A near-IR
laser isolates the two electrons (empty circles) from the two kinds of holes in
the lower right (solid circles). The terahertz laser's oscillating electric
field accelerates the charges away from each other (grey wave). The charges are
then dragged toward each other by the changing field, where they unite and
generate two flashes of light. Time flows from the bottom right to the top left
as the paths are portrayed in one dimension of space. (Photo credit: Brian
Long) |
For the first time in a laboratory experiment, researchers at the University of California, Santa Barbara, have rebuilt a representation of the electron's wave nature — the Bloch wavefunction. The findings could be useful in the creation and design of next-generation electrical and optoelectronic devices.
Electrons,
like all matter, behave as both particles and waves. Understanding how the
wavelike passage of electrons through periodically-arranged atoms gives rise to
the electrical and optical properties of crystalline materials is one of the
main goals of condensed-matter physics. According to Joseph Costello, who
co-led the UC Santa Barbara research with Seamus O'Hara, Mark Sherwin, and Qile
Wu, having such an understanding is especially critical for constructing
devices that take use of the electron's wavelike nature.
A Bloch
wavefunction is a mathematical representation of the electron's wavelike
behaviour. These wavefunctions are complex – that is, they have both real and
imaginary components – and are named after the 20th-century physicist Felix
Bloch, who was the first to describe the behaviour of electrons in crystalline
minerals. As a result, the Bloch wavefunction of an electron cannot be directly
measured.
Heavy and
light holes
However,
certain wavefunction-related physical features can be seen. This fact was used
by the UC Santa Barbara team to determine a system's Bloch wavefunction using
these observable properties.
The
researchers achieved this by employing a powerful free-electron laser to create
an oscillating electric field within a semiconductor, gallium arsenide (GaAs),
while concurrently exciting its electrons with a low-intensity infrared laser.
When an electron is energized, a positively charged "hole" is left
behind. Sherwin says that in GaAs, these holes exist in two types: heavy and
light, and act similarly to particles with varying masses.
The
researchers discovered that if they created electrons and holes at the correct
time in relation to the electric field oscillations, the components of these
quasiparticle pairs (known as excitons) would accelerate away from each other,
slow down, stop, and then accelerate towards each other before colliding and
recombining. They emit a pulse of light, known as a sideband, with a certain
energy at the moment of recombination. This sideband emission carries
information on the electrons' wavefunctions, including their phases, or how far
the waves are offset from one another.
Because
light and heavy holes accelerate at various rates in the electric field, their
Bloch wavefunctions take on different quantum phases before recombining with
electrons. Their wavefunctions interfere as a result of the phase difference,
resulting in the final emission, which can then be measured. The polarization
of the final sideband, which might be circular or elliptical, is likewise
determined by interference (even though the polarization of both lasers is
linear to start with).
One free
parameter
According
to Wu, a single free parameter, which is a real number, ties fundamental
quantum mechanical theory to a real-world experiment via this straightforward
relationship between interference and polarization. According to O'Hara, this
value properly describes the Bloch wavefunction of the hole they make in GaAs.
He continues, "We can get this value by detecting sideband polarization
and then reconstructing the wavefunctions, which vary depending on the angle at
which the hole propagates in the crystal."
Sherwin
adds that before now, researchers had to rely on theories with a lot of unknown
characteristics. "If we can reliably recreate Bloch wavefunctions in a
range of materials," he continues, "then that will inform the design
and engineering of all kinds of useful and intriguing things like lasers,
detectors, and even some quantum computing systems."
The
researchers, who published their findings in Nature, admit that they didn't
grasp the importance of sideband polarization in recreating the electron
wavefunction at first. They say they'd like to use their technique on different
materials and unusual quasiparticles than excitons in the future.
References:
Costello,
J.B., O’Hara, S.D., Wu, Q. et al. Reconstruction of Bloch wavefunctions of
holes in a semiconductor. Nature 599, 57–61 (2021).
https://doi.org/10.1038/s41586-021-03940-2
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