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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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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Diagonal elements of the transition dipole moment

I'm currently doing some work in Quantum Optics and now have a question about the transition dipole moment. We were told in class that the off-diagonal elements of this matrix, namely $\langle n|d|m\...
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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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Increasing the resolution of detecting different OAM modes

I am not very familiar with various OAM sorters and how they work. However, my understanding is that the main goal is to have high resolution in detecting different OAM modes. According to a paper (...
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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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What does $\partial_{k_\mu}$ mean on the Simon Laboratory site at Stanford University? (condensed matter physics and quantum optics)

I realize this is a strange question, but I have come upon the Simon lab site a lot, and that symbol or motto of theirs is everywhere, and I am just wondering if it means anything..... http://simonlab....
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Rabi oscillation in a solid

I have 2 questions regarding Rabi oscillation: Can we observe Rabi oscillation in a solid? Most of the articles that measured Rabi oscillations were made either on single atom, quantum dot, but ...
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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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Is this novel experimental arrangement for generating pure photon energy superposition states valid?

I came up with the following experimental arrangement for producing a "photon in a box" superposition state which is "pure" in the sense of not being entangled with any other ...
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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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What kind of interaction does $\sigma_z(g \hat{A} + g^* \hat{A}^\dagger)$ represent?

Given an atom interacting with a bosonic field with operator $\hat{A}$, the quantity $g \sigma_+ \hat{A} + g^* \sigma_- \hat{A}^\dagger$, with $\sigma_{\pm}$ the raising/lowering operators tells us ...
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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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How to transform any pure two-mode Gaussian state into "canonical two-mode squeezed state form"?

I'm new to quantum optics and am going through a review paper by Braunstein & Loock. There, after calculating the partial von Neumann entropy for a two-mode squeezed vacuum $$\hat{S}(\zeta)|00\...
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Covariance matrix and amplitude of some well known states

I am familiar with the notion of covariance matrix as described here in Wikipedia. But what this article doesn't tell me is what are the Covariance matrix and Amplitude for some well known states in ...
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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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1 answer
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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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How to simulate a Mach-Zehnder Unbalanced Interferometer with Single Photons?

I'm currently working on a project using a Mach-Zehnder Interferometer (MZI) with weak coherent pulses (single photons). In order to simulate the results I would like to use the Qutip library of ...
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Optical dipole trap - Spatial dependence

I am currently reading lecture notes on quantum optics and encountered the following section (two-level system excited by a laser with detuning $\Delta$): "When a strongly detuned field interacts ...
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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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2 votes
1 answer
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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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Spontaneous emission rate with coherent and incoherent sources

I want to study the emission and absorption of photons by atoms. I start with a quantized field and a two level atom interacting. Suppose our field has frequency $\omega_0$ and the energy gap has a ...
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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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Mirror from beam-splitter

The input-output relations for the beam-splitter (BS) shown in figure are $$c=\cos(\theta/2) a -i\sin(\theta/2)b,\qquad d=\cos(\theta/2)b -i \sin(\theta/2)a.$$ Now if this BS has to become a mirror, ...
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Photon number distribution VS quantum state

Let's suppose that I'm generating two-dimensional Bell state $|00\rangle_{si}+|11\rangle_{si}$ of two photons, signal and idler, from a spontaneous parametric down-conversion process. If I just only ...
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Do microwave oven doors use specular reflection as shown in this video. If so, what allows light to ignore imperfections based on wavelength?

I will attempt to restate the question asked here in another way without as much rambling/thought process included, as the provided 'duplicate' was actually both linked and quoted in my OP, and did ...
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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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Heterodyne measurement on Gaussian state

How can one justify/prove that the Heterodyne measurement on an N-mode Gaussian state with expectation value $\mu$ and covariance matrix $\textbf{V}$ leads to Gaussian probability distribution given ...
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