  Detection and manipulation of excitations with non-Abelian statistics, such
as Majorana fermions, are essential for creating topological quantum computers.
To this end, we show the connection between the existence of such localized
particles and the phenomenon of unitary subharmonic response (SR) in
periodically driven systems. In particular, starting from highly nonequilibrium
initial states, the unpaired Majorana modes exhibit spin oscillations with
twice the driving period, are localized, and can have exponentially long
lifetimes in clean systems. While the lifetime of SR is limited in
translationally invariant systems, we show that disorder can be engineered to
stabilize the subharmonic response of Majorana modes. A viable observation of
this phenomenon can be achieved using modern multiqubit hardware, such as
superconducting circuits and cold atomic systems.
