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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
39 views

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 ...
user avatar
0 votes
0 answers
19 views

Approximation for two level system differential equations

I am currently reading the book "the quantum theory of light" link: http://rplab.ru/~as/2000%20-%20R.Loudon%20-%20The%20Quantum%20Theory%20of%20Light%20-%203rd%20ed%20Oxford%20Science%...
user avatar
0 votes
0 answers
12 views

How to model a Josephson junction as a two-level atom?

I have seen people saying that under certain condition, the dynamics in the Josephson junction can be simplified to that of a two-level system, governed by a the following Hamiltonian which ...
user avatar
1 vote
1 answer
48 views

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 ...
user avatar
  • 385
1 vote
0 answers
50 views

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>...
user avatar
  • 432
0 votes
0 answers
32 views

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: ...
user avatar
1 vote
0 answers
23 views

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 ...
user avatar
0 votes
1 answer
65 views

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}^{\...
user avatar
2 votes
1 answer
60 views

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 ...
user avatar
2 votes
1 answer
41 views

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 ...
user avatar
  • 1,626
0 votes
1 answer
104 views

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=\...
user avatar
  • 15
2 votes
1 answer
61 views

What is integration time in microscopy?

What is the "integration time" in Two-photon excitation microscopy?
user avatar
  • 43
0 votes
0 answers
32 views

Parameters for Spacelike Entanglement Harvesting with Compact Switching Functions

Entanglement Harvesting is a protocol where one extracts entanglement from a quantum field by coupling local probes to it. However, in order to make sure that the entanglement was harvested from the ...
user avatar
  • 967
2 votes
2 answers
212 views

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 \...
user avatar
  • 691
0 votes
1 answer
28 views

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|...
user avatar
2 votes
1 answer
191 views

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 ...
user avatar
0 votes
0 answers
9 views

Maximum of Schottky Peak for two level system with degeneracy

Context : I am following E.S.R. Gopal' s "Specific Heats At Low Temperatures" and I have been able to successfully obtain the same results they obtain from Equations 4.24 - 4.28 on the ...
user avatar
  • 58
0 votes
1 answer
53 views

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 ...
user avatar
  • 11
1 vote
1 answer
46 views

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 ...
user avatar
  • 11
2 votes
2 answers
346 views

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 ...
user avatar
  • 1,155
0 votes
1 answer
238 views

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, ...
user avatar
0 votes
1 answer
71 views

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?
user avatar
  • 395
0 votes
2 answers
325 views

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 ...
user avatar
  • 1,273
0 votes
1 answer
74 views

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 ...
user avatar
0 votes
1 answer
86 views

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, $$i\hbar\frac{dC_{II}}{dt}=(E_0-A)C_{II}+\mu\mathcal{E}C_I.\tag{9.38}$$ ...
user avatar
1 vote
1 answer
78 views

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 ...
user avatar
  • 111
2 votes
0 answers
47 views

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 ...
user avatar
  • 553
0 votes
1 answer
72 views

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 \...
user avatar
  • 3
0 votes
1 answer
123 views

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 ...
user avatar
  • 3
1 vote
2 answers
70 views

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 ...
user avatar
  • 57
0 votes
1 answer
207 views

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 $\...
user avatar
0 votes
1 answer
82 views

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 $H = H^{0} + W$....
user avatar
0 votes
0 answers
87 views

Excitation of $n$ inhomogenous two-level atom with different detunings? Bloch sphere

I am learning about the bloch sphere and how it is used to to in two level systems. I have done some research already but I am slightly confused. Suppose you have an $n$ number of inhomogenous atoms ...
user avatar
2 votes
1 answer
137 views

How to make a $2\times 2$ Hamiltonian using any $2$ levels of an $N$-level Hamiltonian?

Is there a standard way for me to isolate 2 of N bands of a general $N\times N$ Hamiltonian? That is, I want to make a $2\times 2$ Hamiltonian given a larger one. I was told that there is a general ...
user avatar
2 votes
0 answers
65 views

QM course question about a two-level system with energy splitting coupled to a harmonic oscillator

I am fine with part a, if I drop all the terms of the same and smaller magnitudes than $O(1/\eta)$ after expansion. For part b and c, although I don't understand why "only the second term is ...
user avatar
  • 177
2 votes
1 answer
69 views

Radiative transfer equation for a three-level system

I am trying to derive the radiative transfer equation for a three-level system, which is supposed to be given by: $\frac{dI(\omega,x)}{dx}+N [\alpha\rho_{11}-\beta( \rho_{22}+\rho_{33})]I(\omega,x)=\...
user avatar
  • 161
0 votes
0 answers
212 views

Are the matrix elements of the position operator in the energy representation real?

$\newcommand{\Ket}[1]{\left|#1\right>}$ $\newcommand{\Bra}[1]{\left<#1\right|}$ Hello! I am working with the following hamiltonian $$ \hat{H}= \frac{\hat{p}^2}{2m} + \hat{V}(x) $$ where $\hat{p}$...
user avatar
  • 193
1 vote
2 answers
271 views

Transformation to rotating frame

I want to apply a transformation to the rotating frame of a two level system such that a state in the transformed frame is $ |\hat{\phi} \rangle = U |\phi \rangle$, where U is the generator of ...
user avatar
  • 161
0 votes
1 answer
111 views

Derive Susceptibility from Density Matrix of Two-Level System

I have come to this as the Time Dependent Equations for the Density Matrix for a Two Level System. $$\frac{d}{dt}\Big(\begin{matrix}ρ_{11}&ρ_{12}\\ρ_{21}&ρ_{22} \end{matrix}\Big)=\Bigg(\begin{...
user avatar
2 votes
1 answer
77 views

Question about an Exercise with Time-Dependent Hamiltonian

I've been recently been assigned this exercise: Consider two spin 1/2 particles which are coupled through a time dependent interaction: $$ H(t) = a(t) s_1 \cdot s_2 $$ where $a(t)$ is a ...
user avatar
1 vote
0 answers
37 views

Why does the transition probability resemble the Fraunhofer diffraction pattern for single slit?

For a two-level system having an arbitrary state, $\Psi=c_1(t)|1\rangle+c_2(t)|1\rangle$ the transition probability from state $|1\rangle$ to state $|2\rangle$ ,i.e., $|c_2(t)|^2$ can be calculated ...
user avatar
  • 395
2 votes
1 answer
598 views

Parity and the Dipole Operator for a Two-Level System

I attempt to understand the parity and dipole operator from Daniel Steck's notes: Quantum and Atom Optics (page no. 152, section 5.1.1). I have also attached a screenshot at the end of the question. ...
user avatar
  • 2,701
0 votes
1 answer
67 views

Hermiticity of momentum space Hamiltonian

I have managed to confuse myself with the notion of hermiticity in momentum space. In most quantum mechanical applications we assume: $$ H(R) = H^{\dagger}(R) $$ For $R$ some position vector. Now ...
user avatar
  • 961
3 votes
2 answers
423 views

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^...
user avatar
  • 67
0 votes
1 answer
93 views

EM Field Interacting with Two Level System (With Permanent Dipoles)

I have started from Schrodinger equation: $${i\hbar\frac{\partial}{{\partial}t}}|Ψ(t)\rangle=H(t)|Ψ(t)\rangle$$ With Hamiltonian of this kind: $$H(t)=H_0+V_{int}$$ With eigenstates $$H_0|n\rangle=\...
user avatar
3 votes
1 answer
149 views

How is the two-level atom dipole force modified for a real, multi-level atom?

I was trying to compute the dipole force exerted by a laser beam at $1064$ nm on a $^6{\mathrm{Li}}$ atom (the most important transition being around $671$ nm, the laser is greatly red-detuned), when ...
user avatar
  • 1,702
1 vote
4 answers
622 views

Interpretation of the photon scattering rate?

The photon scattering rate $\Gamma$ describes the rate at which photons scatter off an atom$^1$. In a two-level system, the ansatz for the photon scattering rate often is given by \begin{equation} \...
user avatar
  • 47
0 votes
0 answers
238 views

Partition function of a two level system

So I have a system made up of $N$ indistinguishable fermions that interact with each other. Also, the system is made up of two energy levels, and their gap is $D$. Therefore, trying to write down ...
user avatar
0 votes
1 answer
418 views

What is Rabi splitting? Is it related to Autler-Townes splitting?

A quantum optics text I am reading claims that the proper way to analyze a two-level atom's interaction with light is to, conceptually speaking, consider four states: $|g, n\rangle, |e, n\rangle, |g, ...
user avatar
0 votes
1 answer
152 views

Different formula to find $2\times 2$ Hamiltonian's eigenvalues [closed]

Consider the Hamiltonian $$ \left[ \begin{matrix} E_1 & -A\\ -A& E_2\\ \end{matrix} \right] $$ where $A$, $E_1,E_2$ are real numbers. I have seen a different formula to ...
user avatar