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 ...
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Normalization of squeezed vacuum for QFT in the black hole background (Hawking radiation)
In the context of BH evaporation, one can represent an initial vacuum as the final state containing particles, following Polchcinski (2016, page 9)
$$|0\rangle_{a}=\mathcal{N} \exp \left(\int_{0}^{\...
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Theoretical description of a two-mode squeezed state with continuous modes
Given two distinguishable modes $a$ and $b$ with $[a,a^\dagger]=1$ and $[b,b^\dagger]=1$ and $[a,b^\dagger]=0$, the two-mode squeezed vacuum state is given by
\begin{equation}
\exp (\zeta^* a b - \...
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two mode squeezed state in coherent state basis
It is known that, in the Fock basis, the two-mode squeezed state takes the form
$$
\vert TMSS \rangle = \sum_n \dfrac{(-e^{i\phi} \tanh(r))^n}{\cosh(r)} \vert n,n \rangle \;.
$$
An other possibility ...
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Interpreting Hamiltonian of single-mode squeezing
Hamiltonian represents energy. I can understand this when considering about harmonic oscillator, whose Hamiltonian is expressed as:
$$ \hat{H} = \frac{1}{2m}\hat{p}^2 + \frac{m\omega^2}{2}\hat{q}^2$$
...
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Can I create squeezing with a $P^2$ interaction?
One approach to squeeze light is through the one-mode squeezing operator, which can be written as $e^{-i H t}$ with $H \sim (a^2 - (a^\dagger)^2)$. My question is, can I create squeezing with $H \sim ...
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Photon number basis representation of a displaced single-mode squeezed thermal state
I am looking for a relatively clean expression for matrix elements for states of the form $$\rho_{\alpha,r,\bar{n}} = \hat{D}(\alpha)\hat{S}(r)\rho_{th}(\bar{n})\hat{S}^\dagger(r)\hat{D}^\dagger(\...
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Normalising squeezed position eigenket?
I want to find the effect of squeezing operator $S(r) = \exp \big[r(\hat{a}^2 - \hat{a}^{{\dagger}^2})\big]$
on $|q\rangle$ i.e. $S(r)|q\rangle$.
I proceed as follows:
$$S(r)\hat{q}|q\rangle = S(r)...
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Derive explicit expression of squeezed vacuum state in the Fock basis
I'm learning quantum optics, and I'm starting to manage boson algebra.
In particular, as a pure exercise, I would like to express a squeezed vacuum state in the Fock basis, which, according to ...
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Find the Bogoliubov transformation $b=SaS^\dagger$ induced by the squeezed operator
A definition a bogoliubov transformation is defined as $$b=ua+va^\dagger~,~ b^\dagger=u^*a^\dagger+v^*a$$
But, using squeeze operator $$S=\exp{\left[\frac{1}{2}(z (a^\dagger)^2-z^*a^2)\right]}$$ we ...
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Inverting squeezing and displacement operators: how do I turn $D(\alpha)S(\xi)$ into $S(\xi')D(\alpha')$?
This question is about inverting the product of squeezing operator and a displacement operator in the following way:
I have $D(\alpha)S(\xi)$ and I'd like to turn it into $S(\xi')D(\alpha')$,
where
$$...
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