Correlated many-body noise and emergent \(1/f\) behavior in an anharmonic fluctuator model

Fluctuating electric fields emanating from surfaces are a primary source of decoherence in trapped ion qubits. Here, we show that superradiant phonon-induced excitation exchange between adatoms can lead to a reduction of electric field noise at low temperatures. We derive an exact mapping between the noise spectrum of \(N\) fluctuators with \(M\) vibrational levels to \(N+M-1 \choose N\)-1 two-level dipoles. We provide conditions for which the ubiquitous \(1/f\) noise can emerge, even though the system is composed of only a single type of fluctuator, thus suggesting a new mechanism for the phenomenon.