  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.
