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 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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Finding expectation value of $J^2_\phi(t)$ to calculate the spin squeezing parameter for the One Axis Twisting (OAT) model hamiltonian

I am trying to calculate the spin squeezing parameter $\zeta = \frac{\Delta \hat J_\phi(t)_{min}}{\sqrt{J/2}}$ from this paper. In order to calculate $\zeta$, the expectation value of $J^2_\phi(t)$ ...
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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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Transform two-mode squeezed state (TMSS) to its covariance matrix

The two-mode squeezed state can be written as: ${\left| \chi \right\rangle _{AB}} = \sqrt {1 - {\chi ^2}} \sum\nolimits_n^\infty {{\chi ^n}} {\left| n \right\rangle _A}{\left| n \right\rangle _B}$ ...
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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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1answer
52 views

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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48 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 ...
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1answer
67 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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73 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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58 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
102 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
857 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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1answer
880 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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414 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 $$...