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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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Quantum sensing using Ion penning traps[[ODF, Dicke states and pi/2 pulse]]

I am reading the article https://www.science.org/doi/full/10.1126/science.abi5226 It's about Quantum sensing in ion penning traps. Question 1. Does the axial mode of the penning trap have nothing to ...
lalala's user avatar
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What does "not applying the CCR" mean exactly?

I've seen mentioned in a number of posts that some relations do or do not apply depending on whether one is "applying the CCR". For example, In Relationship between normal-ordered vacuum ...
glS's user avatar
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Quantised optical cavities with non zero decay rate

The quantised electric field of an optical cavity can be described as a harmonic oscilator, $$\hat{H}_{\mathrm{c}}=\hbar\omega_{\mathrm{c}}\hat{a}^{\dagger}\hat{a}.$$ If the cavity mirrors are ...
Adrien Amour's user avatar
3 votes
3 answers
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Prove that integrating a displacement operator with a Gaussian gives $\int d^2\gamma e^{-|\gamma|^2/2}D(\gamma)=\pi|0⟩\!⟨0|$

I'm looking for "nice" ways to prove the following identity for displacement operators: $$\int d^2\gamma e^{-|\gamma|^2/2}D(\gamma)=\pi|0⟩\!⟨0|,$$ with $|0\rangle$ the vacuum state and $D(\...
glS's user avatar
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What happens if obstacles (walls) been put where destructive interference occurs in double slit experiment?

If photon doesn't have probability to be in dark (destructive interference) area, what will be the effect of adding obstacles (walls) in the dark (destructive interference) area for the double slit ...
Wael Khatib's user avatar
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What happens to a coherent state when it passes through an optical amplifier?

I learned from this article that when a quantum state passes through an optical amplifier based on stimulated emission (e.g., EDFA), the variance of its quadrature becomes: $(\Delta X)^2 = G(\Delta ...
Godfly666's user avatar
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Systematic and comprehensive definition and classification of a mode (electromagnetism)

I am currently having a hard time understanding which is the deciding factor/quality for the definition of a light mode. I will give a couple of examples and also what I think regarding as to how we ...
imbAF's user avatar
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Closed expression for expected values of $\hat{p}\,\,^{2j}$ for the vacuum state

I am wondering if there is a closed expression for the expected value $\left<0\lvert \hat{p}\,\,^{2j}\lvert 0\right>$ with $j\in\mathbb{N}$, where $\left|0\right>$ is the vacuum state of the ...
Camilo160's user avatar
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Is there a non-negative normalized Wigner function that doesn't correspond to a physical state?

This is related to Is the Wigner function non-negative only for convex mixtures of Gaussian states? and Can the characteristic function $\chi_\rho(\beta)={\rm tr}[\rho D(\beta)]$ be an indicator ...
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Is the Wigner function non-negative only for convex mixtures of Gaussian states?

Hudson's theorem, the result usually cited in this context, tells us that for a pure state, the Wigner is non-negative iff the state is Gaussian, but doesn't in general say anything about mixed states....
glS's user avatar
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Can the characteristic function $\chi_\rho(\beta)={\rm tr}[\rho D(\beta)]$ be an indicator function?

Given the characteristic function defined as: $$\chi(\beta)=\text{tr}[\rho D(\beta)],$$ with $D(\alpha)=e^{\alpha a^\dagger-\bar\alpha a}$ the displacement operator. Is it possible that for some $\rho$...
Nicolas Medina Sanchez's user avatar
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Helmholtz paraxial approximation

I have two questions regarding this case. In our lecture it was said that once the paraxial approx. is applied, the field $\vec E$, no longer obeys the Maxwell euqations. Why is that and how can one ...
imbAF's user avatar
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Impact of obstacles on Single/ Double split interference pattern

What is the impact of obstacles on the interference pattern if the obstacles are arranged to be located in the destructive interference locations as follow: According to my understanding to classical ...
Wael Khatib's user avatar
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Solution of the (Paraxial) Helmholtz equation and angular spectrum representation of optical fields

In my lecture today, we were discussing the Helmholtz equation and it's approximation to the paraxial Helmholtz equation. For the Helmholtz equation the solutions to it are of several kind: 1 - The ...
imbAF's user avatar
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Quantum Master Equation-Reservoir Correlations

n the book, Statistical Methods in Quantum Optics Volume 1, while writing the master equation for the damped harmonic oscillator system, I am not able to understand how the reservoir correlations have ...
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Quantum Master Equation for Damped Harmonic Oscillator

In the book, Statistical Methods in Quantum Optics Volume 1, while writing the master equation for the damped harmonic oscillator system, I am not able to understand how the system operators S1 and S2 ...
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Prove that a displaced thermal state evolves into a displaced thermal state

Considering the physical model of a harmonic oscillator at frequency $\omega_0$, which interacts with a heat bath at temperature $T$. The relevant Hamiltonians for this model are given as \begin{...
Yashovardhan Jha's user avatar
1 vote
1 answer
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Is the annihilation operator an observable (it is non-Hermitian)?

In most treatments of quantum mechanics that I have seen, observables of a quantum system are defined using Hermitian operators. The most intuitive reason for this is that Hermitian operators have ...
Biophysman's user avatar
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What is the observable for the optical field?

Typically, observables in quantum mechanics are associated with Hermitian operators. However, Glauber argues in 1963 ([1]) that the electric field operator $\hat{\mathbf{E}}(x,t)$ is not the relevant ...
Biophysman's user avatar
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Inverting an integral relation involving a set of continuous modes

Consider a continuous system of bosonic modes $a(x)$, and the transformation $$U a^\dagger(x) U^\dagger = \int A(x,y)a^\dagger(y) \ dy. $$ My goal is to find $U^\dagger a^\dagger(x) U$ in terms of a ...
Phil K.'s user avatar
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1 answer
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Expected position of squeezed state

I want to compute the expected position $\langle \alpha,r | x | \alpha, r \rangle$ of a squeezed state defined as $$ | \alpha, r\rangle = S(r)|\alpha\rangle\ , $$ where $S(r)$ is the operator $$ S(r) =...
SrJaimito's user avatar
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Partial trace on a two-mode continuous-variable quantum state

I have the following continuous-variable entangled state $$ \left|\psi\right\rangle_{1,2}= \int_{-\infty}^{+\infty} dq_{1} dq_{2}~\psi(q_{1}) f_{G}(q_{2})e^{\frac{i}{2} q_{1}q_{2}}\left|q_{1}\right\...
Julio Abraham Mendoza Fierro's user avatar
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Relationship between decay rate and stationary state for the Lindblad Equation

I would like to know what is the role of the decay rate $gamma$ in the Lindblad equation written in the diagonal form \begin{equation} \dot{\rho}(t)= i[H,\rho(t)]+\gamma\sum_{\alpha}L_{\alpha}\rho(t)L^...
GSLAM's user avatar
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Conservation of angular momentum when absorbing a single photon (Jaynes-Cummings model)

Consider a two-level atom of with energy levels $|g\rangle$ and $|e\rangle$, such that dipole transitions are allowed between these two levels. Let $l_{e}=l_{g}+1$ where $l_{e},l_{g}$ are the total ...
Adrien Amour's user avatar
1 vote
0 answers
32 views

Multimode squeezed operator

Given CCR (bosonic) algebra, with creation / annihilation operators $a_{i}^{\dagger}, a_i$ acting on a single particle Hilbert space $\mathbb{h}$, let's introduce the multimode squeezed operator for $...
MBlrd's user avatar
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3 votes
1 answer
50 views

Renormalisation in quantum optics

When reading about QED in QFT books, renormalisation seems to be essential to get results eventually. It also seems absolutely necessary even for low energies, since the internal lines lead to ...
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Conceiving an entangling measurement on copies of a two-mode Fock state

Consider two copies of a general pure two-mode Fock state with a definite number of photons $N$ as follows. $|\psi\rangle^{\mathrm{TMFS}}=\sum_{n=0}^{N} c_{n}|n\rangle_{a}|N-n\rangle_{b}$ where $c_n$ ...
JayanthJ's user avatar
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Can Fock states be teleported using conventional boson-based platforms in continuous variables? [closed]

Is it possible to teleport Fock states using conventional bosons-based platforms in continuous variables? Usually with bosons-based platforms people perform two-mode squeezing, beam splitter, and EPR (...
Camilo160's user avatar
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Spontaneous transfer (decay) between Zeeman states

In a paramagnetic substance like Rubidium (due to its unpaired valence electron), under the influence of a DC magnetic field, the degenerate electronic energy states split into Zeeman states. Let's ...
Omid's user avatar
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Book Recommendation [duplicate]

I am a first year PhD student and I am going to work in Quantum Optics ahead in my PhD. I am right now undergoing my coursework and I want to read the subject from the scratch to build a good ...
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Choice of axes in resonantly driven two level system

Consider a two-level atom with a transition at angular frequency $\omega_0$ and $\mu_{12}=2 \times 10^{-29} \text{Cm}$ subjected to a sequence of two resonant pulses. The first pulse has electric ...
Anchal Kumar Sharma's user avatar
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A question on emission spectrum and two-time correlation function

Here, the expression of the emission spectrum is $$S(\omega)=\int_{-\infty}^{\infty}\langle A^\dagger(t+\tau)A(t) \rangle e^{-i\omega\tau}\text{d}\tau=2\Re\left\{\int_{0}^{\infty}\langle A^\dagger(t+\...
Young Q's user avatar
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1 answer
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The relativity of simultaneity in two-photon absorption

In the two-photon absorption (TPA) process, when there is no intermediate state, it's required that two photons are absorbed either simultaneously or semi-simultaneously, with a relatively short time ...
Omid's user avatar
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0 answers
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Photon speed in a medium with negative electric susceptibility

In optical media, the real part of the electric susceptibility, Re{$\chi$}, can, in general, become negative for certain frequency ranges (near the absorption resonance). This leads to the refractive ...
Omid's user avatar
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3 votes
0 answers
57 views

Unitary evolution of the displacement operator in terms of positions and momenta

Consider a set of $M$ signal modes described by the creation operators $\mathbf a^\dagger = (a_1^\dagger,...,a_M^\dagger)$, and let $\Phi_U$ be the channel defined by the conjugation $\Phi_U(\cdot)=U(\...
Phil K.'s user avatar
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2 votes
2 answers
138 views

Linearity of Lindblad equation in the Heisenberg picture

I am interested in solving the dual (adjoint) Lindblad master equation for a time-dependent operator $O(t)$ as follows \begin{equation} \dot{O}(t) = i[H, O(t)]+\sum_{\alpha\in I} L_\alpha ^\dagger O(t)...
GSLAM's user avatar
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1 vote
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Multimode unitary channel in terms of action on characteristic function

Consider a set of $M$ signal modes described by the creation operators $\mathbf a^\dagger = (a_1^\dagger,...,a_M^\dagger)$, and let $\Phi_U$ be the channel defined by the conjugation $\Phi_U(\cdot)=U(\...
Phil K.'s user avatar
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1 vote
1 answer
37 views

Creating Schrödinger cat states with trapped ions

We will consider an ion is in an harmonic trap. The ion has two internal states \lvert g\rangle and \lvert s\rangle and it interacts with a laser that induces a state-dependent force. The quantum ...
Mario's user avatar
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2 votes
2 answers
410 views

Doppler shift of a single photon

I'm curious to understand how the Doppler shift phenomenon occurs and is mathematically expressed for a single photon emitted by a stationary single photon emitter, such as a quantum dot, and observed ...
Omid's user avatar
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0 votes
1 answer
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How to distinguish a doppler-shifted photon from a non-doppler-shifted photon of the same frequency?

Can one physically distinguish a photon of frequency $\omega$, generated by a stationary laser, from a photon generated by a mechanically moving laser (a different laser from the first one) which, due ...
Omid's user avatar
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1 vote
2 answers
72 views

Tightly-focusing a single photon

I'm curious about the feasibility, both theoretically and experimentally, of tightly focusing (or spatially trapping) a single photon to guarantee its precise targeting. If it’s possible, isn’t it ...
Omid's user avatar
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Do the states $|01\rangle$, $|10\rangle$ span the space of a single photon?

i nave included some simple information about Fock states for photons in a work. I wanted to know if: in the context of a beam splitter when we suppose to have only one photon, always entering from ...
forgetfuled's user avatar
2 votes
1 answer
64 views

Trying to learn input-output formalism: 2-photon Fock state entering a cavity

I really don't understand the input-output formalism. I've gone through the 1985 paper, and I get completely lost when the following formula is written: $$b_{out}(t)-b_{in}(t) = \sqrt{\gamma} c(t)$$ ...
Steven Sagona's user avatar
1 vote
2 answers
46 views

The relative phase of photons in two-photon absorption

In two-photon absorption (TPA), the relative polarization of the two photons about to be absorbed simultaneously by an atom is crucial in determining the TPA rate. However, there is a lack of ...
Omid's user avatar
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1 vote
2 answers
100 views

Why does the Lamb-Dicke parameter decrease with the number of ions in an ion chain

I would like to understand (ideally with a nice pedagogic reference), why the fidelity of quantum gates in long ion chain decreases with the number of ions in the chain. In this reference, it is ...
StarBucK's user avatar
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Can we get quasiprobability distributions other than $P,Q,W$ from generalised characteristic functions?

It's a standard result that the three well-known quasiprobability distributions can all be expressed in terms of the "$s$-ordered characteristic functions" as $$ W(\alpha) = \int\frac{d^2\...
glS's user avatar
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How to get good visibility in Single-photon_interference?

This question is specific to the experimental quantum optics community. I am attempting to perform a Mach-Zehnder interference experiment using single photons as a source. However, I am encountering ...
Kanad Sengupta's user avatar
2 votes
0 answers
17 views

What happens when two photon of same polarization enters in the polarizing beam-splitter(PBS)?

It is well established that if two photons of the same polarization, identical wavelength, phase, and spatial distribution of wavefunction enter a non-polarizing beam splitter (N-PBS), they exhibit ...
Kanad Sengupta's user avatar
1 vote
0 answers
24 views

How Does Laser Light Maintain Coherence Amid Photon-Atom Entanglement?

Laser light is known to produce "coherent state light," which consists of a superposition of different photon numbers. However, wouldn't the entanglement between the atoms and the light ...
Steven Sagona's user avatar
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5 answers
95 views

How to rotate the polarization of photons?

What device is used to rotate photons from H to V. Does it change the energy of the photons? I heard about half wave plate?
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