Questions tagged [rabi-model]

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State Evolution in Cavity QED

Part 1 $\newcommand{\ket}[1]{|#1\rangle}$ If a general state of a 2-level atom can be represented by: $$\ket{\psi} = \cos(\frac{\Omega t}{2} + \phi)\ket{g} + \sin(\frac{\Omega t}{2} + \phi)\ket{e} $$ ...
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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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Rabi-like Model for $N$-Level Systems coupled to one or more quantized field modes

I'm doing a literature review on the history of model development in the scope of light-matter interaction. I've studied in depth the two key tools for a lot of the research in this field, two level ...
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Rabi oscillations within the adiabatic theorem?

I'm studying Rabi oscillations in a two-level system (TLS) with Hamiltonian \begin{align}H(t)=\omega_0 \sigma_z + \Omega \cos(\omega_1 t) \sigma_x.\end{align} The model is usually treated within the ...
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Is there any summary of cavity QED and spin resonance related effects and splittings?

I recently started working on NMR-based qubits and I have lots of confusion regarding the definitions of different interactions and energy level splitting phenomenon. I wonder if you know any ...
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Spontaneous emission rate with coherent and incoherent sources

I want to study the emission and absorption of photons by atoms. I start with a quantized field and a two level atom interacting. Suppose our field has frequency $\omega_0$ and the energy gap has a ...
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Eigenvectors of dressed states [closed]

Given the following hamiltonian: (basis $|1 \rangle ; |2 \rangle) $ $$H = \frac{\hbar}{2}\begin{bmatrix} \Delta & - \Omega \\ - \Omega & \Delta\\ \end{bmatrix}$$ I found the ...
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Rabi as limit of Jaynes-Cummings model

I was wondering how to get back the Rabi oscillations from the Jaynes-Cummings model. My first intuition is to let the coupling parameter go to zero, however this does not make the electromagnetic ...
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Rabi Hamiltonian with three instead of two Pauli matrices

This question was motivated by a question on Mathoverflow, in which a Hamiltonian is considered that looks like the Rabi Hamiltonian, but with three instead of two Pauli matrices: $$H=\omega a^\dagger ...
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Rabi Oscillations: $\pi$-Pulse vs a single photon

I am puzzled by the following: Assume an atom as a two-level-system. A $\pi$-Pulse acting on an atom in the ground state promotes this atom in the excited state. This is done by a continuous ...
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Factor of 2 in the Rabi frequency

This is a question about a strange literature discrepancy which I can't seem to resolve for myself. In the wikipedia article on the Maxwell-Bloch equations, the Rabi frequency is defined as $$\Omega = ...
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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 to to distinguish two photon Dicke/Rabi model from one photon Dicke/Rabi model in circuit QED?

I read papers about the Dicke model and Rabi model. There are many discussion about $A^2$ term in circuit QED [Gu, Xiu, et al. "Microwave photonics with superconducting quantum circuits." ...
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Two photons Rabi oscillation

Assuming we have a 2 level system (e.g. an atom with 2 energy levels) and the lifetime of the upper level can be neglected, if we make the atom interact with a laser at a fixed frequency, we would get ...
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Single photon detection problem [closed]

In 1999 the Haroche group in Paris performed the measurement of a single photon without destroying it. The experimental setup comprises a standard cavity-quantum-electrodynamic (cavity-QED) setting: ...
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Rabi oscillation in the Jaynes-Cummings model

Consider a qubit-cavity system governed by the usual Jaynes-Cummings Hamiltonian in the dispersive regime $$ H_0 = \omega_q \frac{\sigma_z}{2} + \omega_a a^\dagger a + \chi a^\dagger a \frac{\sigma_z}{...
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Spin precession for Rabi oscillations : interpretation with magnetic field in rotating frame

The model considered Consider an atom modeled by a two level system of energy $\hbar \omega$. We assume this atom is interacting with an electric field through electric-dipole interaction. The full ...
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When one can reduce the Hilbert space in Jaynes-Cummings Model?

I found that : $[N,H] = 0$ , With $N=|e><e|+a^+a$ is the number of excitations and $H$ is the Hamiltonian of Jaynes-Cummings. and i want to describe the dynamics of the system(atom of two ...
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Why we neglect the $\hbar ω/2$ in the Hamiltonian of the the Electromagnetic Field?

After the quantization of the electric and the magnetic field, we get the Hamiltonian of the electromagnetic field: $$H= \hbar ω(a^{\dagger}a +1/2) .$$ with $\hbar$ the planck constant and $a^{\...
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Two different expressions for Rabi Frequency (on resonance)

I've been searching through several articles and books and I found two different expressions for the Rabi Frequency on the semiclassical rotating-wave approximation, and they are different by a factor ...
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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 ...
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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 ...
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Calculating the Rabi frequency of a pulse

If I apply a $\frac{π}{2}$ pulse of linewidth 5MHz centred at 99MHz to a nuclear spin also centred at 99MHz, is there a way to calculate a Rabi frequency of this interaction? I realise the Rabi ...
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Off-resonant Rabi oscillations

If I have a laser field that causes Rabi oscillation of a two-level system, I can use the Hamiltonian $H=-\frac{\Delta}{2}\sigma_z+\frac{\Omega}{2}\sigma_x$ where $\Omega$ is the Rabi frequency of ...
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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 ...
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Is the total number of excitation conserved with Rabi Hamiltonian?

From quantum optics textbooks, I have learned about Jaynes-Cummings Hamiltonian for a description of atom and field interaction, as an approximated model under the so-called rotating wave ...
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Violation of energy conservation by counter-rotating terms in Rabi model for atom-field interaction

When we describe the interaction between two-level atom and single-mode electromagnetic field in quantum optics, we have the so-called Rabi-model before the rotating-wave approximation, by which the ...
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General Two-State Systems and Rabi Oscillations

I've been working on this for quite a while now and can't seem to figure it out. I am concerned with the dynamics of a general two-state system, specifically the case of a particle in a constant ...
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How do Rabi oscillations act on the relative phase of state kets

Suppose we have a system with a lower state $\left|{\downarrow}\right\rangle$ and and upper state $\left|{\uparrow}\right\rangle$, coupled by a pulsed electromagnetic field. I thought that from an ...
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How many photons are absorbed during Rabi oscillations?

In my understanding, Rabi oscillations are derived using the classical approximation for the electromagnetic field. I don't get how this picture fits with a quantized EM field though. Say you excite a ...
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Deriving Rabi rotation matrix

I want to understand where the matrix: $$ \left|\psi(t)\right> = \binom{a(t)}{b(t)} = \begin{bmatrix} cos(\Omega t/2)&-ie^{i\phi_L t}sin(\Omega t/2) \\ -ie^{-i\phi_L t}sin(\Omega t/2) & ...
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What are the "strong", "ultrastrong" and "deep strong" coupling regimes of the Rabi model?

The Rabi model describes a two-level system interacting via a linear coupling with a quantized harmonic oscillator, and it is described by the hamiltonian $$ H_{\rm{Rabi}}=\hbar\omega\, a^\dagger a +\...
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