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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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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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95 views

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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2answers
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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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1answer
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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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157 views

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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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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51 views

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}\...
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Furry's theorem and spontaneous parametric down-conversion

In spontaneous parametric down-conversion, a single photon interacts with a nonlinear medium to produce a pair of lower energy photons. It is observed that energy, momentum, and orbital-angular-...
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Evolution of the operators in Mach-Zehnder interferometer

I have trouble understanding how the operators that change the initial state, change when adding extra splitters. As an example, I will use an idealized Mach-Zehnder interferometer where the splitters ...
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Can we always find a Quasi-Probability distribution representation for density operator of any physical system?

For a pure, quantum optical system, the QPD formalism is straightforward and possible because of the existence of coherent states. The question is whether we can find coherent states for any quantum ...
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What is the principal cause of diffraction?

I have found another question similar to mine here. But I want to know why does diffraction of light happen in the first place. I have found other resources on google which explain the topic partially ...
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Does it give sense to speak about field distribution of a single photon?

A Point source of light has radial symmetry. If the source gets attenuated so that only a single photon is leaving each hour, can I still argue, that the field of the single photon is radial but the ...
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The role of the harmonic oscillator eigenfunctions in quantum optics

In quantum optics we quantize the electromagnetic field and describe it using the harmonic oscillator model and the formalism of annihilation and creation operators. For the electric field operator we ...
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Scalar product of squeezed coherent states

Consider two states of the type $|\alpha,\xi \rangle = \hat{D}(\alpha) \hat{S}(\xi) |0\rangle$, where $D$ and $S$ are the displacement and squeeze operators, respectively, and $|0\rangle$ is a 1D ...
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What is the interpretation of a photon in quantum mechanics? [duplicate]

Without considering the absorption and emission, can we define a wavefunction for a photon? If so, can we ever have monochromatic photon? Or is it equivalent to the free particle? In that case, would ...
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Delayed choice experiment for misaligned Mach-Zender interferometer

In quantum Mach-Zender interference, a single photon can be prepared to have a 100 percent probability of traveling through a particular path (that classically would be a 50 percent chance). This can ...
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1answer
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How to bound the dimension of infinite dimensional Hilbert space?

Lets say I have a density matrix $\rho$ encoded into a physical system. Lets say I can have access to as many copy of $\rho$ as I want. I perform hmodyne detection on the copies in phase and out of ...
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Projective measurement using two mode squeezed state?

Let me define two mode squeezed states as $ \left | \xi \right>_n=\exp\left(\xi \hat{a}^\dagger \hat{b}^\dagger-\hat{a} \hat{b} \xi^\star\right)\left | n,0 \right>$ where $\left|n,0\right>$ ...
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Material on Coherent Control

I'm looking into coherent control for a new module, I was hoping to find some material that is beginner friendly be a book, website, video etc. . All books I have found on my own all expect some ...
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Shot noise in optics

There are many explanations to be found about shot noise in optics, but the answers I find are incompatible. There are three ways shot noise in optics is explained. (Note that according to ...
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1answer
79 views

Laser power and coherent state amplitude

How it is possible to relate the power $P$ of a laser light with frequency $\omega$, to the amplitude $\alpha$ of its description as a coherent state $\vert \alpha \rangle$ ? For a massive particle in ...
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1answer
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Non deterministic quantum gates

There are situations (e.g. in quantum optics) where local non-unitary operators can be defined. In these cases, people say that the operation is non-deterministic. Could you please clarify how the ...
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Eigenstates of the creation operator

We know that coherent states $\vert\alpha\rangle$ are eigenvectors of the annihilation operator $\hat{a}$, i.e. $$ \hat{a} \vert\alpha\rangle = \alpha \vert\alpha\rangle $$ while the creation operator ...
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Single Photon though prism

What will happen to a single photon when it goes through a prism? Will it just be deflected in the direction related to its frequency? I made this drawing for better understanding, here if I place a ...
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Calculate variance of number of photon counts in detector with second coherence function

Knowing the second coherence function of the light beam that's normally incident to a detector how do can you find the variance of the number of counts $n$ received in the time interval $T$.
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Blackbody photon variance and number of modes [closed]

In an experiment to measure the photon statistics of thermal light, the radiation from a black- body source is filtered with an interference filter of bandwidth 0.1 nm centered at 500 nm, and allowed ...