  Long-lived coherences, emerging under periodic pulse driving in the
disordered ensembles of strongly interacting spins, offer immense advantages
for future quantum technologies, but the physical origin and the key properties
of this phenomenon remain poorly understood. We theoretically investigate this
effect in ensembles of different dimensionality, and predict existence of the
long-lived coherences in two-dimensional and infinite-dimensional (where every
spin is coupled to all others) systems, which are of particular importance for
quantum sensing and quantum information processing. We explore the transition
from two to infinite dimensions, and show that the long-time coherence dynamics
in all dimensionalities is qualitatively similar, although the short-time
behavior is drastically different, exhibiting dimensionality-dependent
singularity. Our study establishes the common physical origin of the long-lived
coherences in different dimensionalities, and suggests that this effect is a
generic feature of the strongly coupled spin systems with positional disorder.
Our results lay out foundation for utilizing the long-lived coherences in a
range of application, from quantum sensing with two-dimensional spin ensembles,
to quantum information processing with the infinitely-dimensional spin systems
in the cavity-QED settings.
