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Rice University physicists have gone to
extremes to prove that Isaac Newton’s classical laws of motion can apply in the
atomic world: They’ve built an accurate model of part of the solar system
inside a single atom of potassium.
In a paper published in Physical
Review Letters, Rice’s team and collaborators at the Oak Ridge National
Laboratory and the Vienna University of Technology showed they could cause an
electron in an atom to orbit the nucleus in precisely the same way that Jupiter’s
Trojan asteroids orbit the sun.
The findings uphold a prediction made in 1920 by famed Danish physicist
Niels Bohr about the relationship between the then-new science of quantum
mechanics and Newton’s
tried-and-true laws of motion.
“Bohr predicted that quantum mechanical descriptions of the physical
world would, for systems of sufficient size, match the classical descriptions
provided by Newtonian mechanics,” said lead researcher Barry Dunning,
Rice’s Sam and Helen Worden Professor of Physics and chair of the Department of
Physics and Astronomy. “Bohr also described the conditions under which
this correspondence could be observed. In particular, he said it should be seen
in atoms with very high principal quantum numbers, which are exactly what we
study in our laboratory.”
Bohr was a pioneer of quantum physics. His 1913 atomic model, which is still
widely invoked today, postulated a small nucleus surrounded by electrons moving
in well-defined orbits and shells. The word “quantum” in quantum
mechanics derives from the fact that these orbits can have only certain
well-defined energies. Jumps between these orbits lead to absorption or
emission of specific amounts of energy termed quanta. As an electron gains
energy, its quantum number increases, and it jumps to higher orbits that circle
ever farther from the nucleus.
In the new experiments, Rice graduate students Brendan Wyker and Shuzhen Ye
began by using an ultraviolet laser to create a Rydberg atom. Rydberg atoms
contain a highly excited electron with a very large quantum number. In the Rice
experiments, potassium atoms with quantum numbers between 300 and 600 were
studied.
“In such excited states, the potassium atoms become hundreds of
thousands of times larger than normal and approach the size of a period at the
end of a sentence,” Dunning said. “Thus, they are good candidates to
test Bohr’s prediction.”
He said comparing the classical and quantum descriptions of the electron
orbits is complicated, in part because electrons exist as both particles and
waves. To “locate” an electron, physicists calculate the likelihood
of finding the electron at different locations at a given time. These
predictions are combined to create a “wave function” that describes
all the places where the electron might be found. Normally, an electron’s wave
function looks like a diffuse cloud that surrounds the atomic nucleus, because
the electron might be found on any side of the nucleus at a given time.
Dunning and coworkers previously used a tailored sequence of electric field pulses
to collapse the wave function of an electron in a Rydberg atom; this limited
where it might be found to a localized, comma-shaped area called a “wave
packet.” This localized wave packet orbited the nucleus of the atom much
like a planet orbits the sun. But the effect lasted only for a brief period.
“We wanted to see if we could develop a way to use radio frequency
waves to capture this localized electron and make it orbit the nucleus
indefinitely without spreading out,” Ye said.
They succeeded by applying a radio frequency field that rotated around the
nucleus itself. This field ensnared the localized electron and forced it to
rotate in lockstep around the nucleus.
A further electric field pulse was used to measure the final result by
taking a snapshot of the wave packet and destroying the delicate Rydberg atom
in the process. After the experiment had been run tens of thousands of times,
all the snapshots were combined to show that Bohr’s prediction was correct: The
classical and quantum descriptions of the orbiting electron wave packets
matched. In fact, the classical description of the wave packet trapped by the
rotating field parallels the classical physics that explains the behavior of
Jupiter’s Trojan asteroids.
Jupiter’s 4,000-plus Trojan asteroids—so called because each is named for a
hero of the Trojan wars—have the same orbit as Jupiter and are contained in
comma-shaped clouds that look remarkably similar to the localized wave packets
created in the Rice experiments. And just as the wave packet in the atom is
trapped by the combined electric field from the nucleus and the rotating wave,
the Trojans are trapped by the combined gravitational field of the sun and
orbiting Jupiter.
The researchers are now working on their next experiment: They’re attempting
to localize two electrons and have them orbit the nucleus like two planets in
different orbits.
“The level of control that we’re able to achieve in these atoms would
have been unthinkable just a few years ago and has potential applications in,
for example, quantum computing and in controlling chemical reactions using
ultrafast lasers,” Dunning said.
