frischsegre-cqd-be
Spin-flip Majorana transitions in the Frisch-Segre experiment using co-quantum dynamics theory
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Spin-flip Majorana transitions in the Frisch-Segre experiment using co-quantum dynamics theory
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README.md
Numerical modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Bloch equation
Numerical computation of the fraction of spin flip in the Frisch-Segrè experiment using co-quantum dynamics theory
August, 2022
Authors
- K. Titimbo
- D.C. Garrett
- S.S. Kahraman
- Z. He
- L.V. Wang
Affiliation
Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138-78, Pasadena, CA 91125, USA
Description
This repository contains FS-BE-spinflip.jl, it computes the fraction of spin flip as in the Frisch-Segre experiment using the co-quantum dynamics concepts. The details and results are discussed here.
We model the dynamics of the electron and nucleus magnetic moment of single potassium-39 atoms entering the so-called inner rotation chamber, where a varying weak magnetic field is present. The dynamical equation for the magnetic moments is the Bloch equation, while the interaction between the magnetic moments is described by means of the torque-average magnetic field generated by the opposite system.
The Julia code generates 3 files as outputs: 1. Data (.csv file): organized as follow
| n | Initial conditions | $I_{1}$ | $...$ | $I_{8}$ | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $\theta_{n,0}$ | $\phi_{n,0}$ | $\theta_{e}$ | $\phi_{e}$ | $\theta_{n}$ | $\phi_{n}$ | flip | ... | $\theta_{e}$ | $\phi_{e}$ | $\theta_{n}$ | $\phi_{n}$ | flip | |||||
| 1 | |||||||||||||||||
| $\vdots$ | |||||||||||||||||
| $N$ | |||||||||||||||||
Summary (.txt file): contains metadata about the parameters used for the simulation
Experiment = Frisch-Segre filename = FS_curr_15000_20220816T143123 ODE System = BE3 ensemble = currents coord. = spherical Excep.Hand = wrapping z_a = 0.000105 k_i = 0 field = quadrupole ang. dist. = hs N sampling = 15000 time span = (-11.0, 20.0) us tiny angle = 1.0e-6 reltol = 1.0e-10 abstol = 1.0e-10 dtmin = 1.0e-40 start date = 2022-08-16T14-31-23 end date = 2022-08-17T08-07-47 run time = 17 hours, 36 minutes, 23 seconds, 249 milliseconds hostname = COMPUTERNAME Code name = FS_BE_spinflip.jl flip prob = [0.003533, 0.057071, 0.14867, 0.268067, 0.333, 0.2374, 0.113267, 0.0668]Fraction Spin flip obtained from the code compared with the experimental data reported by Frisch and Segre (.png file)
Typical figure generated is as this one [^1]
[^1]: Obtained sampling N=15000 atoms via Monte Carlo method
Owner
- Name: Kelvin Titimbo
- Login: ktitimbo
- Kind: user
- Location: Pasadena, CA
- Company: Caltech
- Website: https://ktitimbo.github.io/
- Twitter: ktitimbo
- Repositories: 2
- Profile: https://github.com/ktitimbo
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!
cff-version: 1.2.0
title: >-
Numerical computation of the fraction of spin flip in the Frisch-Segrè experiment using co-quantum dynamics theory
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
contact:
- affiliation: "California Institute of Technology"
email: titimbo@caltech.edu
family-names: Titimbo
given-names: Kelvin
year: 2022
authors:
- given-names: Kelvin
family-names: Titimbo
email: titimbo@caltech.edu
affiliation: Caltech
orcid: 'https://orcid.org/0000-0002-4700-3482'
- given-names: David C.
family-names: Garrett
affiliation: Caltech
- given-names: S. Suleyman
family-names: Kahraman
affiliation: Caltech
- given-names: Lihong V.
family-names: Wang
affiliation: Caltech
url: https://github.com/ktitimbo/FrischSegre-CQD-BE
date-released: 2022-08-12
repository: "https://github.com/ktitimbo/FrischSegre-CQD-BE"