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The wave function—an abstract concept used to predict the behavior of quantum particles—is the bedrock on which physicists have built their understanding of quantum mechanics. But this bedrock itself is not something physicists have a perfect grasp of, literally or philosophically. A wave function is not something one can hold in their hand or put under a microscope. And confusingly, some of its properties simply seem not to be real. In fact, mathematicians would openly label them as imaginary: so-called imaginary numbers—which arise from seemingly nonsensical feats such as taking the square roots of negative integers—are an important ingredient of a wave function’s well-proved power to forecast the results of real-world experiments. In short, if a wave function can be said to “exist” at all, it does so at the hazy crossroads between metaphysical mathematics and physical reality.

Now researchers at the University of California, Santa Barbara, and their colleagues have made big strides in bridging these two realms: for the first time, they reconstructed a wave function from a measurement of how a semiconductor material responds to an ultrafast pulse of light. Appearing in Nature in November, the team’s work may help take electronics engineering and quantum materials design into a new era of fine-tuned understanding and precisely controlled innovation.

For real-world applications, such as modern electronics, the somewhat mysterious wave function is physicists’ best source of information about what actually happens inside of some new gadget. To predict how fast an electron moves inside a material or how much energy it can carry, they must start their calculations with the so-called Bloch wave function—named for physicist Felix Bloch, who devised it in 1929. This is especially important for engineering quantum devices, says Joe Costello, a physics student at U.C.S.B. and co-lead author of the recent study. “If you’re thinking about building any sort of device that takes advantage of quantum mechanics, you’re going to need to know its [wave function’s] parameters really well,” he emphasizes.

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