# Questions tagged [squeezed-states]

Light with reduced quantum uncertainty: its electric field strength Ԑ for some phases ϑ has a quantum uncertainty smaller than that of a coherent state. Do not use for plain coherent states.

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### Squeezed vacuum state

From: Loudon, Rodney. The quantum theory of light. OUP Oxford, 2000. Consider the single-mode quadrature-squeezed vacuum state defined by $| \zeta \rangle = \hat{S} (\zeta) | 0 \rangle$ where the ...
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### Normal ordering of an exponential [duplicate]

I would like to recalculate Eq.(2.4) in PRA, 31,4,(1985), which expresses the exponential of operators as a normal ordering form. This equation reads \begin{equation} D=e^{\alpha K_{+} - \alpha^{*} K_{...
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### Distribution function for squeezed light as a function of energy

For bosons in a thermal state, I know that the Bose-Einstein function reads $$n(\epsilon_n)=\frac{1}{e^{\beta \epsilon_n}-1}$$ where $\epsilon_n$ is the energy and $\beta$ is the inverse temperature. ...
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### Generalized squeezing operators: Are analytic vectors required for unitarity?

The paper Impossibility of naively generalizing squeezed coherent states proves that the generalized squeezing operators $$U_k(z)=\exp(z a^{\dagger k}-z^* a^k)$$ have some of their matrix elements ...
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### Wigner Function of Squeezed Vacuum state

I am trying to figure out how to derive the wigner function of the squeezed vacuum state, \begin{align} W(\alpha,\alpha^*)& =(2/{\pi})\times{e^{-2|\alpha'|^{2}}}\\ \alpha'& =\alpha \cosh{r}-\...
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### Squeezed quantum states of light

I am a beginner in quantum optics and started from reading the Fox's book. I got to Ch.7, where there is a discussion about the amplitude-squeezed states. I am really puzzled by the effect of phase ...
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### Derivative of a multimode squeezed vacuum state

Let us suppose we have a multimode squeezed vacuum state of the form \begin{equation} |\psi\rangle = \exp[A]|0\rangle= \exp \big[\sum_{ij}G_{ij}(t) (a_i a_j -a_i^\dagger a_j^\dagger)\big] |0\rangle\...
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### How to resolve the action of an operator in a power?

I'm deriving the action of the squeezing operator on a non-vacuum Fock state and I have almost finished but can't work out how to apply an operator that is stuck in the power of a constant, not an ...