Using magnets to cloak matter waves

By Chris Lee | Ars Technica

Cloaking started out as a cool way to demonstrate an insight that Pendry had: you can run the mathematics for electromagnetism in any coordinate system, and the differences between the arbitrary coordinate system and real space can be interpreted as physical properties of the medium through which real light waves propagated. (We'll explain this idea more in a minute.)

This is a fantastic insight, and cloaking is only one of many ideas to spring forth from that fount.

Of course, there are many physics situations that are similar to electromagnetism in terms of their mathematics. Acoustic cloaking joined the bandwagon early. Cloaking matter waves joined the club a couple of years ago. The matter waves considered were rather special, but now matter waves and structures that you can test in the real world have turned up in a Physical Review A publication.

Designing the light flow you need

Where to start? Perhaps by returning to the start of the story. The movement of light through a medium is described by a type of equation called the wave equation. It doesn't really matter what the medium is, or what wavelength the light is; this equation will let you predict what the light will do.

But this is just an equation, and the form of an equation depends on the coordinate system we use (e.g., what sort of grid we use to divide up space). This is actually quite helpful. For instance, if you want to look at light propagating inside a sphere, you can use a spherical coordinate system that makes the math easy to solve. This makes life simpler. But what if you don't like the easy life and wanted to make things more difficult?

Then you might do what Pendry did and use a coordinate system that is "irregular." Imagine a grid where the squares change size and shape depending where you are. This makes the wave equation a proper nightmare to solve—at least as far as I'm concerned; others probably dream of the challenge—but Pendry had good reason to do this.

You see, if you choose this coordinate system correctly, you can create regions of space where the light waves simply will not go. Instead, they travel around the region and return to their original path as if it had not deviated at all—the perfect optical cloak.

At this stage, such ideas are just so much mental wankery because, although we can imagine stretched and deformed space, we have difficulty making them. Pendry's genius was to note that stretched and deformed space in a vacuum looks identical to physical structures with particular optical properties as far as the light is concerned.

In other words, he had just created a tool that lets you design the light flow you want and then calculate backwards to figure out exactly the structure and optical properties that would allow you to create such a light flow. This work has been vindicated with experiments showing that cloaking does actually work.

No invisibility cloak yet

Now the story repeats itself, with De Hone-Lin of National Sun Yat-Sen Univeristy of Taiwan figuring out how to cloak matter waves.

Instead of the wave equation for light, we use the quantum mechanical wave equation for particles that have spin half—electrons and protons are spin half particles and fit the bill here—and are moving at a fair clip.

Spin—a type of angular momentum similar in properties to, but in no way physically the same as, the angular momentum associated with a spinning top or the Earth's rotation—is important to the story only insofar as it makes the math more difficult, but also far closer to something physically realizable.

Hone-Lin showed that to cloak an object from a stream of electrons, for instance, one needed to vary the electrons' effective mass and energy and have some kind of vector field present. Now, if one were to think of something like neutrons, this would be pretty difficult to achieve, but for electrons this appears to be feasible.

Hone-Lin points out that the effective mass and energy of an electron in graphene (a single layer of graphite) can be varied by a magnetic field, which just also happens to be a vector field. He concludes that a cloaked region of graphene could be created by placing concentric rings of magnets with different strengths around the region.

So, what are the applications? On this point Hone-Lin has some interesting suggestions. One of the interesting questions in materials science is often how strongly particles with spin interact; being able to cloak and uncloak spins at will could make these measurements easier. It could also provide new tests for nonlocality and entanglement in quantum systems. This should herald more good times for the graphene community.