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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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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Countable basis of coherent states used to express coherent states
Let $|\alpha \rangle$ be coherent state in Fock space. According to the paper "Coherent-state representation for the photon density operator" by Cahill (Phys. Rev. 138, B1566 (1965), §VII), every ...
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How are coherent states in the real world made?
Coherent states are quantum states that are said to act "as classically as possible". You can define coherent states for the harmonic oscillator, or more generally for any collection of harmonic ...
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Is the vacuum state a coherent state?
I'm asking because I got introduced to the state $|0\rangle$ as a fock-state. Nevertheless:
$$
\hat{a} |0\rangle = 0 |0 \rangle
$$
It is an eigenstate of $\hat{a}$ with eigenvalue $0$, and it can be ...
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Why is laser light described by a coherent state?
This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.
I have read the papers by Mølmer, Bartlett et al., Wiseman, and ...
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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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How to compute expectation value $\langle e^{iH}\rangle$ for quadratic Hamiltonians?
I have a rather basic, but actually non-trivial question:
We consider a bosonic system with creation operators $\hat{a}_i^\dagger$ and annihilation operators $\hat{a}_j$ and vacuum state $|0\rangle$ ...
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Eigenstates of the creation operator
We know that coherent states $\vert\alpha\rangle$ are eigenvectors of the annihilation operator $\hat{a}$, i.e.
$$
\hat{a} \vert\alpha\rangle = \alpha \vert\alpha\rangle
$$
while the creation operator ...
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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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Calculating free energy from coherent state path integral
Edit: It turns out that problem encountered in this question is not limited to BdG Hamiltonians.
I am having trouble in using the coherent state path integral approach to calculate the free energy. ...
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Equivalence between grassmann fermion states and $SO(2N,\mathbb{R})$ fermion coherent states
I am importing this question from https://www.physicsoverflow.org/39342/equivalence-between-grassmann-fermion-mathbb-fermion-coherent
Cahill and Glauber in the paper 'Density operators for Fermions' ...
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In what sense are spin coherent states "classical"?
Spin coherent states are often introduced as "the most classical states of a finite-dimensional system", or as the analogous of coherent states of light for finite-dimensional systems. See e....
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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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Derivation of $P$ representation of the thermal density operator
I'm trying to derive the P representation for the thermal state
$$
\rho = \sum_{n=0}^\infty \frac{\mathrm{e}^{-\beta \omega n}}{Z} |n\rangle \langle n |
$$
where $\beta$ is the inverse temperature, $...
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Basic question on holomorphic formalism in QM
In my course, the teacher introduced us the holomorphic formalism in Quantum Mechanics.
What I basically understood is that initially, we work in the Hilbert space of square integrable functions $\...
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