0
votes
0answers
43 views

What is the transpose of the displacement operator? [closed]

How do we calculate the transpose of this expression? $$ \hat{D}(\alpha) = \exp \left( \alpha \hat{a}^\dagger - \alpha^* \hat{a}\right) $$ What is the simplified result? Displacement Operators: ...
1
vote
0answers
25 views

Radius dependence of Energy levels of spherical Quantum dots

I have frequently read in articles that the energy level of spherical quantum dots depends on radius. We simply match the wave functions inside and outside the particle and find the intersection of ...
0
votes
1answer
55 views

Ultrafast photon detectors

Are there already photon detectors that can resolve the shape of photons in the time domaine if it looks like below where the two humps are separated by a time of the order of femtoseconds? What I ...
2
votes
1answer
44 views

Paraxial wave equation solution?

I am looking for a worked solution to the paraxial wave equation, since most sources just say that clearly Gaussians are solutions but they do not explicitly show so. This equation is equivalent to ...
0
votes
0answers
26 views

Two-photon absorption and 3rd order susceptibility

I am referring to introduction of Section 12.5 Multiphoton Absorption and Multiphoton Ionization (Page no. 550 of Nonlinear Optics, Boyd-3rd edition) where it has been said that the two-photon ...
0
votes
1answer
36 views

Conservation of probability in Jaynes-Cummings model

I was reading about Jaynes-Cummings model. I've studied Bachelor level QM. In the interaction picture the solution with rotating wave approximation and initial conditions $C_g(0)=0$ and $C_e(0)=1$ is ...
2
votes
0answers
38 views

Electron momentum distribution and wavefunction in momentum space

Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction ...
1
vote
0answers
27 views

Continuous Variable Entanglement Measure for the Statistically Mixed State

Can anybody tell me, which is the best entanglement measure for the Continuous Variable Entanglement of a Statistically Mixed State ? I have read that Schmidt decomposition is not valid in this ...
0
votes
0answers
16 views

Numerical Computation of Linbald Equation

Can anybody suggest me a good algorithm for the time evolution of the reduced density matrix using Linbald equation. My Hamiltonian is time dependent. I am aware about Qotoolbox and Qutip. I have ...
7
votes
3answers
171 views

Runge Kutta Method for a Lindblad Equation

I am solving a Lindblad equation for a dissipative Harmonic Oscillator. My Hamiltonian is time dependent, My Lindblad Equation can be written as \begin{equation} ...
0
votes
0answers
21 views

Exhaustive list of assumptions for the Clauser-Horne-Shimony-Holt inequality

I am trying to create an exhaustive list of all assumptions which work as the base of the CHSH inequality. Locality - this means an object can be influenced only by its surroundings. So, the events ...
3
votes
1answer
40 views

Off-diagonal terms of the Husimi $Q$ function?

The Husimi $Q$ function of a quantum state $\rho $ is defined as $ Q (\alpha)=\langle \alpha \vert \rho \vert \alpha \rangle $, where $\alpha = (x, p) $ is a phase space coordinate and $\vert \alpha ...
0
votes
0answers
38 views

Proving two forms of atom-field interaction perturbation Hamiltonian are equivalent

In the presence of an electromagnetic field in the dipole-approximation (${\boldsymbol A} = {\boldsymbol A}(0,t)$) we have the two forms $$H_{{\boldsymbol d}\cdot {\boldsymbol E}} = - q {\boldsymbol ...
2
votes
1answer
61 views

What are “parity considerations” in deciding the form of the Hamiltonian?

In "introductory Quantum Optics", by Gerry and Knight, the Jeynes model is considered. In this model of electron-EM field interaction the electron is approximated by a two state system ($\lvert ...
3
votes
1answer
78 views

What low-level process drives a frequency-doubling crystal?

I was reading about second-harmonic generation (SHG) crystals (or frequency-doubling crystals) used to produce green laser light from IR. What low-level process in the crystal is actually driving ...
1
vote
0answers
142 views

How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
3
votes
1answer
119 views

Shot noise at high frequencies (can it really be ideal white noise?)

Quantum shot noise (either optical intensity noise or electrical current noise) described by the noise spectral density of $2 e I$ (electrically) or $2 h \nu P$ (optically). So it is white noise. I ...
2
votes
1answer
80 views

Is boson sampling a problem in 'continuous variable' quantum information?

When people generally speak of quantum information in the context of continuous variables, what is generally meant is that observables, like position/momentum or the field quadratures of quantum ...
6
votes
4answers
318 views

Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{n!}|n\rangle$$ for a given complex number $\alpha$ and where $|n\rangle$ is a Fock ...
0
votes
0answers
53 views

normal ordering from anti normal ordering of creation and anhilation operators

I am working on entanglement of systems in beam splitters. I constantly come across equations of creation and annihilation operator (ladder operators) in anti normal ordering. I want those equations ...
2
votes
0answers
93 views

How do we show that photons generated by a constant electric current are distributed according to a Poisson distribution?

I saw the answer sometimes ago in a book "Quantum Electronics" or similar title. I don't remember the author since I lost the book. The book sets ( I believe so ) a constant electric current $I$ in a ...
4
votes
3answers
361 views

Beam splitters and Mach-Zender interferometers

I have a question (my very first here) related to 50/50 beam splitters as used in the Mach-Zehnder interferometers (see for example http://en.wikipedia.org/wiki/Mach-Zehnder_interferometer). Let's ...
0
votes
1answer
92 views

Time duration for pulse of single electron viewed as a wave

Electron as an example has a de Broglie wavelength and could diffract. If it has a single wavelength the time extent of the particle's pulse duration would be infinite .. If it carries a broadband ...
5
votes
1answer
158 views

Are Rabi oscillations a pure quantum process?

Rabi oscillations are commonly known as the oscillations in time of the occupation probability of a quantum two-level system under the action of a coupling interaction between the two-levels. ...
3
votes
1answer
81 views

Quantum Cascade Laser [closed]

I want to learn about quantum cascade laser in a six month time. Can anyone please suggest me any reading materials or video lectures. I have background in calculus and linear algebra. I am learning ...
4
votes
2answers
230 views

Polarisation of Light and Atomic Excitation

How does an atomic transition between ground and excited states depend upon the direction of polarisation of incident light?
1
vote
1answer
206 views

Derivation for 7.14 in Atomic Physics by Foot

I was going thru Ch7 of Foot and trying to fill in the gaps. However I got stuck on (7.14). So Foot was working with a two level system with a small perturbation in the Hamiltonian resulted from an ...
2
votes
0answers
63 views

Adiabatic theorem in the regime of quantum optics

I am wondering whether there is a version of adiabatic theorem in the regime of quantum optics. My understanding of quantum optics involves with the interaction between photon and atom. This ...
6
votes
1answer
2k views

Why does the refractive index depend on wavelength? [duplicate]

Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the ...
1
vote
1answer
244 views

Formula for Rabi frequency

I have calculated the dipole transition elements of electronic states $\langle a|D_1^m|b \rangle$ following the book of Cohen-Tannoudji (Complement $E_X$) and tried then to calculate from that the ...
6
votes
3answers
305 views

Commutator with a square root

How to find the commutator $[a, \sqrt{a^\dagger a}]$? Here $a$ is a usual bosonic annihilation operator, and $[a, a^\dagger] = 1$. The first thing I tried is $$ [x,A] = [x, \sqrt{A}]\sqrt{A} + ...
1
vote
1answer
221 views

In terms of covariance matrices, are partial measurement and partial trace equivalent?

Partial measurement and partial trace There is a connection between a measurement of a part of a system and tracing this subsystem out. Say, we have a system composed of subsystems $A$ and $B$ in a ...
2
votes
1answer
127 views

when is coherent state a good approximation?

Consider a Hamiltonian of a system coupled to a bath. Let $H_{sys}=\nu c^{\dagger}c$ ; $H_{env}=\Sigma \omega_r a^{\dagger}a$ ; $H_{int}=\Sigma (g_r ac^{\dagger}+g_r^* ca^{\dagger})$. Then it is ...
5
votes
2answers
205 views

Quantum Mechanical Operators in the argument of an exponential

In Quantum Optics and Quantum Mechanics, the time evolution operator $$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$ is used quite a lot. Suppose $t_i =0$ for simplicity, and say the ...
2
votes
0answers
64 views

What is three-photon interference?

Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is ...
2
votes
1answer
68 views

State emitting from an extended thermal source

This calculation is for a double slit experiment setup which is experiencing a far field radiation from an extended monochromatic thermal source. I assume the source is 1-D and it's length is $b$. ...
2
votes
1answer
133 views

Physical significance of effective wave function

In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets. To derive the coherence ...
6
votes
1answer
289 views

Can a photon exhibit multiple frequencies?

Can a photon be a superposition of multiple frequency states? Kind of similar to how an electron can be a superposition of multiple spin states.
3
votes
1answer
149 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
4
votes
1answer
188 views

double slit experiment with two opposite quarter waveplates

Consider the usual double slit experiment involving laser and a double slit and a screen. Now place in front of the left slit a quarter waveplate (let's call it QWP1) that changes a certain linear ...
7
votes
2answers
582 views

What is the “direction” of the transition dipole moment? (Understanding Eq. 9.29, Charge and Energy Transfer 3rd Ed, May & Kuhn)

For a real vector $\mathbf{r}$, the direction is given by: $\hat{\mathbf{n}}=\mathbf{r}/\left|\mathbf{r}\right|$. The transition dipole moment is a complex vector. How do you define its direction? ...
0
votes
0answers
13 views

Image formation [duplicate]

What is the real cause behind the formation of an image? It is explained as" when rays of light focus at a point image is formed." So here we have two events, one focusing of light and another ...
0
votes
1answer
542 views

Stark effect in two level atomic, laser-driven system?

In a two level atomic system (Rabi oscillating problem) the perturbative potential is oscillating / sinusoidal because it comes from the electric field from the laser. Now stark effect is the ...
0
votes
1answer
74 views

Photon detection rate for pure / mixed states coming from single mode point source

Let the pure states be in superposition of horizontal and vertically polarized basis states. They are arriving at the point detector one at a time. So, a pure state is $|\Psi\rangle = \alpha|V\rangle ...
3
votes
0answers
116 views

Dyson Series Second Order Term Importance vs. Time

Given a time ordered Dyson series expansion of $$H_I=e^{-\frac{i}{\hbar}\sigma_3t}V_0\sin(\omega t)\sigma_1e^{\frac{i}{\hbar}\sigma_3t}$$ $${\cal ...
1
vote
0answers
173 views

Polarization photon and Stokes parameters

I have the following situation: About the polarization of the photon, I introduce the basis: Horizontal polarization $|\leftrightarrow>=\binom{1}{0}$ Vertical polarization ...
2
votes
0answers
188 views

How to calculate radiative transition rate of exciton in a quantum dot with specific dimension?

I am writing rate equations for a nanophotonic system including three quantum dots. I need to calculate that radiative transition rates of exciton in ground state in those quantum dots. In the paper ...
2
votes
0answers
65 views

fiber optic second order PMD as an operator on the tensor product Hilbert space

Second order polarization mode dispersion (SOPMD) is a coupling mechanism between polarization and frequency. Take our photon to be the following tensor product: $\psi = \int \gamma_{\omega} | ...
0
votes
0answers
323 views

Intensity of the diffraction pattern of the double slit

I am trying another approach for my last unanswered question. (Bounty still on for 3 days. Anyone? Please?) Note that this is not the same question but a greatly simplified version concerning a much ...
2
votes
3answers
370 views

Is there a simple approximation to calculate the index of refraction of water?

A very rough approximation from first principles, from the elementary charge and hbar, would suffice. But is there such an approximation at all? (Alternatively, if water is too difficult: is there ...