Questions tagged [two-level-system]
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.
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Absorption Cross Section for Two-Level Spin System in an AC Magnetic Field - Photon Picture
For a two-level spin with a energy difference of $E = h f$, where the two levels have zero dipole electric coupling and can only be driven by a magnetic field, how do I calculate the absorption cross ...
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Solving time-dependent two-levels hamiltonian [closed]
I would like to solve the time-dependent Schrodinger equation for a two-levels system with a time-dependent Hamiltonian ($ \hbar = 1 $)
$$ H(t) = \frac{\Omega_R}{2} i (\sigma_+ e^{i t \Delta}-\sigma_- ...
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Why in 2-level system can a diagonal lindblad equation be used to describe decay, when $|0\rangle$ and $|1\rangle$ aren't energy eigenstates anymore?
Citing Wikipedia (https://en.wikipedia.org/wiki/Lindbladian), the Lindblad equation takes the following form:
\begin{align}
{\displaystyle {\dot {\rho }}=-{\frac {\mathrm {i} }{\hbar }}[H,\rho ]+\sum ...
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Implement Adiabatic Elimination on Hamiltonians?
Adiabatic elimination is the process of truncating a Hamiltonian's Hilbert space to the "slow" states you care about. You throw out the "fast" eigenstates to produce a smaller ...
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Time evolution operator for 2-level system hamiltonian
I'm trying to compute the time evolution operator of a system with the following hamiltonian:
$$ H(t) = g(t)[\sigma^+ e^{i \omega t } + \sigma^-e^{-i \omega t }] $$
I tried to use the Magnus expansion,...
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Coherent photon scattering on a 2-level system: How can the commutator of the Electric field and the dipole operator be nonzero?
Girish Argawal writes in his book Quantum statistical theories of spontaneous emission and their relation to other approaches (1974) at the end of chapter 7:
It may appear from (7.13) that the equal-...
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Maximum entropy of a two-level system
Consider a 2-level system of $N$ particles with energies and degeneracies $g_0=1, g_1=2$, is there a way to demonstrate mathematically what is the maximum entropy?
Here’s my attempt:
Using Boltzmann ...
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When can we apply Rabi oscillations in an energy transition?
I'm reading a quantum mechanics book which states that:
"For ω close to Ω, where ω is the frequency of the external field and Ω is the transition frequency, all states with other frequencies are ...
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Theory of 2D electronic spectroscopy
I'm learning about two-dimensional electronic spectroscopy (2DES) right now, and its ability to pick up on quantum coherences between different eigenstates of a system. I understand that the two axes ...
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Q-factor decomposition of superconducting resonators
The internal Q-factor of superconducting resonator can be described by the following formula (B. Mergant et al. "Dielectric surface loss in superconducting resonators with flux-trapping
holes&...
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Wavefunction collapse of Identical two particle system- What does following wavefunction tell us?
What is this equation telling us?
$\psi_a$ and $\psi_b$ are the wave functions of particle 1 and 2 respectively;
and $r_1$ and $r_2$ are position vectors of particle 1 and particle 2 respectively.
\...
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Time evolution operator of a two-level system with a completely general Hamiltonian
Using the identity ($\sigma_{0}$) and the Pauli operators ($\sigma_{i}$) as a basis, the Hamiltonian of any two-level system can be expressed as follows
$$
H =\alpha \cdot \sigma _{0}+\textbf{r}\cdot\...
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The integral for Berry curvature dipole
In this paper, the author proposed that the nonlinear Hall effect can exist in time-reversal-invariant systems, driven by Berry curvature dipole (BCD), in which a two-band model
$$H_{s\Lambda}=s\alpha ...
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Relative frequency of measurement results of an observable in a two-level system
I just had a question about the solution given to the following problem:
The Hamiltonian of a two-level system is $\hat{H} = \Sigma_{i=0,1} \epsilon_{i} |i⟩⟨i|$. A set of repeated independent ...
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Two-level system with natural frequency $\omega_{21}$ exposed to an EM radiation of frequency $\omega$
Consider a two-level system with energies $E_1$ and $E_2(\gt E_1)$, and an energy gap $$E_2-E_1=\hbar\omega_{21}.$$ If this system is excited by an EM radiation of frequency $\omega(\lll\omega_{21})$, ...
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Collapse operators of two-level atom
Currently I am learning about the Lindbladian. I want to derive the optical bloch equations for a two-level atom interacting with monochromatic light from the Lindbladian. However I am having troubles ...
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AC Stark shift in a 3 level system
If we have a 2 level system and I send a laser on resonance, when working in the dressed atom description, each level gets split by $\pm\Omega$ i.e. the Rabi frequency of the laser. Now if we send a ...
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Adiabatic elimination of the excited state for a light field beam splitter
I am going through the derivation of the eoms for a matterwave beam splitter based on Bragg diffraction from counter-propagating laser beams of frequencies $\omega_a$ and $\omega_b$ interacting with a ...
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Help with expanding to second order in perturbation theory
In McIntyre's Quantum Mechanics: a Paradigms approach (pg 318), we solve for the energies of a perturbed 2 level system to get that
$$E_1= E^{(0)}_1+\lambda H'_{11}+\frac{\lambda^2|H'_{12}|^2}{(E^{(0)}...
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Evolution operator of a two-level system in atomic clocks
I have a few questions concerning equation (6) from this (http://arxiv.org/abs/1610.02537) paper from Weinberg in which he describes the time evolution of a two level system e.g. a Cs atom in an ...
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Berry's phase for an electron in a two-level system
I am trying to reconcile two seemingly contradictory statements about Berry's phase for a two-level system in a magnetic field. Consider the Hamiltonian $H(t) = -\mathbf{B}(t)\cdot\pmb{\sigma}$ where $...
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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 ...
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Conservation of symmetrization in quantum mechanics
I recently read about the symmetrization requirement, which my book states is axiomatic of quantum mechanics:
$$
\psi(\mathbf r_1, \mathbf r_2) = \pm \psi(\mathbf r_2, \mathbf r_1). \tag{*}
$$
It ...
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Specific heat of a two-level quantum system [closed]
A two-level quantum system has the hamiltonian
$$ H = \begin{pmatrix} E_0 & 0\\ 0 & E_1 \end{pmatrix}
+ \begin{pmatrix} 0 & g\\ g & 0 \end{pmatrix} $$
where $g<<E_0$ and $E_1>...
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Spin Hamiltonian for 2 electron system
I am currently studying exchange interaction and came across the spin operator in Ashcroft and Mermin Chapter 32 page 680 which states that the spin hamiltonian can be defined as:
...
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For a generic two-state quantum system, are there interpretations for the observables corresponding to all Hermitian operators?
The simplest non-trivial system is a two-level system. Classically, it is a system which can be in one state labelled $H$ or another state labelled $T$.
There is no necessary reference to any ...
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Density matrix element in Jaynes-Cummings model
In the Jaynes-Cummings model, when using the density matrix to describe mixed states for the atom-field system, after some calculations I got to this matrix element:
$$ \rho_{ee}^A = \sum_{n=0}^{\...
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Two-level system interaction with light
Im brooding about this now for a long time and I dont get why this equals 0. Its an excerpt from the book " R.Loudon - The Quantum Theory of Light " (Link to the full Book). This excerpt is ...
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Why is spontaneous emission neglected in standard discussions of the two-level system?
When discussing two-level systems, spontaneous emission is often neglected `until later'. However, when discussed later, the two-level system is no longer discussed. For example, see Straten and ...
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Unitary transformation in rotating frame for two-level atom
Considering an atom with two states: $|g\rangle$ and $|e\rangle$, its Hamiltonian, when illuminating with some drive frequency $\omega_d$, which couples two states (according to wiki):
$$H/\hbar=\...
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What is integration time in microscopy?
What is the "integration time" in Two-photon excitation microscopy?
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Can a projector serve as an operator for observable?
Suppose I have a two-level quantum system whose orthonormal basis is $\{ |0\rangle,|1\rangle \}$. Consider the projector onto the one-dimensional space spanned by $|1\rangle$: $P_{1} = |1\rangle \...
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Meaning of different phases in two-state system
Assuming we have the state of some particle (maybe in this case an electron).
Is there an intuitive explanation what the difference between
$|\psi\rangle = a|0\rangle+b|1\rangle$ and $|\psi\rangle = a|...
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Population inversion two-level system
I was studying the classic two-level system where population inversion can be realized through a $\pi$-pulse or Rapid Adiabatic Passage, like the landau-zener case. The professor said that such an ...
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How do I calculate the expectation value $\langle\Psi_0| H | \Psi_1\rangle$ for column vector wave functions?
I am trying to perform a perturbation for a system but I get really confused when trying to calculate an expectation for a column vector wave function. Hamiltonian is a 2×2 diagonal matrix and I am ...
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What other possible quantum systems are there besides two-level/two-state quantum systems? [closed]
Sorry for the rather odd question, but here it is:
There are a ton of references and research literature on two-state quantum systems, and their derived properties and mathematics. I'm familiar with ...
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Time-independent perturbation theory applied to the most general two-level system?
My question relates to problem 7.4 in Griffiths intro to QM (3rd Ed). In it, we are asked to apply pertubation theory to the most general two-level system where the unperturbed Hamiltonian $H^0$ and ...
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Degeneracy in $N$-particle Quantum System [closed]
I was recently introduced to the concept of $N$ particle systems in Quantum Mechanics, and the concept of indistinguishable and distinguishable particles. While reading the following material online, ...
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Time Reversal Operator for two-level system
Does the time-reversal operator have the same effect on on the Pauli matrices if we consider a two-level system which does not represent a physical spin-1/2 particle?
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Procedure to cut an Harmonic oscillator to two first level to obtain a qubit
Let us consider a (quantum) Harmonic oscillator:
$$H=\frac{p^2}{2m}+\frac{1}{2} m \omega^2 x^2$$
Using the annihilation/creation operators defined as:
$$a=\sqrt{\frac{\hbar}{2 m \omega}}(x+\frac{i}{m \...
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Degeneracy in a two-level system of distinguishable particle
If we consider $2$ distinguishable particles and two possible energies: $0$ and $0.01$eV.
Then while reading about this in books it's mentioned that this is considered as a non-degenerate system.
But ...
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How do you derive (9.10) from the Feynman lectures Vol. III? [closed]
The Feynman lectures volume 3 chapter 9 analyzes the ammonia molecule. It assumes there are only two base states. The amplitude, $C_1$, to be in the first state, $\lvert1\rangle$, in which the ...
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How do you derive (9.38) of Vol. III of the Feynman lectures?
The Feynman lectures volume 3 chapter 9 shows equation $(9.38)$, which is the equation I don't know how to derive, as follows,
$$i\hbar\frac{dC_{II}}{dt}=(E_0-A)C_{II}+\mu\mathcal{E}C_I.\tag{9.38}$$
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How to understand the relation of the two representation of dipole moment?
On one hand, the dipole moment is define as
$$\vec{\mu} = q\vec{r},$$
where q is the charge and $\vec{r}$ is a position vector.
On the other hand,
I know the transition dipole operator of a two level ...
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Change of reference frame in quantum mechanics
I am dealing with a problem of a 2 level system (an ion in my case) placed in a Penning trap. Basically the ion is moving inside the trap under the influence of the magnetic and electric field and I ...
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Ammonia in an electric field - Hamiltonian in different bases
The ammonia molecule in an electric field seems to be a popular two-state system used in introductions.
The hamiltonian (in the state basis?) is usually written as:
$$\begin{pmatrix} E_1 - \mu \...
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Unequal superpositions of energy eigenstates in two-state quantum systems?
Two-state quantum systems in a superposition of energy eigenstates oscillate with time between the possible states. If both energy eigenstates contribute with the same amplitude, the oscillation is ...
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What enduces transition in a two-state Quantum Mechanical system?
Assume we have a two-state system, with an excited state, $ | e \rangle $, and a ground state, $|g\rangle$. The states have an energy difference of $E$. I want to talk about the transition frequency ...
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Understanding the Derivation of Rabi-Oscillations
In his scriptum, Jan Krieger proves on page 56 the probability of finding a system in a state $\vert2\rangle$ if it was at time $t = 0$ in the state $\vert1\rangle$, where both $\vert1\rangle$ and $\...
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Plotting the Energies of the Perturbed Hamiltonian in the Two-state Quantum System
I would like to understand the following Figure, taken from the German Wikipedia site:
First of all, the German Wikipedia site denotes as $E_{\pm}$ the energies of the new Hamiltonian $H = H^{0} + W$....
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