Skip to main content

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
2 votes
0 answers
33 views

Correlation function of a two-level quantum system coupled to a thermal bath

I am trying to quantify the temporal correlations of observables in an open quantum system, i.e. calculate a quantity of the type, \begin{equation} \langle n(t) n(t') \rangle - \langle n(t)\rangle \...
A G P's user avatar
  • 31
3 votes
1 answer
104 views

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 $\...
A. Radek Martinez's user avatar
0 votes
1 answer
165 views

Finite-time effects in Landau Zener

Consider a two level system with a Landau-Zener Hamiltonian of the form $$\hat{H}=\begin{pmatrix}v t&\beta\\\beta&-v t\end{pmatrix}.$$ The Landau-Zener formula provides a closed form for the ...
TopoLynch's user avatar
  • 503
1 vote
0 answers
23 views

Laser resonance phase shift

I understand in classical mechanics, for an driving force to be resonant with the oscillator and give force to it, there must be a $\pi/2$ phase shift (lag). My first question: is this the same for ...
lalala's user avatar
  • 39
0 votes
0 answers
14 views

AC Stark shift in the non-perturbative regime

I am trying to simulate the following situation. I have a 2 level system, with the energy spacing $\omega_0$. I have a laser, with Rabi frequency $\Omega_1$ and frequency $\omega_1$, which I can scan ...
Alex Marshall's user avatar
0 votes
0 answers
44 views

Choice of axes in resonantly driven two level system

Consider a two-level atom with a transition at angular frequency $\omega_0$ and $\mu_{12}=2 \times 10^{-29} \text{Cm}$ subjected to a sequence of two resonant pulses. The first pulse has electric ...
Anchal Kumar Sharma's user avatar
0 votes
0 answers
46 views

Decay rates, time-energy uncertainty, and photon spectrum in two-level system

This question concerns mainly a few statements from the following article https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.063839. It states: "Early studies of two-level quantum systems ...
AlienTek's user avatar
1 vote
2 answers
127 views

Understanding Exceptional Points

Exceptional points occur generically in eigenvalue problems that depend on a parameter. By variation of such parameter (usually into the complex plane) one can generically find points where ...
ZHENGYAO HUANG's user avatar
1 vote
1 answer
71 views

Two-dimensional Two-particle system [closed]

I have to find the energy levels of a two dimensional system with two energy eigenstates $|0\rangle$ and $|1\rangle$ with energies $E_0$ and $E_1$. Furthermore there are two noninteracting particles $...
Einmi's user avatar
  • 11
1 vote
0 answers
23 views

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 ...
SpinSensor's user avatar
1 vote
1 answer
63 views

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_- ...
XxscheggiaxX's user avatar
3 votes
1 answer
460 views

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 ...
Quantumwhisp's user avatar
  • 6,773
4 votes
0 answers
264 views

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 ...
KF Gauss's user avatar
  • 7,931
2 votes
1 answer
248 views

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,...
AndreaMaestri18's user avatar
1 vote
1 answer
142 views

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-...
Quantumwhisp's user avatar
  • 6,773
0 votes
1 answer
185 views

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 ...
Michael's user avatar
  • 129
1 vote
1 answer
117 views

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 ...
MTYS's user avatar
  • 369
0 votes
0 answers
277 views

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\...
QuantionQuestums's user avatar
0 votes
0 answers
36 views

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 $\omega(\lll\omega_{21})$, ...
Solidification's user avatar
4 votes
1 answer
426 views

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 ...
peter mafai's user avatar
2 votes
0 answers
102 views

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 ...
JohnDoe122's user avatar
1 vote
0 answers
93 views

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 ...
jamie1989's user avatar
  • 1,816
0 votes
0 answers
113 views

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)}...
SalahTheGoat's user avatar
  • 1,581
0 votes
1 answer
104 views

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 ...
YordanToshev's user avatar
2 votes
1 answer
551 views

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 $...
vpflynn19's user avatar
2 votes
1 answer
395 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 ...
peter mafai's user avatar
1 vote
1 answer
80 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 ...
Chris Yang's user avatar
1 vote
0 answers
143 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>...
Andrea's user avatar
  • 735
0 votes
0 answers
103 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: ...
VATSAL JAIN's user avatar
1 vote
3 answers
230 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 ...
tomdodd4598's user avatar
0 votes
1 answer
209 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}^{\...
MicrosoftBruh's user avatar
2 votes
1 answer
179 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 ...
peter mafai's user avatar
2 votes
1 answer
164 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 ...
jamie1989's user avatar
  • 1,816
0 votes
1 answer
855 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=\...
Curious's user avatar
  • 115
2 votes
2 answers
591 views

What is integration time in microscopy?

What is the "integration time" in Two-photon excitation microscopy?
tom's user avatar
  • 43
2 votes
2 answers
906 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 \...
ocf001497's user avatar
  • 766
0 votes
1 answer
37 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|...
Hell stormer's user avatar
2 votes
1 answer
778 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 ...
quantumik's user avatar
0 votes
1 answer
164 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 ...
bidon's user avatar
  • 17
1 vote
1 answer
51 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 ...
hype's user avatar
  • 11
2 votes
2 answers
2k 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 ...
SalahTheGoat's user avatar
  • 1,581
0 votes
1 answer
1k 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, ...
Nakshatra Gangopadhay's user avatar
0 votes
1 answer
214 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?
oweydd's user avatar
  • 455
3 votes
3 answers
268 views

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 \...
StarBucK's user avatar
  • 1,450
0 votes
2 answers
1k 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 ...
Lost's user avatar
  • 1,441
0 votes
1 answer
76 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 ...
Physics Student's user avatar
0 votes
1 answer
97 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, $$i\hbar\frac{dC_{II}}{dt}=(E_0-A)C_{II}+\mu\mathcal{E}C_I.\tag{9.38}$$ ...
Physics Student's user avatar
1 vote
1 answer
191 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 ...
Peace Wan's user avatar
  • 111
2 votes
0 answers
96 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 ...
JohnDoe122's user avatar
0 votes
1 answer
188 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 \...
brunni's user avatar
  • 13