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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Photon number autocorrelation in Cavity QED
I am studying this paper dealing with optomechanical strong coupling, and I don't understand one very relevant part of it.
In particular, the authors define (equation (8)) a photon number ...
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Parallel transport geometric phase derivation
In Modern Foundations of Quantum Optics by Vlatko Vedral, he derives an expression for the change in phase under parallel transport after completing a small loop as
$$\begin{align} \delta \theta &=...
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Why image of vertical object is always a straight line and perpendicular to principal axis?
I am a high school student and I am very confused in geometrical optics, In all textbooks the mirror formula is derived by already assuming that the image of any vertical object (perpendicular to the ...
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Two coherent state input to a beam splitter
A beam splitter transforms incoming mode operators $\hat{a}_{i}, \hat{b}_{i}$ to outgoing operators $\hat{a}_{o}, \hat{b}_{o}$ as
$$
\begin{aligned}
&\hat{a}_{o}=\sqrt{\eta} \hat{a}_{i}+i \sqrt{1-\...
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Spin conservation in indirect optical transitions in bilayer TMDC
While I was reading this paper (https://arxiv.org/abs/2108.09129), I got confused with the spin conservation in optical transitions in bilayer 2D semiconductors. In figure 3(d), indirect transition ...
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Purcell effect for large cavities
The model of interest is a 2-level system (e.g. an atomic transition) inside a damped single-mode cavity.
The purcell effect states that the atomic decay rate inside the cavity $\Gamma_{cav}$, on ...
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Why is Dirac's Phase Operator Non-Hermitian?
I'm self-studying Gerry and Knight. To prove Dirac's phase operator is non-existent, the book makes the following argument.
The conventions used are as follows: $\hat{n}$ is the number operator, $\hat{...
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Strange behaviour of ultra dark image in a CMOS camera? [closed]
Samsung Galaxy S21 Plus has a CMOS camera.
I recorded an ultra dark raw (DNG format) image using its Pro mode in the following conditions:
ISO 50
Shutter speed 1/12000
Cover the aperture with ...
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Is it possible to define the operator similar to the Displacement $|\alpha\rangle = \hat D|0\rangle$ but from the coherent state to the Fock space?
I am looking for the theory of electro-optical modulator with Fock states as an input and I know how the modulator acts on the coherent states. Knowing the connection between coherent and Fock states. ...
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Conditional Measurement on a Beam Splitter
What is meant by conditional measurement? In many research papers, it is written that "we condition the detector on the one of the output ports of the beam splitter to detect 'm' number of ...
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Difference between two forms of the electric field operator
I'm currently taking a course in Quantum-optics, focusing primarily on the book Introductory to quantum optics by C. Gerry & P. Knight. In the book they first present the quantization of a single ...
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What Happens When Three Photons Enter a Non-Polarizing Beam Splitter?
When a single photon enters a non-polarizing beam splitter, in any of the two inputs, it has 50% chance of leaving by each of the two outputs.
When two photons enter this beam splitter, each by one ...
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Analytical solution of the Fokker-Planck equation for a damped harmonic oscillator
I was having some trouble while trying to understand the solution for the Fokker-Planck equation for a damped harmonic oscillator, as given in chapter-3 of the textbook "Statistical Methods for ...
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If I split coherent state light in half (by a beam splitter) are the 2 output intensities correlated?
From what I have been told and understand, if I use a simple beamsplitter to split coherent state light, I will obtain 2 coherent states as a result.
Are the intensities of these two output states ...
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Multi-mode Jaynes-Cummings Model
The Jaynes Cummings Model describes that a qubit coupled to a harmonics oscillator. The Hamiltonian of this model can be written as
$$H_1=\omega_c a^{\dagger}a+\omega_a\sigma_z+\Omega(a^{\dagger}\...
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Difference between Wigner function in coherent space and coordinate space
Such a density operator $\hat{\rho}$ match with a Wigner function in coherent space: $$W(\alpha,\alpha^{*})$$
$\alpha$ and $\alpha^{*}$ are $C-number$ ( $\alpha^{*}$ denotes complex conjugate of $\...
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What is the physics corresponding to the "wave function of a single photon"?
Some of you may have seen my post yesterday which asked essentially the same question as I'm going to ask here and has since been deleted, for which I apologize. I noticed some egregious errors in my ...
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Is the optical phase space the same thing as the Hilbert space $L²(R^2)$?
I have trouble figuring out what Hilbert space it is mathematically. It looks similar to $L²(R^2)$ where each state is a distribution of over all the quadratures $(q,p)$
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Polaron transformation in quantum optics
I'm trying to understand the so-called polaron transformation as frequently encountered in quantum optics. Take the following paper as example: "Quantum dot cavity-QED in the presence of strong ...
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Three input/output generalization of 50:50 beamsplitter
A symmetric 50:50 beamsplitter can be represented by a unitary 2x2 matrix acting on a vector of creation operators for the input states:
$$ \begin{pmatrix}
\hat{a}_c^\dagger\\
\hat{a}_d^\...
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Wavelength-dependence of optical elements in integrated photonic circuits
I am interested in integrated photonic circuits or silicon photonic circuits. In the long run, I would like to analyze these circuits using a rigorous and analytical mathematical approach, taking the ...
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Rabi-like Model for $N$-Level Systems coupled to one or more quantized field modes
I'm doing a literature review on the history of model development in the scope of light-matter interaction. I've studied in depth the two key tools for a lot of the research in this field, two level ...
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How does an attenuator inside a polarization interferometer change polarization?
Suppose you have source of coherent light, a laser beam, with +45 polarization. A polarizing beam splitter (PBS) splits the beam into its horizontal and vertical components. The second polarizing beam ...
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How to scale Poissonian light?
In quantum optics, coherent light with constant frequency, phase, and amplitude shows poissonian photon number statistics:
$$P(n) = \frac{\bar{n}^{n}}{n!}e^{-\bar{n}}.$$
A well-known result for ...
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What does expectation value being equal to zero have to do with the condition of being a state of an operator?
In Gerry & Knight's Introduction to Quantum Optics book under the "Quantum fluctuations of a single-mode field" section it is claimed that the number state $|n>$ is not a state of ...
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Rabi oscillations within the adiabatic theorem?
I'm studying Rabi oscillations in a two-level system (TLS) with Hamiltonian
\begin{align}H(t)=\omega_0 \sigma_z + \Omega \cos(\omega_1 t) \sigma_x.\end{align}
The model is usually treated within the ...
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Single State Coupled to a Continuum of States
I have been reading a book on Quantum Optics and I have a question about a step.
Consider a system in state $\vert{i}\rangle$ at $t=0$ ($E_i = \hbar \omega_i$), and this state is coupled to a ...
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How to experimentally find the retardation of a wave plate?
I've been trying to understand how to experimentally verify the retardation of a given wave plate. It is pretty easy to distinguish between HWPs and QWPs but what if the retardation was random (i.e. ...
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Collision Broadening - Spontaneous emission
I am currently reading Loudon's "The Quantum Theory of Light" and get stuck about the following sentence:
Consider a particular atom radiating light of frequency $w_0$ . A train of
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A symmetric representation of the displacement operator
Say that an operator is given by
$$D(\alpha) = \exp(\alpha a^{\dagger} - \alpha^{*}a) = \sum_{n=0} ^ {\infty} (n!)^{-1}(\alpha a^{\dagger} - \alpha^{*}a)^n.$$
Define $\{(a^{\dagger})^m a^n\}$ as the ...
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What are some ways to find the second order quantum phase transition (PT) critical point?
The standard way appears to be finding the steady state (ss) solutions of the order parameter of the system of interest. Since the ground state properties of the system changes before and after ...
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Why does a higher temperature increase absorption / optical density?
Suppose we have for example a gas of bimolecular iodine. Suppose we shine ultraviolet laser light on it.
Then the absorption of ultraviolet increases when we increase the temperature. From what I read ...
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What interferes in an astronomical interferometer?
As I understand it, in an astronomical interferometer, both telescopes need to be aimed at the same light point in space to get an interference pattern. But I also understand that a single photon ...
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Confusion about quantum optic modes -- How to gain intuition?
I have started reading some materials on quantum optics and one concept I can't seem to wrap my head around is the concept of a mode. I'd appreciate if someone could point me towards some materials or ...
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Gaining Quantum information without destroying the coherence
I've read about new optical interference among several telescopes all around the globe. It is supposed to work by combining the quantum states of a photon A arriving at once in every telescope of the ...
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Does radiation pressure affects cavity lenght of laser?
In a simple laser cavity two mirrors reflect light creating standing waves. Light exchanges momentum creating radiation pressure on the mirror. This force accelerates mirrors, changing the cavity ...
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From Heisenberg to Schrodinger picture in second quantization formalism
I'm a bit confused about the QM representations: I know that in the shrodinger picture, the operators stay the same, and the quantum state rotates in the hilbert space. In the heisenberg picture it's ...
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Do microwave oven doors use specular reflection, if so, how does that occur in microwave vs visible light? [duplicate]
Please comment if you're gonna down vote so i can improve :)
I have poured over a lot of resources in the past few hours but have been unable to reach a satisfying answer, this question is more about ...
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Eigenvectors of dressed states [closed]
Given the following hamiltonian: (basis $|1 \rangle ; |2 \rangle) $
$$H = \frac{\hbar}{2}\begin{bmatrix}
\Delta & - \Omega \\
- \Omega & \Delta\\
\end{bmatrix}$$
I found the ...
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Density matrix element in Jaynes-Cummings model
In the Jaynes-Cummings model, when using the density matrix to describe mixed states for the atom-field system, after some calculations I got to this matrix element:
$$ \rho_{ee}^A = \sum_{n=0}^{\...
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Rabi as limit of Jaynes-Cummings model
I was wondering how to get back the Rabi oscillations from the Jaynes-Cummings model.
My first intuition is to let the coupling parameter go to zero, however this does not make the electromagnetic ...
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How are single photons correlated inside the "coherence time" of the laser? (And how would this affect a random number generator?)
This review on quantum random number generation describes how random numbers can be generated from a simple optical setup. In one example setup they give: weak light travels through a beam splitter ...
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Physical intuition for coherent states look like classical
In my course on quantum mechanics, we have seen that coherent states look classical. Since the expectation value of the electric field is similar as for the classical expression. Furthermore they look ...
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Is there any physical explanation for the synthetic Landau levels?
Apparently, synthetic Landau levels are formed in light which exhibits orbital angular momentum in a resonator. This was shown by this paper: https://arxiv.org/abs/1511.07381. There's a part which ...
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What kind of phase it is when a photon gain a quantum phase, a dynamical one or a geometrical one?
It's known$^1$ that the phase factor in quantum mechanics can be divided into geometric phase and dynamical phase. Since in quantum optics, light is treated as a quantum object, i.e., the photon. So ...
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Displacement measurement in quantum optics
I was following a talk where it was stated that performing a displacement $D(\alpha)$ on an optical mode, followed by a single-photon detection without number resolution, corresponds in the case of no-...
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Approximation for average thermal photon number
I am currently reading the book Introductory Quantum Optics by Gerry and Knight and I am having trouble understanding an approximation they make. In the chapter on thermal fields they derive the ...
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Expected value of the electric field operator in the superposition of two number states
Good morning everyone!
I have recently started a course of introductory quantum optics, but unfortunately by quantum mechanics background is not very good - so I'm having some problems when it comes ...
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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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If we have a state with 1/4 quadrature fluctuation, can we say it's a coherent state?
We know that the variances of quadrature components for a coherence state satisfies:
$\langle(\Delta \hat{X}_{1})^2=\langle(\Delta \hat{X}_{2})^2 = \frac{1}{4}$
However, is its converse proposition ...
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