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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questions
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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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35 views
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 ...
2
votes
1answer
45 views
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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Is this two-mode squeezed vacuum state for a continuum of modes physical?
In the book 'Methods in theoretical quantum optics' the squeezing operator for a continuum of modes is given by
\begin{equation}
S \equiv S [\{ \zeta (\omega)\}] = \exp \bigg[ -\frac{1}{2} \int_0^ {2\...
3
votes
1answer
62 views
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 ...
2
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0answers
35 views
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 $$\rho_{\alpha,r,\bar{n}} = \hat{D}(\alpha)\hat{S}(r)\rho_{th}(\bar{n})\hat{S}^\dagger(r)\hat{D}^\dagger(\...
0
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1answer
85 views
Normalising squeezed position eigenket?
I want to find the effect of squeezing operator $S(r) = \exp \big[r(\hat{a}^2 - \hat{a}^{{\dagger}^2})\big]$
on $|q\rangle$ i.e. $S(r)|q\rangle$.
I proceed as follows:
$$S(r)\hat{q}|q\rangle = S(r)...
2
votes
1answer
698 views
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 ...
6
votes
1answer
779 views
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 ...
2
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2answers
335 views
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
$$...
