  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.
