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Questions tagged [two-level-system]

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2
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1answer
54 views

Times associated with Absorption and Emission Processes

I am currently reading the book "Advances in Atomic Physics: An Overview" by Cohen-Tannoudji and Guéry-Odelin. In pages 29-31 the authors discuss a two-level atom subject to a broadband radiation ...
0
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2answers
65 views

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 ...
2
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0answers
100 views

2-level system of indistinguishable particles

It is a typical introductory problem in classical statistical physics to calculate the entropy of a two-level-system: say we have a N particle system in which particles can have energy E or 0. ...
0
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1answer
47 views

Two-level system Hamiltonian from electric-dipole approx

After making the electric-dipole approx., I can express the interaction of a monochromatic field with angular frequency $\omega$ and a dipole moment ${\bf \mu(x)}$ as $V({\bf x},t) = - {\bf \mu(x)} \...
2
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0answers
90 views

What is the simplest model of a quantum measurement on a 2 level system

What is the simplest physical system which can be used to model the quantum measurement of a 2 level system? For example, can the following, spin coupled to a harmonic bath, be used to model a ...
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0answers
33 views

How to transform coordinates of two-level system's eigenstates from spherical to momentum space?

In almost all references for some two-level quantum system (for example, this Wikipedia article), arbitrary eigenstates are defined in spherical coordinates, and can be written separately as follows (...
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0answers
21 views

Rabi flopping via density matrices?

Is it possible mathematically to derive Rabi flopping in a two-level atom with the machinery of density matrices? If so, how would one go about it? In particular, let the Hamiltonian of the system be ...
0
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0answers
132 views

Solving density matrix in a two-level atom

I'm working through some parts of Stephen C. Rand's Lectures on Light: Nonlinear and Quantum Optics, specifically sections in which he works with density matrices. In several places he makes ...
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0answers
18 views

What is the difference between arriving at the 'avoided crossing' point of a two level system adiabatically and non-adiabatically?

In the simplest case of the 'avoided crossing phenomenon' we can assume a two level system that its eigenstates $E_1(n)$ and $E_2(n)$ are functions of some continuous variable n, and there is some ...
2
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2answers
61 views

Why are degenerate states more likely to be filled at a given temperature?

Consider if we have a simple two-level toy model, where the ground state has energy $E_0 = 0$ and the excited state has energy $E_1 = \epsilon$ and degeneracy $g$. The partition function for this ...
0
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1answer
102 views

Matrix of Hamiltonian $H=\frac{ħω}{2}(|1〉〈1|−|2〉〈2|)+\frac{iħχ}{2}(|1〉〈2|−|2〉〈1|)$ [closed]

I have a second order system, with a Hamiltonian $$H=\frac{ħω}{2}(|1〉〈1|−|2〉〈2|)+\frac{iħχ}{2}(|1〉〈2|−|2〉〈1|)$$ where $|1〉,|2〉$ form a complete basis for the system. I'm trying to get the matrix that ...
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0answers
43 views

Quantum Coherence in a Two-level System in the Density Matrix Formalism

Dealing with semiclassical light-matter interaction, in particular the interaction between an electromagnetic field and a two level system using the density matrix formalism, I learned that the system ...
0
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1answer
35 views

Does pseudospin necessarily carry angular momentum?

And if so, why? I was told that anything that mathematically transforms like a spin must carry angular momentum. Is this true? One example of pseudospin is electrons in graphene on the A and B ...
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0answers
30 views

Imaginary Transmission

Note that the exact context of Rydberg EIT in the following is, I believe, unimportant. In the paper "Nonlinear quantum optics mediated by Rydberg interactions," O. Firstenberg et al. (J. Phys. B. ...
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0answers
48 views

How does decay rate depend on energy difference?

From Fermi's golden rule, one knows that transition rate is $$\Gamma_{i \to f} = \frac{2\pi}{\hbar} \left \lvert \langle f | H' | i \rangle \right \rvert^2 \rho \, .$$ However, can we make the ...
3
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1answer
162 views

What is the inner product between a position ket and a two-state (or multi-state) ket?

I am recently studying the two-state system in quantum mechanics. As I learned, in the Hilbert space of a spinless particle, the relation between a scalar function and a ket state is satisfied as, $$...
2
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2answers
385 views

Two Level Atom Rotating Frame

Introduction I am trying to work out the Rabi problem. In particular I am trying to work it out from a perspective focusing on the operators rather than the kets. Think Heisenberg picture rather than ...
1
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1answer
63 views

How does “coherence” contribute to inverting a two-level system?

In laser physics I am told that inverting a two-level system is not possible, since it will become transparent once the inversion reaches 50% and no longer be able to absorb more photons. This makes ...
0
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1answer
32 views

Rabi oscillation normalisation

Given that the probability of an atom being in an excited state when it is applied by a resonant field is: $$P=\sin^2(\frac{\Omega_0t}{2})$$ Find an analogous formula in the case of non-resonant ...
-1
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1answer
97 views

Jaynes Cummings Hamiltonian [closed]

Hamiltonian of Jaynes-Cummings model has in Schrodinger picture form: $$ H=\frac{1}{2}\hbar\omega\sigma_{z}+\hbar\omega a^{\dagger}a+\lambda\hbar(\sigma_{+}\hat{a}+\sigma_{-}\hat{a}^{\dagger}) $$ ...
1
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1answer
48 views

Are $|\pm x\rangle$ and $|\pm y\rangle$ always defined the same way for a two-level system?

I'm a little confused about the definitions of the states $|+x\rangle$ and $|+y\rangle$. We've started out talking about spin-${1\over 2}$, and in this first chapter of my textbook (A Modern Approach ...
0
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1answer
48 views

Allowed 2-qubit gates [closed]

I was working on some Quantum Information problems regarding allowed 2-qubit gates and got stuck. These are the proposed transformations: $|A\rangle |B\rangle \rightarrow |B\rangle|\overline A\rangle ...
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0answers
123 views

Natural line width for doubly excited transitions

So a simple derivation for natural single electron emission line broadening is this: $\Delta E \Delta t \approx \frac{h}{2\pi} \Leftrightarrow h\cdot\Delta f_{1/2}\cdot\tau \approx \frac{h}{2\pi} \...
0
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1answer
122 views

Setting up differential equations for two-level Rabi problem

I try to follow the derivation of Rabi two-level problem but I went into trouble when attempting to set up the equations as many notes have suggested. Using the book (Laser cooling and trapping by ...
2
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0answers
49 views

What is the difference between complex and real coherneces?

If we have one density matrix $$\rho=\begin{bmatrix}1/2&&1/2\\1/2&&1/2\end{bmatrix}$$ for the state $\lvert\psi\rangle=\frac{1}{\sqrt2}(\lvert g\rangle+\lvert e\rangle)$ and a ...
0
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1answer
189 views

Writing Hamiltonian matrix elements for a two non-interacting particle system

Let's say I have two non-interacting particles in the classic infinite well boxes of length L. I know the total energy is given by: $$E_{n_1,n_2}=\dfrac{\pi^2\hbar^2}{2mL^2}(n_1^2+n_2^2)$$ where n_1,...
1
vote
2answers
190 views

Dipole matrix element in Jaynes Cummings model

In Jaynes-Cummings model, atom (two-level system, b) to photon (single radiation mode, a) coupling strength $g$ is written in terms of dipole matrix element $\mathbf{d}_{ba}$, $$ \mathbf{d}_{ba} = q ...
0
votes
1answer
865 views

matrix of rotation for quantum states [duplicate]

For the two-level quantum system, we have the bloch sphere representation, and for a rotation we have the exponential operator: $$\text{exp}(\frac{-i \sigma \cdot \hat{n} \phi}{2})$$ where $\sigma = (\...
2
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0answers
60 views

Open orbits on the Bloch sphere of two level atom

I am studying the Bloch sphere representation of a two level atom in a classical electric field, starting in the ground state at t=0. The Bloch equations for the time evolution are $$ \begin{align} ...
4
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2answers
2k views

Matrix for $\pi/2$ pulse?

If we have a two-state system \[ \newcommand{\p}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\f}[2]{\frac{ #1}{ #2}} \newcommand{\l}[0]{\left(} \newcommand{\r}[0]{\right)} \newcommand{\mean}[1]{\...
0
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1answer
49 views

Force on two level system in standing wave electric field

Given external radiation, produced from an electric field travelling from the left and an electric field travelling from the right, producing a standing wave $$E_0e^{i(kx - \omega t)} + E_0e^{-i(kx - ...
0
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0answers
338 views

Hamiltonian of two level system under radiation

In quantum mechanics, as I understand, the Hamiltonian for a two level system is given as $$\hat{H} = \frac{1}{2}\hbar \omega_0 \hat{\sigma_{z}},$$ does anyone know why the perturbation term of the ...
0
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1answer
226 views

States of two particles in 2-level system

I have a question regarding the 2 Fermions in Two-level system and the possible states and resulting partition function. As far as I know, Fermions are forbidden from occupying same quantum states by ...
1
vote
1answer
509 views

Is the Einstein A coefficient the same as the natural line width $\Gamma$?

Given a two-level system, the rate of decay from the excited state via spontaneous emission is given by the coefficient $A$ in Einstein's rate equations. However, there is also the natural line width $...
1
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1answer
159 views

Equivalent two-levels systems Hamiltonians

I've once read somewhere that the following two Hamiltonians each describing a two-level system (TLS) are equivalent to each other and can thus be used in describing the same TLS. $$\mathcal{H}_1=\...
4
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1answer
1k views

Pure dephasing $\gamma_\phi$ in a master equation and noise power spectral densities

In its simplest form, my question is regarding a two level system of transition frequency $\omega_0$ given by the Hamiltonian \begin{equation} H = \frac{\hbar \omega_0}{2}\sigma_z \end{equation} ...
2
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2answers
353 views

Dipole interaction for a two-level system in a trap potential

Consider a two-level system under the following Hamiltonian: $H=H_{I}+H_{E}+H_{dip}$ where $H_I$ is the Hamiltonian for the two internal states of the two-level system $span \{\left |e \right> {,}...
0
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1answer
455 views

probability of finding the system in the ground state [closed]

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ Assume that a quantum mechanical system is described by two orthonormal states $\ket{+}$ and $\ket{-}$, defined by the property of being the ...
2
votes
1answer
668 views

Relation between Canonical and Grand Canonical Ensemble for a two levels system

For a two-level system of classical non interacting distinguishable paricles, labelling energy levels as $+\epsilon, -\epsilon$, in the canonical ensemble I found for the partition function Q$=2\cosh(\...
2
votes
1answer
281 views

Decoupling coupled differential equations in dynamically coupled two state system

Consider the following dynamically coupled two state hamiltonian, $$H=-B\sigma_z-V(t)\sigma_x.$$Taking the eigenfunctions of $\sigma_z$ ($|+>$ and $|- >$) as basis vectors, we have the wave ...
4
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1answer
382 views

Transformation of Jaynes-Cummings Hamiltonian

This is the Jaynes-Cummings Hamiltonian in the interaction picture: $H_i^n = \hbar g \sqrt{n+1}\begin{pmatrix} 0 & \exp(-i\delta t)\\ \exp(i\delta t) & 0 \end{pmatrix}$ I want to transform ...
0
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0answers
307 views

General two state system with general pertubation

I am trying to solve this two-level system with time independent perturbation problem Consider an atomic system with only two stationary states $|1\rangle$ and $|2\rangle$ , of respective energies $...
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2answers
97 views

How do we prove that two conjugate operators $X$ and $Y$ induce $\sigma_x$ and $\sigma_y$ driving terms when restricted to a two level subspace?

Suppose I have a Hamiltonian for a particle moving in a one dimensional potential $$H = H(X,Y) \qquad [X,Y] = i$$ where $X$ is the dimensionless position, $Y$ is the dimensionless momentum, and $\...
7
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1answer
785 views

Analytical solution of two-level system driving by a sinusoidal potential beyond rotating wave approximation

A quantum mechanical two-level system driven by a constant sinusoidal external potential is very useful in varies areas of physics. Although the widely used rotating-wave approximation (RWA) is very ...