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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57 views

Non-quantum explanation for Mach-Zehnder interferometer effect

The phenomenon of all photons being detected at only one detector seems quite reasonable to me, classically. If a photon gets deflected at the first beam splitter for whatever reason, it gets ...
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Can a photons wavelength be independent of its associated temporal wavefunction?

Typically a traveling photon is described as being in a superposition of frequency modes $\hat{E} = \int g(\omega) a^\dagger_\omega d\omega + h.c. $ where often the $g(\omega)$ is some kind of pulse. ...
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44 views

Matrix representation of the $\mathfrak{su}(1,1)$ $K$ operators

I am trying to find the matrix representation of the $\mathfrak{su}(1,1)$ $K_{-}$, $K_{+}$ and $K_0$ matrices commonly used in quantum optics defined as $$K_{-}=\frac{1}{2}\hat{a}\hat{a},\quad K_{+}=\...
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How to represent the evolution operator of Jaynes-Cummings model interaction hamiltonian in two level basis

I am reading "Quantum optics" by Gerry and Knight. By the JCM(Jaynes-Cummings model), the interaction hamiltonian of the field and the atom can be written $ \hat{H}_I = \hbar \lambda(\hat{a}\...
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How can one use the Kubo Formula to calculate the optical conductivity for superconductors?

In the 1993 paper titled "Theory of optical conductivity in BCS superconductors", the authors derive an exact relation for the optical conductivity of a BCS superconductor, but this only ...
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Single-mode electromagnetic field on cavity of length $L$

I'm studying C. Gerry and P. Knight's Introductory quantum optics, and in section 2.1 they give the solution of the EM field to the Maxwell equations on a cavity on length L. I'm a little troubled of ...
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Separation of occupancy and propagation in single mode optical fibre

How can we separate the propagation mode and occupancy mode for light propagation of a single mode optical fibres?
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1answer
59 views

How does the Weyl transform take into account which quasiprobability distribution was used?

I'm trying to get a better understanding of the Weyl correspondence which, as described e.g. on Wikipedia, gives "an invertible mapping between functions in the quantum phase space formulation ...
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36 views

Why does the star product satisfy the “Bopp Shift relations”: $f(x,p)\star g(x,p)=f(x+\frac{i}{2}\partial_p,p-\frac{i}{2}\partial_x) g(x,p)$?

In (Curtright, Fairlie, Zachos 2014), the authors mention (Eq. (14) in this online version) the following relation, known as "Bopp shifts": $$f(x,p)\star g(x,p)=f\left(x+\frac{i}{2}\...
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55 views

What are the Fock-state probabilities of general Gaussian states?

A general (pure) Gaussian state has the form $\newcommand{\on}[1]{\operatorname{#1}}\newcommand{\ket}[1]{\lvert #1\rangle}\ket{\alpha,\xi}\equiv D(\alpha)S(\xi)\ket{\on{vac}}$, with $\ket{\on{vac}}$ ...
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Measurement of photon incident at an angle on detector

Let us consider an experiment where photons of some frequency $\nu$ are incident on a photo detector. Now, say the photons are incident at some angle $\theta$ with the normal, then the component of ...
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1answer
8 views

What is the formal definition of Coupling efficiency

Does anyone knows the formal definition of Coupling efficiency? I have been reading the term in photonics devices and optics. I have been searching for it, but I could not find any. Thanks for the ...
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Confusion about OPTIC axis of an crystal

Why it is essential to set a particular direction for an OPTICS axis of a crystal (e.g. Calcite)? What is the importance of that direction?
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1answer
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Is there a list of computed Wigner distributions of notable states?

I'm looking for a list of explicit expressions of Wigner distributions of notable functions (e.g., Fock states, Gaussian states, thermal states, etc). Is there a paper, book, or other online source ...
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1answer
19 views

Double Potential Well (Hubbard Model)

The Hamiltonian from the Hubbard model for the double well potential $V(x) = V_0 \frac{x^2 - q^2}{q^2}$ is given by \begin{equation} H = -J(a_L^\dagger a_R + a_R^\dagger a_L) + \frac{U}{2} (a_L^\...
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Plugging a global phase into an operator

Cheers to everyone. I' ve got a serious doubt about the following: consider the annihilation operator $\hat a$. For practical reasons, I sometimes find useful redefining it in the following way : $\...
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43 views

Are polarization-entangled photons correlated spatially?

Are polarization-entangled photons correlated spatially? That is, if I took a pair of entangled photons and looked at their spatial modes with two cameras (one for each photon), would I expect to see ...
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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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1answer
50 views

Two different to do Bogobliubov transformation but sees to be contradictary

When try to do bogoliubov transformation on a weak-interaction cold atoms with uniform velocity $\vec{v}$, I used two different approaches, giving two different results. The Hamiltonian is $$\hat{H}=\...
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1answer
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Confusion about optic axis

In the book 'OPTICS' by Eugene Hetch it is written that, "the optic axis is actually a direction and not merely a single line". I can't understand why it is a direction, not a single line?
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25 views

Is mirror a beam splitter with reflectence=1?

By definition from Wikipedia, the beam splitter (BS) operation $U_{BS} = \begin{pmatrix} t & r \\ r & t \end{pmatrix} = \begin{pmatrix} \cos\theta & -i\sin\theta \\ -i\sin\theta & \...
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6answers
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Photon description of quantum-optical interference experiments

I am currently studying the textbook The Quantum Theory of Light, third edition, by R. Loudon. In the introduction, the author says the following: In the customary photon description of quantum-...
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Some questions about Bogoliubov transformation

consider a Hamiltonian, after mean-field approximation, can be written as $$\hat{H}=\sum_{p}(\epsilon_{p}+gn_{0})a_{p}^{\dagger}a_{p}+\frac{1}{2}gn_{0}(a_{k+p}a_{k-p}+\hat{a}^{\dagger}_{k+p}\hat{a}^{\...
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Is one photon the quanta of excitation between modes or Energy eigenstates?

When we quantize a EM field with appropriate boundary conditions (say in a waveguide/cavity) we get modes denoted by the $\vec{k}$ and we know that $\omega = c|\vec{k}|$ so do modes represent ...
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41 views

How does mirror create stimulated atoms in laser

I know excited atom can emit photon at any direction as long it stays consistent so the total angular momentum and spin states are conserved, this is spontaneous emission. What about stimulated ...
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1answer
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What do scientists mean when they talk about two-dimensional photon gas in Photon BEC?

In a photon BEC, people are talking that cavity consisting of $2$ highly reflective mirrors make the photon gas $2$ dimensional by freezing out one wavevector $k_z$, which stays constant: $$ k_z=n\pi/...
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How is the Wigner characteristic function defined?

When defining the Wigner characteristic function of a state represented by the density matrix $\rho$, I have seen various sources [including https://arxiv.org/abs/1110.3234] first define the Weyl ...
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In what sense are spin coherent states “classical”?

Spin coherent states are often introduced as "the most classical states of a finite-dimensional system", or as the analogous of coherent states of light for finite-dimensional systems. See e....
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34 views

How does interference occur in interferometers?

The Mach-Zehnder interferometer (FIG. 1) is constituted by two arms. It is said to be (un)balanced if the two arms have (un)equal lengths. The difference in lengths generates different interference ...
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1answer
39 views

Modification of Atom-Field interaction Hamiltonian in the Knight optics textbook

I am reading Quantum optics textbook of Peter Knight. From the Eq 4.3 $ \hat{H} = \frac{1}{2m}[\hat{P}+e\hat{A}]^2-e\Phi + V(r) $ Using $ \hat{H}' = \hat{R}\hat{H}\hat{R}^{\dagger} + i\hbar\frac{\...
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Resources to learn about spontaneous parametric down conversion

I have recently begun working on a project where I will be modeling some experiment that uses SPDC to generate entanglement. However, I have not formally studied SPDC in any capacity. Is there any ...
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1answer
29 views

Can a material have infinite or zero opacity?

My current understanding is that materials found in nature attenuate light as a function of some fixed constant, according to this equation: $ I(x) = I_0 e^{-\kappa_v \rho x} $, where $ I_0 $ is the ...
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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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34 views

Derivatives of creation and annihilation operators over coordinate

I meet a problem about how to understand derivatives of creation and annihilation operators. Let's look at the following example: $$H=\int dr [-\hat{a}^{+}(r)\frac{\hbar^{2}}{2m}\nabla^{2}\hat{a}(r)]\...
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How to represent the square root of a density matrix via the Glauber-Sudarshan representation?

I am trying to calculate the quantum Fisher Information of some quantum states which are represented via their P (Glauber-Sudarshan) representation, $$\rho = \int P_\rho(\alpha) |{\alpha}\rangle \...
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22 views

Photon rate definition in input-output formalism: why such definition commonly used?

I consider a one dimensional waveguide. I study free field propagation on it. I apply periodic boundary condition with periodization length $L$ to describe the physics with Fourier series and not ...
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Nonlinear Absorption Coefficient

How is Absorption Coefficient related to Susceptibility. I want to find linear, 3rd and 5th order absorption coefficient from linear, 3rd and 5th order susceptibility.
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1answer
38 views

Finding the effective drive on the emitter when driving the cavity in the jaynes-cummings model

I'm trying to figure out what the driving term in the Hamiltonian is when you drive an emitter (say a transmon qubit) through a coupled cavity (such as a CPW resonator). For this I am considering a ...
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1answer
89 views

Transition rates with incoherent radiation

When deriving the transition rates for atoms in radiation, one calculates the rate for a single frequency and then adds the rates corresponding to all frequencies in the spectrum. The reason for this ...
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80 views

Matrix representation of beamsplitter, for numerical computation of output based on given photon number (Fock state) input

Question: Is it possible to express the effect of a simple 50% beamsplitter on photon number states using matrices, such that the output can be computed by matrix calculations rather than manual ...
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Intuitive derivation of the Husimi Q function from the Wigner function

The Wigner function is given by $$W(\alpha)=\frac{1}{\pi^2}\int \text{e}^{\alpha \beta^*-\alpha^*\beta}\text{Tr}\left(\hat \rho \hat D(\beta) \right) \text{d}^2\beta,$$ where $\hat D(\beta)=\text e^...
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How to understand scale expansion in Fokker-Planck equation Part 2

The background of the question is given in How to understand scale expansion in Fokker-Planck equation. Using Taylor expansion $\bar{a}_{k}(x)$ as a funciton of $\epsilon$ around $\bar{x}_{0}(t)$, we'...
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How to understand scale expansion in Fokker-Planck equation

I read the book Statistical Methods in Quantum Optics 1 (Master equations and Fokker-Planck equations), published by springer. In Chapter $5$, to do scale expansion, the writer introduces a system-...
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What is the typical efficiency/probability of success of producing a pair of photons in SPDC?

In Spontaneous Parametric Down Conversion process pump photons are broken up into pairs of photons. What is the typical probability of success or the efficiency of this process in practice?
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Is there a way to go from the continuous variable quantum computer model to the qubit model?

There are some papers such as https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 that discuss going from qubit to the continuous model. But I'm curious if there is a way to ...
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Rotating Wave Approximation and External Force on a Mechanical Oscillator

There is a Hamiltonian term describing an external time-dependent force on a mechanical oscillator as follows: $$ H_{ext} = x_{zp} F(t) (a^\dagger + a) $$ where $a$ is annihilation operator of the ...
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1answer
55 views

Can a balanced homodyne detector measure instantaneous change in frequency?

I am reading a paper(https://arxiv.org/abs/1906.03540) where a Balanced Homodyne detector is producing a homodyne signal that is the instantaneous change in the oscillator's frequency. I know that a ...
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Relationship between optical coherence and spin dephasing?

I'm curious if there's a relationship between the inhomogeneous spin dephasing and the optical coherence of a material. Certainly, in many applications quantum information applications, you want both ...
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How to prove a specific relation of the type $\left[\hat{V}, \hat{V}^{\dagger}\right]=0$

I have the operators $\hat{V}=\sum_{j=-\infty}^{\infty}\hat{a}_{j}^{\dagger} \, \hat{a}_{j+1}, \qquad \hat{V}^{\dagger} = \sum_{j=-\infty}^{\infty} \hat{a}_{j+1}^{\dagger} \, \hat{a}_{j}$, where $\...
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Does $[A , B] \not = 0 $ necessarily mean $\Delta A \Delta B \ge k$ where $k \not = 0$?

For example : $[\hat{x},\hat{p}] = i \hbar \hat{I}$ and $\Delta x \Delta p \ge \hbar/2$ but in case of number states $|n \rangle $ $$[\hat{C},\hat{n}] = i \hat{S}\\ \Delta C \Delta n \ge 0 $$ where ...

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