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Questions tagged [quantum-optics]

A research field within general optical physics concerned with light and its material interaction: where light is modelled by full quantum mechanical description.

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Do the results of this laser experiment demonstrate nonlinear optical phenomenon?

In my photonics class, we conducted an experiment to observe the Beer-Lambert law and the effects of filters(absorption, transmittance, and reflection). We shined a red(632nm) 5mW Helium-Neon laser ...
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Normal ordering of operators: Commutator or no commutator [duplicate]

My exercise for a quantum optics course tells me to "find a normal ordering" for an Operator $\hat{O}(\hat{a},\hat{a}^\dagger)$, which is given as a (rather complicated) string of $\hat{a}$'s and $\...
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Why is EIT needed to story memory using rydberg atoms?

I was going through a paper explaining how the write-in and read-out efficiencies can be increased using cold atoms where they used Rydberg atoms, and mentioned that they were probed using EIT(...
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Spatial wave-function of a single photon and its measurement

In the last decade there were several papers claiming that they've measured a "transverse quantum state" / "quantum wave-function" / "spatial Wigner function" of a single photon: Measurement of the ...
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How to usefully calculate using “dark state polariton” framework?

I'm interested in looking at calculations related to storage of light in atomic systems. This paper discusses how these types of systems can act as "memories" by generating "dark state polaritons." ...
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Question about Homodyne detection

In this Review of modern physics, section "II. A.", optical homodyne detection is briefly reviewed. In equation (9), it is stated that the fields after the beam splitter are $$E_{1}=\frac{E_\text{L}+...
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The action of a lens on a point dipole (Fourier optics)

I want to model the action of a lens on radiation from a point dipole. I have found examples but am struggling to interrupt them. My knowledge of Fourier optics is that from the Helmholtz equation, $...
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Upper State Lifetime vs Exited State Lifetime vs Gain Recovery Time

Could any one explain differences between these three terms about semiconductors and semiconductor optical amplifiers.
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Is the polarisation field stimulated emission?

I'm told that polarisation happens due to the oscillation of an electric dipole and stimulated emission is due to the excitation of an electron between energy levels but both depend on the incoming ...
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Wigner phase space operator correspondence: how to order?

According to Gardiner-Zoller (Quantum Noise), operators acting on the density matrix can be mapped via e.g. (I'm taking Wigner space as an example, but the same holds for P and Q) $$a\rho\...
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How does weak measurement affect quantum state?

I'm trying to understand how to describe the quantum state after weak measurement using these two toy examples. Hopefully, these simple examples and your answer will help others who want to learn ...
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Tensor product of photon number states

I'm looking to compute the tensor product of photon number states. I suspect this is a fairly simple quantum optics problem, but am having the following problem. Consider a qubit which is in the ...
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Transient solution system of differential equations obtained from master equation

I have to solve the following equation (or at least obtain an approximate estimate) for the diagonal terms of the density matrix. We consider that the initial state is a coherent state $\rho_{n,n}(0)=...
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Derivation of Yurke-Stoler state

The evolution of a coherent state $\vert\alpha\rangle$ in a Kerr-nonlinear medium $H=\Omega (a^\dagger a)^2$ is given by $$ \vert \psi(t) \rangle = e^{-\vert\alpha\vert^2/2}\sum_{n=0}^{\infty} \dfrac{\...
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Why are single mode vacuum fluctuations important in Quantum Optics?

There answer here by @ACuriousMind explains that the vacuum fluctuations of a quantum field, free or interacting, always diverge irrespective of spin of the field. But in quantum optics, people ...
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Two-level system Hamiltonian from electric-dipole approx

After making the electric-dipole approx., I can express the interaction of a monochromatic field with angular frequency $\omega$ and a dipole moment ${\bf \mu(x)}$ as $V({\bf x},t) = - {\bf \mu(x)} \...
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Generic modes of light

Typically in second quantization one employs creation and destruction operators for modes which are eigenstates of the momentum: $a_{k}, a^{\dagger}_{k}$ where $k$ is the momentum eigenvalue. The "...
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Spontanous emission Hamiltonian model

I am looking for a clear (and not too long) model of spontaneous emission, for an atom modeled by a two level system in a cavity where the field is multimode I am looking for model bases on ...
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Coherent state under Kerr evolution

I have a bosonic mode associated to the usual operators $a$, $a^\dagger$. I'm interested in knowing the evolution of a coherent state $\vert \alpha \rangle = e^{\alpha a^\dagger - \alpha^\ast a}\vert ...
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Approximations in article on phonon-assisted emission

I am trying to reproduce the calculations from an old article by J.J. Hopfield (J. Phys. Chem. Solids, vol.10, pp.110-119 (1959) - A theory of edge emission phenomena in CdS, ZnS and ZnO - found here)....
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Why does the read-out efficiency increase when coupling an atomic ensemble to an optical cavity?

I went through a paper where it mentioned that the read-out efficiency of a quantum memory would be increased by coupling the atomic ensemble with an optical cavity. I think rydberg atoms were used to ...
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Wigner map of the product of two operators

Does anyone know how to prove that for the product of two operators $\hat{A}\hat{B}$ the Weyl-Wigner correspondence reads $$ (AB)(x,p) = A\left (x-\frac{\hbar}{2i}\frac{\partial}{\partial p}, p+\frac{\...
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Fourier transform of cross-spectral density space matrix elements

In order to derive phase space like equation of motion (e.g. the equation of motion for the Wigner function of a single particle in one-dimension), it is an advantage to work with the Fourier ...
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Can a laser ever run single mode without active stabilization?

So when we talk about the emission wavelength of a laser, what we actually mean most of the time is the central, brightest emission wavelength, e.g. 852 nm on some diode laser. When we look at this ...
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Exercise in Loudon's Quantum Theory of Light

This is problem 3.3 in Loudon's Quantum Theory of Light. A prerequisite for this is problem 3.2. I will state both of them here. 3.2 : Consider the beam of light produced by excitation of two ...
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Effect of complex refractive index on reflectivity in a periodic structure?

I'm studying the effects of absorption in a 1D photonic structure with repeating alternate layers (a Distributed Bragg Reflector). To include absoprtion effects, the refractive index is defined as $...
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Cavity optomechanics Hamiltonian

In cavity optomechanics the radiation pressure exerted by light moves a mirror in a cavity. Because of that the resonance frequency of the cavity changes due to change in length of the cavity (cavity ...
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How can one get the density operator from the characteristic function?

To solve analytically the master equation of two qubits interacting with a cavity mode through their environment we use the charactristic function, $$\chi (\beta)=\operatorname{tr}[\rho D(\beta)],$$ ...
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Does a polarizer affect both entangled photons or only one?

Suppose you have two polarization-entangled photons A and B in the following state: \begin{equation} \Phi=\frac{1}{\sqrt{2}}\bigl(\left|H_{A},H_{B}\right\rangle + \left| V_{A},V_{B}\right\rangle\bigr)...
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Rydberg EIT Off of Single-Photon Resonance

In the phenomenon of electromagnetically induced transparency (EIT), two long-lived atomic states $|1\rangle$ and $|3\rangle$ are coupled by means of a third state $|2\rangle$ of relatively short ...
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Is squeezed state quantum?

The wigner function of squeezed state has no negative values. And as far as I know a nagative value is an indecator of quantum effects. So does that mean a squeezed state is a classical light?
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Why doesn't there exist a wave function for a photon whereas it exists for an electron?

A photon is an excitation or a particle created in the electromagnetic field whereas an electron is an excitation or a particle created in the "electron" field, according to second-quantization. ...
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Can we write the Quantum Fidelity between two density operators in terms of Quasi-Probability Distributions: $P$, $Q$ and $W$?

Quantum Fidelity between two density operators, $\hat{\rho}$ and $\hat{\sigma}$, is given by $F(\hat{\rho},\hat{\sigma})=\left(Tr\sqrt{\sqrt{\hat{\rho}}\hat{\sigma}\sqrt{\hat{\rho}}}\right)^2$, where $...
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Photo-electric effect with light reflected from a blue wall

Suppose we have a metal which has a work function corresponding to yellow. Obviously, if light with frequency greater than yello is made to fall on it, it would show photo-electric effect.Now, ...
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Lindblad and Input-Output Formalism in Quantum Optics

I'm confused about how to apply the Lindblad formalism and the input-output formalism in practice, and how one goes between the two. Suppose I have a cavity (C) coupled to a reservoir (R), with the ...
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Plotting quadrature uncertainties in phase space

In most books like in the picture given below, the uncertainties regarding quantum states like coherent and squeezed states are represented in phase space plot by some area enclosed within a circle or ...
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“Interaction-Free” measurement involving statistical mixtures

What happens in the standard "interaction free measurement" when the detector connected to a bomb is replaced with attenuation (where light is lost through a semi-transparent medium)? Consider the ...
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What does it mean to Fourier transform a ladder operator (in the input-output formalism)?

I am currently trying to get my head around the input-output formalism. In describing the input-output formalism (link) , Gardiner and Collett take ladder operators in the Heisenberg picture and ...
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Calculating Field moments of two mode squeezed state

I am reading through a paper (EDIT: Paper is here) and I actually want to rigorously go through their calculations. I am having some issues, For a two mode squeezed state given by: $$|\psi\rangle = ...
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polarization of ordinary light, laser and photons of atomic transition

The light from thermal sources such as a light bulb is unpolarized but the one from a laser is polarized. Why? Is a photon emitted in an atomic transition linearly or circularly polarized and a ...
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Do polarizers also shift the phase of light?

When does passing through a polarizer change phase besides just changing polarization? Consider three cases: A polarizing beam splitter (PBS) is a clear case. Horizontally polarized light leaves ...
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Description of quantum state of entangled photons after polarizer

I'm wondering if anyone can help me understand how a polarizer changes the quantum state of two polarization-entangled photons. I haven't found a clear description in the literature. Suppose you have ...
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Quantum Optics: entropy doesn't change!

I'm reading a paper and without any justification, the author said: Consider a single-mode cavity field initially prepared in a coherent state $|\alpha_0 \rangle$. It leaks out of the cavity through ...
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Rotating wave approximation and classical Rabi oscillations: why don't the fast oscillating terms seem negligible in the initial frame?

I am trying to understand better the rotating wave approximation (RWA). Consider an atom modeled as a two level system, interacting with a Laser. I have the dipole momentum operator $$\vec{D} = d \...
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59 views

What's special about infinite squeezing in continuous-variable quantum information? [closed]

Quantum error correction for continuous-variable systems using linear optics only works for the especial case of infinite squeezing? what's especial about infinite squeezing? (For example this paper ...
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Calculating the $g^{(2)}$ correlation function

I want to make sure I am doing this right. I am also lost on how to continue at the end I have to calculate $$g^{(2)}(0) = \frac{G^{(2)}(0)}{|G^{(1)}(0)|^2}$$ for the following states (1) $$\...
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If electric fields add, and intensity is proportional to $E^2$, doesn't superposing light violate energy conservation?

We know that the energy in a wave goes as electric field amplitude squared($E_0^2$) as given by poynting vector but the amplitude of electric fields are added linearly. To see why this creates a ...
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Check if total angular momentum is well-defined for a particular photon wave function

I have an exotic state, which can be expressed in a way: $$\pmb{A}(\rho, \phi, z; t)= \hat{e}_{\pmb k, \sigma} A_0 e^{i (k_z z - m \phi +\omega t)}$$ where $A_0$ is a scalar amplitude of the EM-...
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What's the difference between twisted light and light of circular polarization?

Circular polarization: https://en.wikipedia.org/wiki/Circular_polarization Orbital angular momentum of light: https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light From point of view, ...
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Photon number representation of a position eigenstate

I wanted to calculate the photon number representation of a position eigenstate, so I developed as follows. \begin{align} \vert x\rangle =\sum_{n}\vert n\rangle\langle n\vert x\rangle =\sum_{n}\...