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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.

In quantum physics, light is in a squeezed state, if its electric field strength Ԑ for some phases ϑ has a quantum uncertainty smaller than that of a coherent state: "squeezing" thus refers to a reduced quantum uncertainty.

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How can I write a Gaussian state as a squeezed, displaced thermal state?

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} \hat{D}^\dagger(\alpha) \hat{S}^\dagger(\zeta)…
P. Plowman
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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 can claim that $$b=SaS^\dagger $$ is also a…
quirkyquark
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Normal ordering of passive linear optics

I am trying to normally-order operators in quantum optics. Having normally-ordered expressions is useful when evaluating expectation values in quantum optics, as most of the times we can write the states in terms of coherent states, meaning that the…
Luca Bianchi
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Squeezed Coherent State Overlap and Expectation Values

I am unfamiliar with quantum optics and have recently been struggling to evaluate some expectation values involving squeezed states. Any help and guidance would be greatly appreciated! The matrix elements I am considering boil down to the following…
Green
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Explicit Expression of $S_2(\zeta)$ on a general Fock State?

I would like to know the explicit expression of the two-mode squeezing operator $\hat{S}_2(\zeta)$ acting on a general Fock state $|p,q\rangle$, without including any additional operators in the expression. $\hat{S}_2(\zeta)$ is the two-mode…
Xuemei
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Displacement operator similarity transformation using the squeezed operator

I have been trying to get the analytical expression for the Wigner function of squeezed vacuum states. Using the characteristic function representation, the WF can be written as $$W(\alpha)=\frac{1}{\pi}\int…
Santiago Bermúdez
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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 diverge for integers $k>2$ and bosonic operators…
Quantum Mechanic
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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 $$D(\alpha)=e^{\alpha a^\dagger-\alpha^* a}…
MarcO
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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 $H \sim P^2 \sim (a-a^\dagger)^2$ ? Is this described…
m137
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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 $$\rho_{\alpha,r,\bar{n}} = \hat{D}(\alpha)\hat{S}(r)\rho_{th}(\bar{n})\hat{S}^\dagger(r)\hat{D}^\dagger(\alpha),$$ where $\hat{D}(\alpha)$ is the displacement…
Max Chemtov
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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 Weedbrook et al. is given by: $$|0,r\rangle =…
steg
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Precise form of two-mode squeezed state

Starting with the two-mode squeezing operator $ S_2(\xi) = \exp \left( \xi^* a_1 a_2 - \xi a_1^\dagger a_2^\dagger \right)$, we can factor it into [1] $$ S_2(\xi) = \frac{1}{\cosh r} \exp\left( -a_1^\dagger a_2^\dagger e^{i\varphi} \tanh r\right) …
lionelbrits
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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 squeeze operator is $ \hat{S} (\zeta) = \text{exp}…
MementoMori
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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}-\alpha^{*}e^{i\theta}\sinh{r} \tag 1 \end{align} I came…
HypnoticZebra
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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 being un-determined in a sense of such phase…
MsTais
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