.e. $S^3$ space, but when we write the spin coherent state:
$$|\Omega(\theta, \phi)\rangle=e^{i S \chi} \sqrt{(2 S) !} \sum_{m} \frac{e^{i m \phi}\left(\cos \frac{\...
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How is the BCS ground state a coherent state?
A coherent state is defined as the eigenstate of the annihilation operator $\hat{a}$. It can be obtained from the vacuum of the number operator by acting with displacement operator: $$|z\rangle=\hat{D}...
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What is the best way to describe a classical field in quantum field theory (coherent state)?
In quantum field theory, we have the following expansion on a scalar field (I follow the convention of Schwarz's book)
$$\phi(\vec{x},t)=\int d^3 p \frac{a_p exp(-ip_\mu x^\mu)+a_p^{\dagger}exp(ip_\mu ...
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Off-diagonal elements of density matrix in three-level system
In a three-level system, let's say an atom with three possible states, $|1\rangle$ being the lowest and $|3\rangle$ the highest ($E_1<E_2<E_3$), where
$$\Psi(t)= C_1(t)|1\rangle+C_2(t)|2\rangle+...
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BCS groundstate as eigenstate of the Cooper pair annihilation operator
In section 3.7 of his book Introduction to Superconductivity (2nd Ed.), Tinkham states that
[...] we note that S has the eigenvalue $e^{i\varphi}$ in a BCS state in which the the phase of $\Delta$ [.....
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Temporal stability of multimode coherent states
For the standard quantum harmonic oscillator, the coherent states $\{|\alpha\rangle, \alpha\in \mathbb{C}\}$ are temporally stable. That is,
$$
e^{-iH t}|\alpha\rangle = |e^{-i t} \alpha\rangle,
$$
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Harmonic oscillator in QFT
Given a single bosonic mode with frequency $\omega_0$, such that $\hat{H}=\hbar\omega_0(\frac{1}{2}+\hat{a}^{\dagger}\hat{a})$ how should one show the equivalence between the coherent state path ...
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'Coherent state' for particle in one-dimensional infinite square well
Is there such superposition of states for particle in given infinite square well ('box') in which all expectation values correspond to classical behavior of particle in this kind of potential: time ...
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Coherent state under Kerr evolution
I have a bosonic mode associated to the usual operators $a$, $a^\dagger$. I'm interested in knowing the evolution of a coherent state $\vert \alpha \rangle = e^{\alpha a^\dagger - \alpha^\ast a}\vert ...
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Proof of coherent state displacement operator solution
In $3D$ space I have two $2\times2$ non-Hermitian matrix operators, $A$ and $A^\dagger$, of the form:
$$A=\begin{pmatrix}
A_{11}(x_j,\partial_j) & A_{12}(x_j,\partial_j)\\
A_{21}(x_j,\partial_j) &...
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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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Coherent state path integral for Dirac fermions
I’m trying to derive the fermionic path integral for the Dirac theory using the coherent state path integral, but I’m not able to get around the presence of a $\gamma_0$ making it look different from ...
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Action of quantum channel on the state $|\alpha_x\rangle \langle \alpha_y|$
Suppose we have a coherent state with amplitude $\alpha_x$ and density matrix $\rho_x := |\alpha_x\rangle \langle \alpha_x |$. This state is sent through a quantum channel. We do not have a concrete ...
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Coherent states and QM, Double slit and measurements
In the thread Localization of Electron Matter Field Excitation in Simple Electron QFT Model a vital question about QFT is asked namely ´what keeps the electron matter field excitation localized ...
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What's the difference between coherent states and quasi-classical states?
It's actually a trouble in translation. I got an essay about "some state" that relate to classical states, but we don't have many textbook in our language to compare.
I only know that it's an ...
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