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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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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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\...
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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 ...
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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(\...
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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)...
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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 ...
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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 ...
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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 $$...