A quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. Any two-state system can also be seen as a qubit.
Questions tagged [two-level-system]
124 questions
43
votes
8 answers
Are these two quantum systems distinguishable?
Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two-level atom. Half the time the atom is produced in the ground state, and half the time the atom is produced in the…
Andrew
- 3,501
14
votes
2 answers
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 successful in treating weak coupling and near…
xslittlegrass
- 873
8
votes
1 answer
Intuitive explanation for Rabi oscillations in a two-level system
Is there an intuitive explanation of why the Rabi oscillations with frequency $\Omega$ occur in a two-level systemand why they get faster when the transition dipole moment $M$ ($M\propto V$) gets larger or/and when the frequency of the light…
peter mafai
- 451
7
votes
1 answer
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}
Often (or always?) this transition frequency is not…
user129412
- 1,601
5
votes
0 answers
Implement Adiabatic Elimination on Hamiltonians?
Adiabatic elimination is the process of truncating a Hamiltonian's Hilbert space to the "slow" states you care about. You throw out the "fast" eigenstates to produce a smaller effective Hamiltonian $H_{eff}$ at the cost of having different couplings…
KF Gauss
- 8,314
5
votes
3 answers
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 system is
$$Z = 1 + g e^{-\beta \epsilon}$$
where…
Kai
- 3,930
- 1
- 15
- 29
5
votes
2 answers
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 Schrodinger picture. It's a bit tricky because in…
Jagerber48
- 16,234
5
votes
2 answers
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]{\langle #1 \rangle}\newcommand{\e}[0]{\varepsilon}…
4
votes
1 answer
Two-level system and a classical oscillator - energy
I have solved two related problems and have some questions about the results.
Forced classical oscillator with the following equation:
$$\ddot{x}+\omega_{0}^{2}x=\varepsilon e^{-\gamma t}\sin\omega t,\qquad…
Yuriy S
- 595
4
votes
1 answer
Collapse operators of two-level atom
Currently I am learning about the Lindbladian. I want to derive the optical bloch equations for a two-level atom interacting with monochromatic light from the Lindbladian. However I am having troubles with that.
In general the Lindbladian…
peter mafai
- 451
4
votes
2 answers
Diagonalizing Hamiltonian in Second Quantization
I have a fermionic system with states 1,2. They are coupled by a harmonic oscillator. The Hamiltonian of the system should then be
$$
H=\left[\gamma(a^\dagger+a)-\delta\right]\left( c^\dagger_1 c_2+c^\dagger_2 c_1 \right) + \xi \left ( c^\dagger_1…
Liberty
- 77
4
votes
2 answers
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 field. More concretely, they derive the transition…
eranreches
- 4,249
4
votes
1 answer
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 it impossible to create a laser using two-level…
HerpDerpington
- 975
4
votes
1 answer
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 it into another basis, so that it looks like this:…
Mechanix
- 149
3
votes
1 answer
Adiabatic Approximation in the spin 1/2 System
I am studying the following Hamiltonian:
$$H(t) = \begin{bmatrix}
\frac{t\alpha}{2} & H_{12} \\
H_{12}^* & -\frac{t\alpha}{2} \\
\end{bmatrix}$$
I want to assume that $\alpha$ is sufficiently small, such that the adiabatic…
A. Radek Martinez
- 325
- 3
- 8