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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Coherent states and thermal properties
I am reading a paper called Thermodynamics of Coherent States and Black Hole Entropy, written by Bashkirov and Sukhanov. If I understand correctly, they define a coherent state by the equation
$$a|d\...
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What defines "minimal coherence" as a condition for the emergence of stationary interference in a chaotic wave field?
Consider the following observations:
A superposition of two electromagnetic waves with different frequencies will never produce visible interference patterns. Such waveforms will produce ...
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Advantage of coherent path integral
I think(?) I am quite familiar with path integral over phase space, but not familiar with the coherent state path integral. What is the advantage of this coherent path integral besides the usual path ...
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Homodyne Detection of Photon Number States
I'm currently trying to understand why you can detect the signal of single photons with homodyne detection. I found that the difference current $i_{34}$ is given by
$$i_{34}\sim -2 ⟨\Psi|_1⟨\alpha|_2\...
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Evolution of Quantum Harmonic Oscillator into coherent state
Why does a quantum harmonic oscillator that is driven by an electromagnetic wave in cosine form with its frequency equal to the resonance frequency of the oscillator evolve from its groundstate into a ...
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Coherent state basis
I'm learning about coherent states in a more in depth lesson the the quantum harmonic oscillator. Coherent states are eigenstates of the lowering operator. In my head this is just saying: since any ...
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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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Driven Quantum Harmonic Oscillator
Consider the Hamiltonian
$$
H = \frac{p^2}{2} + \frac{ x^2}{2} - F(t) x.
$$
This is essentially a time dependent shifted harmonic oscillator, which can be represented as
$$
H' = \frac{p^2}{2} + \frac{...
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Is the wave function of a coherent state just a Gaussian density? [closed]
The formula giving the wavefunction of a coherent state looks pretty complicated, but am I correct in saying it is just a Gaussian distribution function? i.e.
$$\psi(x) = \frac{1}{\sigma \sqrt{2\pi} } ...
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Non-uniqueness of Glauber-Sudarshan $P$-function
For a state $\rho$ acting on single bosonic mode with coherent states $|\alpha\rangle$, one can always define a $P$-function to furnish a diagonal representation of the state in the coherent-state ...
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Trouble proving Wigner function identity [closed]
I am trying to prove $$\int d^2 \alpha W(\alpha)=1$$ where $W(\alpha)$ represents the Wigner funcion. However, I have trouble solving it. I tried solving it as follows but I think I have done some ...
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Application of Schur's lemma to proving the completeness of coherent states
I am studying many-body path integral through Altland & Simons's textbook called "Condensed Matter Field Theory," and the book states the completeness of the coherent states as below:
$$\...
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Overcompleteness of coherent states
I am trying to show that the basis of coherent states,
$$ |\phi\rangle =e^{-\sum_{\alpha'}\phi_{\alpha'}a^\dagger_{\alpha'}}|0\rangle, \quad\text{ where }\quad a_\alpha|\phi\rangle=\phi_\alpha|\phi\...
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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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Fermionic coherent state in Fock representation
The notes I follow define a Fermionic coherent state $|c\rangle$ as
\begin{equation}
\hat{c}|c\rangle=c|c\rangle
\end{equation}
where $\hat{c}$ is the Fermionic annihilation operator and $c$ is a ...
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