# Questions tagged [coherent-states]

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### Coherent States and ladder operators

I am working on a problem involving ladder operators and coherent states. I know that $$a|z\rangle=z|z\rangle$$ and $$\langle z|a^\dagger = \langle z|z^*.$$ I am wondering how I could figure out ...
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### Creation and Annnihilator Operators: generality and meaning

I am studying my fisrst course in quantum mechanichs where we treated the example of the Harmonic Oscillator through the Weyl Heisenberg Spectrum Generating Algebra Method. In that context we ...
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### Laser power and coherent state amplitude

How it is possible to relate the power $P$ of a laser light with frequency $\omega$, to the amplitude $\alpha$ of its description as a coherent state $\vert \alpha \rangle$ ? For a massive particle in ...
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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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### Spread of the (smeared) field observable under time-evolution

Setup: Essentially, I'm interested in performing an analysis which is completely standard in QM, but I've never seen the analogue in QFT: Given I measure a system to have some value of its canonical ...
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### Constructing Gravitational waves with gravitons

Suppose I want to construct a gravitational wave as a coherent sum of many gravitons. It's easy to think of what the frequency distribution of the gravitons should be, as all the LIGO discoveries more ...
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### Experimental aspects of squeezing of photons and phonons

I know that photons have been squeezed to 15 dB and phonons have been squeezed by 7.2 dB. Spins have been squeezed by 20 dB. Why is it so hard to squeeze the states of particles? If I wanted to ...
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### Fock states and beam splitters

A classical beam splitter divides incoming light into two parts according to the reflection and transmission coefficients. A quantum beam splitter on the other hand, can be modelled using Fock states,...
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### Majorana Fermion Coherent States

I was wondering if there are coherent states for Majorana operators, so, states that fulfill the relation \begin{align} \hat{\gamma}_A |a,b\rangle &= a |a,b\rangle \\ \hat{\gamma}_B |a,b\...
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### Coherent states of the form $|{-\alpha}\rangle$

I've a brief question about coherent states in quantum mechanics. As everyone knows, a coherent state is just the proper state of the anhilitation operator $a$, thus they're defined with the ...
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### What is the electric field due to a coherent radiation? Is it polarized?

What is the time-structure (i.e., how does the magnitude and direction change with time) of the expectation value of the electric field $\langle\textbf{E}\rangle(t)$ of a radiation field described by ...
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### Are Bi-photons and Fock States (with $N=2$) the same?

I've been researching about quantum states of light, and I came across with both terms. For what I understand of both, I think they are the same (entangled individual photons with same position and ...
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### Exponential of ladder operators acting on vacuum state [closed]

How would I solve expressions of the following nature: $$<0|e^{Vt(a+a^\dagger)}|0>$$ and $$<0|e^{\omega aa^\dagger t}|0>~?$$ My intuition is that I have to expand the exponent as a ...
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### Displacement operator action on exponential of ladder operators

How do I evaluate the following: $$D_{\alpha}^{-1} e^{-i\Omega aa^{+}t} D_{\alpha},$$ where $D_a$ is the usual displacement operator for coherent states $$D_{\alpha} = e^{\alpha a^{+} - \alpha^* a}.$$ ...
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### Time evolution of operators with explicit time dependence in case of time dependent Hamiltonian

In case of a time dependent Hamiltonian of the sort $$H=\frac{p^2}{2m}+\frac{1}{2}m \omega(t) x^2$$ I have solved for the time evolution operator using the Schrodinger equation and got $U(t,0)$. If, I ...
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### Operator in coherent state basis

I am reading "Introductory to Quantum Optics" by Christopher C. Gerry and Peter L. Knight but I don't understand a solution from which you can obtain the matrix elements of an operator in the number ...
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### Coherent States and their existence

In my Quantum Mechanic class, I have learned that to solve for any quantum system, we solve the time independent Schrodinger equation(for time independent Hamiltonian) and then apply the time ...
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### Determining the Greens function

I understand the basics of greens function. But here in this paper, i am not able to understand how have they solved for the Greens function. In particular, I don't get what $G_{R}$ and $G_{A}$ are....
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### Commutation relation coherent states

I am reading p. 159, chapter 4 of Condensed Matter Field Theory and I don't really get this commutation relation: They want to show that $\left[\hat{a}_i,\hat{a}_j^\dagger\right] = \delta_{ij}$. The ...
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### Classical analogy for why driving a quantum harmonic oscillator creates a coherent state?

If we drive a quantum harmonic oscillator (e.g. starting from its ground state) at its resonance frequency then it will not just create an excitation in the first excited state but will create a ...
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### Is the superfluid state a coherent state?

In the normal to a superfluid phase transition, U(1) symmetry related to particle number conservation is spontaneously broken which seems to imply that the superfluid state is a state in which there ...