Electron’s wave nature constructed in the lab at last


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.


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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