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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.

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Can entanglement cause interaction in a non-interacting system? [closed]

For example, spins of atomic vapor are non-interacting, but they can be entangled by light. If we first use light to prepare these spins into an entangled state, and then let these spins evolve, can ...
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Arbitrary first and second moment for squeezed spin coherent state

Consider a spin coherent state of $N$ spin-$1/2$ atoms polarized in the $+x$-direction, denoted $\lvert \frac{\pi}{2},0 \rangle$. Now, squeeze this state in the $+z$-direction with a one-axis twisting ...
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Free evolution of coherent states

Is there a closed formula to express the time evolution of coherent states in absence of the potential term (only kinetic energy)? The coherent state $|\alpha \rangle$ is defined by $$\hat a|\alpha \...
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Quantum sensing using Ion penning traps[[ODF, Dicke states and pi/2 pulse]]

I am reading the article https://www.science.org/doi/full/10.1126/science.abi5226 It's about Quantum sensing in ion penning traps. Question 1. Does the axial mode of the penning trap have nothing to ...
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Expected position of squeezed state

I want to compute the expected position $\langle \alpha,r | x | \alpha, r \rangle$ of a squeezed state defined as $$ | \alpha, r\rangle = S(r)|\alpha\rangle\ , $$ where $S(r)$ is the operator $$ S(r) =...
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Multimode squeezed operator

Given CCR (bosonic) algebra, with creation / annihilation operators $a_{i}^{\dagger}, a_i$ acting on a single particle Hilbert space $\mathbb{h}$, let's introduce the multimode squeezed operator for $...
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Entropy of squeezed vacuum state

Objective: I am trying to familiarise myself with quantum entropy for squeezed vacuum states. Context: As a previous excercise, I have evaluated von Neumann entropy $\mathcal{S}(\widehat{\rho})=-\text{...
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Spin-squeezing parameter for the coherent spin state

Let us consider the following definition of the spin-squeezing parameter $$ \xi^2 = 2 \frac{\left( \Delta S_{\vec{n}_1} \right)_{\min}^2}{\left| \langle \vec{S} \rangle \right|}, $$ where the value in ...
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Does squeezed light gravitate repulsively? [closed]

Since there are alternate regions of positive and negative energy densities in squeezed light, does that mean that the negative energy density parts gravitate repulsively? Since the stress energy ...
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How does squeezed multimode light, where the modes are entangled, behave in a beamsplitter?

I understand how to work with and describe squeezed single modes going through a beamsplitter, and can conceptually talk about what's happening. If I now take a source of squeezed light that has ...
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What is the state vector of a displaced (single-mode) squeezed vacuum state in the quadrature basis?

I've been hunting through the quantum optics literature for the displaced squeezed state written in the $q$-quadrature basis ($p$-quad would be fine too, since it's just a Fourier transform), but it ...
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Mapping between quadrature squeezing and photon-number squeezing

It is possible to get quadrature squeezed light where on one quadrature the uncertainty is less than the of a coherent state while in the other one, orthogonal to it, it is larger. Is it possible, by ...
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Is Fock state a squeezed state?

Is Fock state a squeezed state? I assume that 'yes', that is how it beats shot-noise limit the next question is that what is its complementary variable? Basically is delta N -> delta p what is its ...
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Calculating the second-order correlation function for a 2-mode squeezed vacuum state

I am trying to calculate the second order correlation function $g^2(τ)$ at τ (delay) equal to zero, for a 2 modes squeezed vacuum state that is given by: According to the following paper https://www....
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How to creat a squeezed-state light in integrated-photonic devices

I am interested in studying (squeezed-state light in integrated-photonic devices by means of four-wave mixing). I would like to be completely familiar with the working method and all the devices that ...
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Which operator can implement a fermionic Bogoliubov Transformation?

In bosonic systems (for example in Quantum Optics), two-mode Bogoliubov transformations are implemented via squeezing operators as $$\hat{S}_2(\xi)=\exp(\xi^{*}\hat{a}\hat{b}-\xi\hat{a}^\dagger\hat{b}^...
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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}{\...
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Phase modulation of beat notes between two large phase different source

I am working on the following experiment: I send a CW laser (whose path has a fiber stretcher can be modulated by a function generator to change fiber length periodically) and a Menlo source (...
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Transformation on Squeeze Operator?

Yesterday, my professor briefly glossed over the following computation without details, and I haven't been able to figure it out for myself. How would I compute $$(\cosh (q) \hat{a} + \sinh (q) \hat{a}...
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What is the difference between commutator of exponential with an operator and the Hadamard's formula? [closed]

I need to compute this: $$ [ e^{-\sigma K_+}, K_{-} ] $$ and $K_{\pm} $ has the following commutator relations $$ [K_0, K_{\pm} ] = \pm K_{\pm}$$ $$ [K_{-}, K_{+} ] = 2K_0 .$$ I tried to expand the ...
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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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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}^\...
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