Mathematicians now suspect quirks in energy-cloaking metamaterials could be exploited to create powerful quantum probes called "Schrödinger's hats."

Although not yet built or proven in the real world, such hats – their name a nod at Erwin Schrödinger's famous cat-boxing thought experiment – might record extremely subtle signals that would otherwise be scrambled by any attempt to measure them.

Should the theoretical work pan out in the laboratory, Schrödinger's hats could be a boon to nanotechnology, where the simple act of observing a nano-scale object can confound a measurement.

"Conceptually, a Schrödinger's hat is like an invisible battery. It captures a tiny bit of energy without fiddling with the [energy] waves so you can later get a measurement," said Allan Greenleaf, a mathematician at the University of Rochester. Greenleaf co-authored a study of the Schrödinger's hats published May 29 in Proceedings of the National Academy of Sciences.

"If you're trying to image something at the nanoscale, say a computer chip or nanodevice, you might get very close to it without disturbing it," continued Greenleaf.

Metamaterials are a class of artificial materials engineered to possess properties not found in nature, such as the ability to render objects invisible by steering magnetism, microwave light, sound and other forms of energy around them. (Cloaking large objects from visible light remains a lofty goal.)

Yet no ideal metamaterials exist. All slightly betray the existence of objects they conceal, and none completely divert a wide range of energetic frequencies. Some metamaterials even resonate like tuning forks at specific frequencies, sounding like an alarm instead of hiding something.

Where some scientists see flaws, however, Greenleaf and his colleagues see opportunity. If the amount of energy going through a metamaterial and the amount of energy coming out are almost perfectly balanced, the resonating metamaterial should trap a signal that describes the environment it was just in. Over time the signal would leak out, allowing researchers to record it.

Greenleaf and four other invisibility researchers tested their idea mathematically. They calculated that Schrödinger's hats might work with sound and electromagnetic waves, but they're especially interested in quantum waves that describe atomic particle properties, which are typically changed by the act of measurement.

The researchers think Schrödinger's hats could perform a paradoxical trick: Signals from atoms would accumulate inside the resonance field, but the atoms themselves wouldn't be disturbed. Once a recording is complete, the signals could be played back to reveal nanoscopic-scale activity.

"One catch is that, in order to use a hat to measure a quantum field, you'd have to make repeated passes to build a valid statistical measurement. That's because in quantum mechanics, everything is probabilistic," Greenleaf said. "So there's an issue as to whether this would involve so many measurements that it'd be impractical."

Despite the potential hurdle, Greenleaf and his colleagues hope to build a prototype of a Schrödinger's hat in the next year or two with the help of physicist Ulf Leonhardt, one of the study's co-authors and a leader in invisibility research.

"We've used our mathematical intuition to cook up a new design, but that doesn't mean we know how to build it," said Greenleaf. "They're always easier to describe than to build."

He noted that appropriate metamerials already exist for sound- or microwave-based Schrödinger's hats. But actually assembling one and verifying it works may become a daunting task. "That's why you find a physicist who knows what they're doing."

Citation: "Cloaked electromagnetic, acoustic and quantum amplifiers via transformation optics." By Allan Greenleaf, Yaroslav Kurylev, Matti Lassas, Ulf Leonhardt, and Gunther Uhlman. Proceedings of the National Academy of Sciences, published online ahead of print. DOI: 10.1073/pnas.1116864109