Taming collective activity to crystallize an oscillator gas

In active matter, where constituents are intrinsically out-of-equilibrium, even the highest-symmetry phases come with surprises. When activity is coupled negatively to density, such as in assemblies of self-propelled units, phase separation can occur without attractive interaction, a well-studied phenomenon known as motility-induced phase separation. In stark contrast, the consequences of a positive coupling between density and activity on the collective behaviour of active matter remain uncharted. Here, we unveil the phenomenon of collective activity, which emerges from this positive coupling among non-motile active units. We demonstrate its genuine propensity for disorder and leverage its potential in guiding self-assembly. To do so, we experimentally study collectives of scalar active units undergoing self-sustained oscillations induced by contact-charge electrophoresis. We explain the spontaneous formation of an oscillator gas by collective activity resulting from super-elastic collisions. Unravelling the origin of binary collisions allows us to tame collective activity, giving us precise control on the structure of the oscillator gas and its eventual crystallization. Our work highlights and quantifies the importance of the coupling between activity and density in active phases. It is a launch pad for exploring lower-symmetry active systems with new eyes where activity may be coupled not only to density, but also to broken-symmetry variables.