Spontaneous emergence of correlated states such as flocks and vortices are prime examples of remarkable collective dynamics and self-organization observed in active matter. The formation of globally correlated polar states in geometrically confined systems proceeds through the emergence of a macroscopic steadily rotating vortex that spontaneously selects a clockwise or counterclockwise global chiral state. Here, we reveal that a global vortex formed by colloidal rollers exhibits state memory. The information remains stored even when the energy injection is ceased and the activity is terminated. We show that a subsequent formation of the collective states upon re-energizing the system is not random. We combine experiments and simulations to elucidate how a combination of hydrodynamic and electrostatic interactions leads to hidden asymmetries in the local particle positional order encoding the chiral state of the system. The stored information can be accessed and exploited to systematically command subsequent polar states of active liquid through temporal control of the activity. With the chirality of the emergent collective states controlled on-demand, active liquids offer new possibilities for flow manipulation, transport, and mixing at the microscale.
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