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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Derivation of Hamiltonian in non-linear optics

I asked this question a few hours ago, but decided to re-post it because I think I can phrase it more clearly. The question is closely related to this one and has to do with the derivation of a non-...
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Complex rabi frequency

I am learning quantum optics. In the book written by Scully includes complex rabi frequency, when dealing with $\Delta$ level configuration, the Hamiltonian including laser-atom interacting concludes ...
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Show $\langle \alpha| (\cos \mu)^{-a^{\dagger} a} | \alpha \rangle =e^{|\alpha|^2(\frac{1}{\cos \mu} -1)}$ for coherent states $|\alpha \rangle$

I am reading"Quantum continuous variables, A primer of Theoretical Methods" by A.Serafini, page 120. Let $ a $ be the annihilation operator for the Fock basis. I want to show $$\langle \alpha| (\...
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38 views

Getting the Bose-Hubbard Hamiltonian from cold atoms

In the famous paper by Dieter Jaksch, it is shown that the usual Hamiltonian for cold bosonic atoms interacting by s-wave scattering (Equation (1) in the paper): $$ \hat{H}=\int d^3 x\hat{\psi}^\...
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Show for $r \in \mathbb R$, $e^{(a_1 ^\dagger a_2^\dagger - a_1a_2)r}|0,0 \rangle = \frac{1}{\cosh r} \sum_{j=0}^\infty (\tanh r)^j |j,j \rangle$

Let $ a_1, a_2 $ be annihilation operators for the first and second component in the product state $|m,n \rangle$ using Fock basis. Following "Quantum continuous variables, A primer of Theoretical ...
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What are the ways we have control over single photon emitters? Are there single photon emitters “on demand?”

I am wondering what are some of the ways we have been able to get more control over single photon emitters. What advances in technology have we made over the past years? Is there anything that ...
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81 views

What would a lens-less world look like to us? [closed]

The images we perceive through our eyes are formed by focusing the incoming light with the eye's cornea and lens. The information is "captured" by the retina and then transmitted to our brains through ...
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Non-normalised Bargmann Coherent States

Currently, I am reading a paper which involves non-normalised Bargmann coherent states as my basis. I am interested in knowing how the creation and annihilation operator acts on these coherent states. ...
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Assumptions in the Tavis-Cummings Model

Consider identical two-level atoms interacting with single mode of light. The interaction Hamiltonian can be written as $$H^{1}=\hbar \sum_{j=1}^{N} \left(g_{j}\hat{S}_{+}^{(j)} \hat{a} + \mathrm{h....
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Derivation for Electromagnetically Induced Transparency

I am looking at the derivation for EIT susceptibility (Equation 6.70) in the textbook Quantum and Atom Optics by Steck. If someone has a better resource then please recommend it, or just how to follow ...
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Hamiltonian for two optical fibers fused together

When two optical fibers A and B are brought close enough that there can be quantum tunneling between the two, we can write the "beam splitter" Hamiltonian as $$H = a^\dagger b + b^\dagger a$$ If, ...
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Trying to understand Wigner function of zero-mean two-mode squeezed Gaussian State

I am trying to understand Wigner functions of Gaussian states, specifically, that of a 2-mode squeezed state. I was wondering if anyone can explain what I am seeing in the context of what these plots ...
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Detuning in Rabi oscillations

Consider a two level atom interacting with the interaction Hamiltonian of the form $$\hat{H} = \hat{V}_{0}\cos(\omega t)$$ The probability of the state to be in the excited state is given by $$P_{e}=...
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What is the most efficient single-photon detector to date?

(This question depends on the current time period, so the reader should make note and be aware of the date of the posted answers.) I am wondering what is the most efficient state-of-the-art single-...
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The “different Hilbert spaces” of a photon?

What I understand of Fock states so far: They describe the quantum state of a bunch of photons. A single photon can be in several different energy states, and when these photons are tensored together -...
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Wave-like and particle-like nature [duplicate]

My notes say Radiation emitted from any source moves discontinuously in form of small packets of energy. Each packet is called quantum. Does this mean that when light travels, it is actually a ...
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Red and blue sideband transitions in ions and two level system approximation

Suppose we have a trapped ion (approximated as 2 level system) of mass $m$ and transition frequency $\omega_{10}$ in a harmonic confinement with frequencies $\omega_x, \omega_y, \omega_z$ such that ...
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Inverse covariance matrix for a Gaussian state

I was reading an article about Gaussian Boson Sampling (https://arxiv.org/pdf/1801.07488.pdf) and following some calculation appear an inverse covariance matrix when he defines the following matrix A. ...
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Why does light come as quanta of the harmonic oscillator?

I've recently been learning the basics of Quantum optics and it seems to be a fundamental concept that light is best described in the framework of the Quantum Harmonic Oscillator. This lead to a ...
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Unitary Transformation of an Interfering Beam Splitter

I was reading this research paper Quantum interference enables constant time quantum information processing and was confused by one particular expression involving the Hamiltonian of a beam splitter. ...
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Spin state of photons inside laser

Can the total spin state of photons inside a laser beam be written as a product of individual spin states ? Tentatively, the answer seems to be yes because single laser beam have a definite ...
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How to calculate $\langle0|S(b) S(b) |0\rangle $ where $S(b)$ is the squeeze operator? [closed]

How to calculate $\langle0|S(b) S(b) |0\rangle $ where $S(b)$ is the squeeze operator
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Why is the spontaneous emission a big deal?

In spontaneous emission, an electron in an energetically higher state jumps to an energetically lower state. This seems a simple phenomenon. Why is it called a quantum mechanical effect? What was so ...
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Limits of polarization-maintaining fiber

PM fiber maintains polarization pretty well if the input polarization is horizontal or vertical. But what happens if the input polarization is in a superposition of H and V? For example, $ \frac{1}{\...
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$s$-parameterized operator-valued Dirac delta function

So I am reading the book named 'Quantum Optics An Introduction' by Werner Vogel, Dirk-Gunnar Welsch, Sascha Wallentowitz and in the section 'Phase-space representations', I struggle to follow one step ...
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Beam splitters: fiber vs. free space

In quantum optics, are fiber beam splitters described by the same operators as free space beam splitters? For example, a free-space non-polarizing beam splitter introduces a phase shift for the ...
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Transformation acting only on one of two qubits

Suppose you have a non-polarizing beamsplitter (NPBS) with 2 outputs: A and B. You place a polarizing beamsplitter (PBS) at the output A, and want to follow the evolution of the quantum state after ...
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Does the amplitude of light increase the more it is squeezed? (Quantum Optics)

If I have a 2 mode squeezed state of light, emitted from some nonlinear parametric process, then the more it is squeezed, the larger the variance of one quadratures $X$, while the variance of the ...
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Where does differntial equation of covariance matrix come from?

Does anyone know where the differential equation of covariance matrix comes from? $$\frac{dC(t)}{dt}=AC(t)+C(t)A^T+D$$ where $C$ is the covariance matrix, $A$ is the drift matrix, and $D$ is the ...
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Why we use $i\hbar(\hat A -\hat A^\dagger)$ in Parametric Down-Conversion?

When we descirbe the degenerate parametric oscillator or the Parametric Down-Conversion, we can use the hamitonian: $$\hat{H}=\hat H_0+\hat H_{int}+\hat H_{irr}$$ \begin{array}{l} \hat H_0=\hbar\omega ...
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Laser power inside a vapour cell

I have a laser beam whose power I measured to be x $\text{mW/cm}^2$. Furthermore, I measured the beam profile of the laser beam and therefore can estimate its intensity. I shine this laser through a ...
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How to differentiate between quantum states based on phase

Imagine you have a source of photons and a single-photon detector. The source emits photons that can be in any of the following four states: $ |1\rangle $, or $ -|1\rangle $, or $ i|1\rangle $, or $ -...
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Characteristic Functions in Quantum Optics for linear amplifiers/attenuators

I am following along with the MIT OCW quantum optical communication course. I have a question about this chapter, concerning the linear attenuators and amplifiers. Specifically, the chapter mentions ...
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Quantum input-output theory : Why do we multiply by density of mode to have a number of photon **per unit of time**

In this paper, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.31.3761, we work with input-output theory. I will first summarize the physics of it and then ask my question. In input-output ...
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Computation of Wigner Functions

The Wigner function can be computed as the Fourier transform of the Weyl-ordered characteristic function: $$ W(\alpha) = \frac{1}{\pi^2} \int e^{\lambda^* \alpha - \lambda \alpha^*} C_W(\lambda) d^2\...
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In practice, how does one work with the phase states?

The phase states are defined usually by the finite sum $$ |\theta \rangle = (s+1)^{-1/2}\sum_{n=0}^s \exp(i n\theta) |n\rangle, $$ where $\theta = 2\pi k/(s+1)$ and $|n\rangle$ is the $n$-th ...
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Photon bunching and polarizers

I'm trying to understand how polarizers affect bunched photons. Or, more generally, how a projection operator affects a two-photon state corresponding to photon bunching. Toy example: Imagine you ...
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How did the book derive the following Unitary Operator expression in Mach Zehnder experiment?

I'm reading Renato Portugal's "Quantum Walks and Search Algorithms". In The Postulates of Quantum Mechanics, under the heading 'Evolution Postulate', there is the Mach Zehnder experiment, with the ...
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Is there any time difference when we see distant a object? [duplicate]

I was just wondering that We see objects thru our eyes and light has to reach our eyes so that our brain can process that light. But then there must be a time difference between that object which I ...
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Manipulating Dirac Notation

I have trouble getting my head around manipulating Dirac notation, it's still new to me and I'm not used to it. I'm following the rotating wave approximation derivation for Rabi oscillations and light ...
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Do the results of this laser experiment demonstrate nonlinear optical phenomenon?

In my photonics class, we conducted an experiment to observe the Beer-Lambert law and the effects of filters(absorption, transmittance, and reflection). We shined a red(632nm) 5mW Helium-Neon laser ...
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Normal ordering of operators: Commutator or no commutator [duplicate]

My exercise for a quantum optics course tells me to "find a normal ordering" for an Operator $\hat{O}(\hat{a},\hat{a}^\dagger)$, which is given as a (rather complicated) string of $\hat{a}$'s and $\...
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Why is EIT needed to story memory using rydberg atoms?

I was going through a paper explaining how the write-in and read-out efficiencies can be increased using cold atoms where they used Rydberg atoms, and mentioned that they were probed using EIT(...
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Spatial wave-function of a single photon and its measurement

In the last decade there were several papers claiming that they've measured a "transverse quantum state" / "quantum wave-function" / "spatial Wigner function" of a single photon: Measurement of the ...
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How to usefully calculate using “dark state polariton” framework?

I'm interested in looking at calculations related to storage of light in atomic systems. This paper discusses how these types of systems can act as "memories" by generating "dark state polaritons." ...
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Question about Homodyne detection

In this Review of modern physics, section "II. A.", optical homodyne detection is briefly reviewed. In equation (9), it is stated that the fields after the beam splitter are $$E_{1}=\frac{E_\text{L}+...
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The action of a lens on a point dipole (Fourier optics)

I want to model the action of a lens on radiation from a point dipole. I have found examples but am struggling to interrupt them. My knowledge of Fourier optics is that from the Helmholtz equation, $...
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Upper State Lifetime vs Exited State Lifetime vs Gain Recovery Time

Could any one explain differences between these three terms about semiconductors and semiconductor optical amplifiers.
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Is the polarisation field stimulated emission?

I'm told that polarisation happens due to the oscillation of an electric dipole and stimulated emission is due to the excitation of an electron between energy levels but both depend on the incoming ...
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Wigner phase space operator correspondence: how to order?

According to Gardiner-Zoller (Quantum Noise), operators acting on the density matrix can be mapped via e.g. (I'm taking Wigner space as an example, but the same holds for P and Q) $$a\rho\...