In a small copper box, resembling a matchbox, magnetic waves reside. They arise in a tiny crystal of yttrium iron garnet when radio waves are passed through it. Two waves with different characters (one fast, the other slow) usually ignore each other. But when their frequencies match, a dance begins: the waves either merge into one strong wave or cancel each other into complete silence.

The scientists measured how this dance depends on turning the tuning knob — the phase of the waves. Phase is like the position of a pendulum at the moment of impact: if you push it at the right point, it swings; if at the opposite, it stops. It turned out that waves can not only cancel each other but also transmit a signal in only one direction, like a turnstile in the subway. This property is called nonreciprocity. Previously, such an effect required bulky magnets, but now it suffices to properly adjust the phase inside a small box.

The result is a simple formula that predicts the behavior of waves at any setting. With it, one can calculate in advance how to make an ideal isolator or circulator for quantum computers, where any extra noise ruins computations. Magnetic waves in garnet turned out to be a pliable instrument, like a guitar string that can be tuned to the desired pitch.