An orchestra without a conductor: each musician tunes to a neighbor, and out of that comes a well-coordinated melody. In the world of microscopic magnets, the role of that orchestra is played by a tiny neodymium sphere levitating above a superconducting film. Its oscillations, if excited in the right way, add up to an orderly spectrum of dozens of equally spaced frequencies, like the teeth of a comb.
Until recently, such levitating magnets were studied only in the simplest regimes: their oscillations either decayed or were amplified at a single frequency. But the nonlinearity of the magnetic trap holds more possibilities. When two types of translational oscillation (along and across the film) are excited simultaneously at the sum frequency, they begin to mix, generating a cascade of new frequencies. The process is like two voices in a choir producing overtones that neither singer has on their own.
Then a third musician joined in: the libration mode, that is, the rocking of the magnet around its magnetization axis. Its natural frequency is six times lower, and when the fifth harmonic of the comb matched twice the libration frequency, the libration mode was excited and synchronized with the rest. The spectrum gained fine structure: it now contains more than sixty teeth, separated from one another by just half a kilohertz. The quality factor of the oscillations reaches 2.95×10⁵, which means that after the pump is switched off, the amplitude falls by a factor of e in almost three seconds.
This multifrequency generation resembles the operation of a laser comb, only in mechanics: instead of light waves, there are oscillations of a tiny magnet. Each line of the spectrum is phase-locked to its neighbors, like the teeth of a single comb, and a shift of any one of them is detectable with high precision. This opens the way to ultrasensitive sensors of magnetic fields and forces: the slightest external influence will shift several lines at once, and such a shift will be clearly visible.
An orchestra without a conductor turned out to be capable not only of playing in time but also of creating new harmonies. In the future, if the magnet is cooled to the quantum regime, its oscillations could become a basis for quantum computing and ultra-precise measurements. For now, this levitating little sphere shows how nonlinearity turns from a nuisance into a tool for creating order out of chaos.
The micromagnet floats above the superconductor with no support whatsoever, and its oscillations can be tuned simply by moving a permanent magnet. What is more, the quality factor is so high that after the pump is switched off, the amplitude decays by a factor of e in almost three seconds.
Arthur C. Clarke's novel "The Fountains of Paradise" describes a space elevator held up by magnetic levitation; here, levitation serves not for transport but for creating a perfectly isolated nonlinear oscillator that generates a frequency comb.