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Quantum Movies Class Info
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Single Atom Physics
There are many difficult and interesting physics situations that occur within a single atom.
One of these situations is when the absorption of a single photon leads
to the ejection of two or more electrons. The difficulty arises because
the 2
or more electrons can interact over extremely large distances. We would
like to
know how the electrons develop correlated motion in the continuum.
Another interesting situation is when a single atom is subject to a
very intense, time varying electric field. This can occur when intense
IR or visible photons interact with the atom. Another interesting case
is when the electric field is essentially a single pulse or a single
cycle.
A final interesting case is when intense X-rays interact with an atom.
Unlike the IR or visible photons, the X-rays themselves need to be
treated quantum mechanically. A common situation is when 2 X-rays
simultaneously Compton scatter from an electron leading to a single
X-ray photon at nearly twice the energy.
The main tool we use to explore this problem is a direct, numerical
solution of the time dependent Schrodinger equation (the last reference
below is to a review article about this method). For electron impact
ionization, we start the wave function with one electron in the ground
state and the other in a continuum wave packet with momentum sending it
to the atom/ion. Here is a movie of a model problem (tpa.avi)
where all angular momenta are set to 0. The wave packet is such that
electron 1 is the continuum electron localized at about 50 a.u. and
electron 2 is in the ground state so is confined to small r. As time
goes forward, the packet moves to small r1. At
about 25 a.u. of time,
electron 1 is at its smallest distance. At later times, the packet has
three interesting pieces: (1) a part that goes back out with electron 1
going to large distance and electron 2 confined to small distances
(this is elastic scattering and inelastic scattering to 2s, 3s states),
(2) a part where electron 2 goes to large distances and electron 1 is
confined to a small region (this is exchange scattering), and (3) a
wide swath where both electrons 1 and 2 are going to large distances
(this is ionization). To get accurate scattering probabilities, the
wave function at late times is properly symmetrized and projected onto
continuum final states.
Below is a brief
description of results in two recent publications.
Akilesh Venkatesh and F.
Robicheaux, “Interference in nonlinear Compton scattering using a
Schrodinger-equation approach,” Phys. Rev. A 103,
013111 (2021). PDF
(456 kB) (data for figures at https://doi.org/10.4231/W4QY-ZB66)
In this paper, we investigated the interference between Compton
scattering one photon of frequency 2f (right case in image below) and
nonlinear Compton scattering of frequency f (left case in image below)
from bound electrons. In nonlinear Compton scattering, the two incoming
photons of frequency f scatter into a single photon of frequency 2f. If
the incoming X-rays are a coherent superposition of a strong field at
frequency f and a weak field at frequency 2f, the scattered photons are
indistinguishable. This leads to interference between the two paths for
a photon of frequency 2f to go into the detector. We found that there
are only two combinations of incident and final polarization of the
photons that lead to interference. We found that the intrinsic phase
difference between the two paths is either 0 or pi depending on the
scattering angle.
A schematic image of the interference between Compton and
nonlinear Compton scattering from a bound electron using a two-“color”
X-ray field. The rate that X-rays scatter into the detector depend on
the phase, phi, between the two X-ray colors. By varying this phase,
the intrinsic phase difference between the scattered photons can be
found.
Xiao Wang and F.
Robicheaux, "Ionization from Rydberg atoms and wave packets by scaled
terahertz single-cycle pulses," Phys. Rev. A 99, 033418 (2019). PDF
(1130 kB)
In this paper, we investigated the ionization of a highly excited
(Rydberg) atom when it is expeosed to a strong, terahertz single-cycle
pulse. The goal was to understand how to connect classical and fully
quantum calculations of this system. We found that a naive application
of classical calculation could lead to large differences with quantum
mechanics. However, using a slightly more sophisticated classical
treatment led to good agreement. We were able to interpret signs of
interference in the quantum calculation using a semiclassical method.
This
image shows the probability for finding the ejected electron at a
distance r and an angle cos(theta) at a specific time after the pulse. The image (a) shows the
result from a fully quantum calculation. The image (b) had a spread of
initial conditions with energies between principle quantum number n-1/2
and n+1/2. The image (c) had initial conditions where the energy was
only at principle quantum number n. There is a large difference between
the two classical calculations with that in (b) much closer to the quantum
result. Note the interference pattern in the quantum result (a). This
interference can be interpreted as two paths reaching the same spatial
point. The maxima and minima can be interpreted from a semiclassical
treatment.
Five Recent Publications
Akilesh Venkatesh and F.
Robicheaux, “Effect of the orientation of Rydberg atoms on their
collisional ionization cross section,” Phys. Rev. A 102,
032819 (2020). PDF
(605 kB)
A.O.
Hernandez-Castillo, C. Abeysekera, F. Robicheaux, and T.S. Zwier,
“Propagating molecular rotational coherences through single-frequency
pulses in the strong field regime,” J. Chem. Phys. 151, 084312 (2019). PDF (2690 kB)
Xiao Wang and F.
Robicheaux, "Interference patterns from post-collision interaction in
below-threshold photoexcitation Auger processes," Phys. Rev. A 98, 013421 (2018). PDF
(1850 kB)
Q. Wang, S. Sheinerman, and F.
Robicheaux, "Comparison of different quantum mechanical methods for
inner atomic shell photo-ionization followed by Auger decay," J. Phys.
B 47, 215003 (2014). PDF
(902 kB)
M. S. Pindzola, F. Robicheaux, S. D. Loch, J. C. Berengut, T. Topcu, J.
Colgan, M. Foster, D. C. Griffin, C. P. Ballance, D. R. Schultz, T.
Minami, N. R. Badnell, M. C. Witthoeft, D. R. Plante, D. M. Mitnik, J.
A. Ludlow, and U. Kleiman, "The time-dependent close-coupling method
for atomic and molecular collision processes," J. Phys. B 40,
R39 (2007). PDF
(386 kB)
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