5. Literature notes#
22/06/24
[Gilb, Torres, and Leone, 2006]
PADs and QB FT analysis.
Basic wavepacket + ionization model, MQDT style.
Brief discussion of entanglement and Bell states.
Should relate to Blum stuff for more…?
Universal alignment function, defines sign of alignment (with \(\Delta J\)), see eq. 16. (Implemented in
qbanalysis.photoionization.A0.)
Where \(t_{\pm1}\) are parity favoured, \(t_0\) is parity unfavoured, and \(t\) denotes angular momentum transfer \(j_t = \Delta j\) (not “time”!).
Hyperfine beats (eq. 22), including depolarisation, and time-integrated case (eq. 24).
# Calculate and plot Universal Alignment Function, per
# Greene, Chris H., and Richard N Zare. 1982.
# “Photonization-Produced Alignment of Cd.”
# Physical Review A 25 (4): 2031–37.
# https://doi.org/10.1103/PhysRevA.25.2031.
from qbanalysis.photoionization import *
import numpy as np
A0table = A0df(np.arange(0,10))
A0table
2025-06-03 16:55:57.311 | INFO | qbanalysis.config:<module>:11 - PROJ_ROOT path is: /home/runner/work/Quantum-Beat_Photoelectron-Imaging_Spectroscopy_of_Xe_in_the_VUV/Quantum-Beat_Photoelectron-Imaging_Spectroscopy_of_Xe_in_the_VUV
* sparse not found, sparse matrix forms not available.
* natsort not found, some sorting functions not available.
* Setting plotter defaults with epsproc.basicPlotters.setPlotters(). Run directly to modify, or change options in local env.
* Set Holoviews with bokeh.
* pyevtk not found, VTK export not available.
* pyshtools not found, SHtools functions not available. If required, run "pip install pyshtools" or "conda install -c conda-forge pyshtools" to install.
2025-06-03 16:56:18.271 | INFO | qbanalysis.hyperfine:<module>:31 - Using uncertainties modules, Sympy maths functions will be forced to float outputs.
/home/runner/work/Quantum-Beat_Photoelectron-Imaging_Spectroscopy_of_Xe_in_the_VUV/Quantum-Beat_Photoelectron-Imaging_Spectroscopy_of_Xe_in_the_VUV/qbanalysis/photoionization.py:40: RuntimeWarning: divide by zero encountered in divide
-1:-2/5 - 3/(5*ji),
/home/runner/work/Quantum-Beat_Photoelectron-Imaging_Spectroscopy_of_Xe_in_the_VUV/Quantum-Beat_Photoelectron-Imaging_Spectroscopy_of_Xe_in_the_VUV/qbanalysis/photoionization.py:41: RuntimeWarning: divide by zero encountered in divide
0:4/5 - 3/(5*ji*(ji+1))}
| 1 | -1 | 0 | |
|---|---|---|---|
| 0 | 0.200000 | NaN | NaN |
| 1 | -0.100000 | -1.000000 | 0.500000 |
| 2 | -0.200000 | -0.700000 | 0.700000 |
| 3 | -0.250000 | -0.600000 | 0.750000 |
| 4 | -0.280000 | -0.550000 | 0.770000 |
| 5 | -0.300000 | -0.520000 | 0.780000 |
| 6 | -0.314286 | -0.500000 | 0.785714 |
| 7 | -0.325000 | -0.485714 | 0.789286 |
| 8 | -0.333333 | -0.475000 | 0.791667 |
| 9 | -0.340000 | -0.466667 | 0.793333 |
import hvplot.pandas
import holoviews as hv
# Quick plot from PD data
A0plot = A0table.hvplot().opts(title="Universal alignment function vs. Ji, lines per dJ",show_grid=True)
# Load ref figure (image) and create layout
height = 600
width = 600
ref = hv.RGB.load_image('greene_zare_1982_fig1.png').opts(height=height, width=width)
layout = A0plot.opts(height=height, width=width) + ref.opts(axiswise=True, xaxis=None, yaxis=None)
layout
Note discrepancy for Ji=0 case (seems to be an error or specific choice that inf == 0, in original plot), otherwise looks good.
Stefan Gilb, Elva A. Torres, and Stephen R. Leone. Mapping of time-dependent electron orbital alignment. Journal of Physics B: Atomic, Molecular and Optical Physics, 39(20):4231, October 2006. URL: https://dx.doi.org/10.1088/0953-4075/39/20/020 (visited on 2024-06-21), doi:10.1088/0953-4075/39/20/020.
Chris H. Greene and Richard N Zare. Photonization-produced alignment of Cd. Physical Review A, 25(4):2031–2037, April 1982. URL: https://link.aps.org/doi/10.1103/PhysRevA.25.2031 (visited on 2017-12-05), doi:10.1103/PhysRevA.25.2031.