ew_djc
Support repository for the upcoming paper "Spectral response of a nonlinear Jaynes-Cummings model
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Repository
Support repository for the upcoming paper "Spectral response of a nonlinear Jaynes-Cummings model
Basic Info
- Host: GitHub
- Owner: rurz
- License: mit
- Language: Jupyter Notebook
- Default Branch: master
- Size: 3.53 MB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 3
Metadata Files
README.md
Spectral response of a nonlinear Jaynes-Cummings model
Here we will show the numerical simulation of the system, and a comparison with the analytical¹ expressions. If you want an interactive preview, launch the Binder server of the repository, or even easily, open the notebook in Colab.
The full-Hamiltonian in consideration to simulate is defined as
$$\hat{H}^{D}_{\texttt{JC}} = \frac{\hbar\omega_{c}}{2}(\hat{A}^{\dagger}\hat{A} + \hat{A} \hat{A}^{\dagger}) + \frac{\hbar\omega_a}{2}\hat{\sigma}_{z} - \mathrm{i}\frac{\hbar\Omega_{0}}{2}(\hat{A}\hat{\sigma}_{+} - \hat{A}^{\dagger} \hat{\sigma}_{-}),$$
where $\hat{A} = \hat{a}f(\hat{n})$ the new deformed annihilation operator, that uses the deformation function $f^2(\hat{n})=1+\chi\hat{n}$, for some parameter $\chi$ that acts a deformation strength.
Algorithmically, we define the deformed operators, then the Hamiltonian is used to obtain the evolution operator. This evolution operator is used to translate the operators in the two-time correlation function to a Heisenberg representation, and then the numerical integration of this correlation function is performed. The result is the frequency spectrum from $0$ to $t_{\mathrm{obs}}$.
¹In a strict way, we do a semi-analytical approach, since we obtain the analytical two-time correlation functions, and then we numerically integrate this expression in order to obtain the frequency-dependent spectrum at time $t$.
Authors: L. Medina-Dozal, A.R. Urzúa , D. Aranda-Lozano, Carlos A. Gonz ález-Gutiérrez , J. Récamier , and R. Rom án-Ancheyta.
Code developer: A.R. Urzúa
Owner
- Name: Alejandro R. Urzúa
- Login: rurz
- Kind: user
- Location: Cuernavaca, Morelos, México
- Company: Instituto de Ciencias Físicas, UNAM
- Website: arurz.xyz
- Twitter: arurzp
- Repositories: 23
- Profile: https://github.com/rurz
Theoretical Physicist at ICF UNAM Interested in group theoretical methods in physics and quantum optical systems.
Citation (CITATION.cff)
cff-version: 1.2.0 message: "If you use this software, please cite it as below." authors: - family-names: "Alejandro R." given-names: "Urzúa" orcid: "https://orcid.org/0000-0002-6255-5453" - family-names: "Luis" given-names: "Medina-Dozal" orcid: "https://orcid.org/0000-0002-4695-5190" - family-names: "Diego" given-names: "Aranda-Lozano" - family-names: "Carlos A." given-names: "González-Gutiérrez" orcid: "https://orcid.org/0000-0002-1734-1405" - family-names: "José F." given-names: "Récamier" orcid: "https://orcid.org/0000-0002-5995-0380" - family-names: "Ricardo" given-names: "Román-Ancheyta" orcid: "https://orcid.org/0000-0001-6718-8587" title: "Spectral response of a nonlinear Jaynes-Cummings model" version: 0.0.1 doi: 10.5281/zenodo.12788271 date-released: 2024-07-20 url: "https://github.com/rurz/EW_DJC"
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Dependencies
- numpy
- pip
- python