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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Time evolution of a spin-coherent state
What i'm struggling with is this question:
Consider a spin S in an external magnetic field along the quantization axis so that the $|S_{z}>$ states are eigenstates with equally spaced eigenvalues ...
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Quantum mechanical spin coherent states
I'm really struggling with how to derive the right hand side of this equation. It's the Spin operator on coherent states of the harmonic oscillator. I've done it for the $S_+$ operator but can't seem ...
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Time Evolution of Coherent State (Gerry and Knight)
I'm stuck on some simple mathematics in finding the time evolved coherent state for a single-mode field from Gerry and Knight, Introductory Quantum Optics page 51.
The Hamiltonian is given by $\hat{H}...
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Why are coherent states of harmonic oscillators called "coherent"?
Why are coherent states of the harmonic oscillator called coherent? Coherent in what sense? Why are these states so special/useful?
From Wikipedia:
In physics, two wave sources are perfectly ...
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Inverting squeezing and displacement operators: how do I turn $D(\alpha)S(\xi)$ into $S(\xi')D(\alpha')$?
This question is about inverting the product of squeezing operator and a displacement operator in the following way:
I have $D(\alpha)S(\xi)$ and I'd like to turn it into $S(\xi')D(\alpha')$,
where
$$...
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What does coherent superposition mean?
There is only one coherent state: $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle
$$
Also, a pure state does not mean a coherent state.
But what does ...
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Why use coherent state path integral? What is its motivation or goal?
In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert ...
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Boundary conditions in holomorphic/coherent state path integral
Consider the holomorphic representation of the path integral (for a single degree of freedom):
$$ U(a^{*}, a, t'', t') = \int e^{\alpha^{*}(t'') \alpha(t'')} \exp\left\{\intop_{t'}^{t''} dt \left( -a^...
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Harmonic oscillator coherent state expectation values
I'm looking to calculate the expected values of a coherent state (of a harmonic oscillator) evolving in time. I know that the $x$ and $p$ expectation values are as in classical motion, but I'm ...
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Definition of spatial and temporal coherence in QM?
It is often said that lasers are spatially and temporally coherent. Is there a simple definition of spatial and temporal coherence in the language of quantum mechanics? More specifically, can these be ...
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Why does $\langle a_-\alpha|\alpha\rangle = \alpha $ for harmonic oscillator?
Given $|\alpha\rangle$ a coherent state, why does $\langle a_-\alpha|\alpha\rangle = \alpha$? Doesn't the ladder operator lower the $\alpha$ so that it becomes $\sqrt{\alpha}\,\delta_{\alpha, \alpha_{...
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Coherent State, Unitary Operators, Harmonic Oscillator
Consider the operator:
$$O = e^{\theta(a^\dagger b - b^\dagger a)}$$
where $\theta$ is a constant.
$O$ is a unitary operator.
$a$, $a^\dagger$, $b$, and $b^\dagger$ are ladder operators for two ...
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What is a coherent state?
In quantum mechanics, what exactly is a coherent state, and how does it differ from other states?
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Scalar product of coherent states
We suppose for simplicity we have a 1D oscillator, but this is a question about the general CCR in oscillators, second quantization, quantum field theory etc.
We know coherent states form a non-...
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