Programmable double traveling waves in living liquid crystals.

Traveling patterns are ubiquitous in nature. Controlling the traveling waves in living active matter systems remains elusive due to their intrinsic chaotic nonequilibrium nature. Here, we show how to control the traveling waves in living liquid crystals (LLCs) which represent a unique class of materials where motile bacteria interact with the anisotropic environment of LCs. The concentrated bacteria form waves propagating along the predefined trajectories, showcasing a dual nature of propagation where both the bacteria and the waves themselves move in concert. The interaction between active bacterial waves and passive LCs triggers a secondary LC wave which runs after the bacterial wave with a constant phase lag, generating double traveling waves. Our experimental and theoretical investigations have unveiled the underlying mechanisms of parity and time-reversal (PT) symmetry breaking in these active-passive wave duets. The interactions between the undulating waves and the director reoriented by the waves, coupled with the symmetry broken in the designed patterns, are key to initiating wave propagation. Capitalizing on this understanding, we have successfully demonstrated the creation of single ring and even multiple rings of traveling waves with same or opposite chirality. These waves can be further programmed into letter shapes. This work opens up new avenues for the design of smart living materials and micromachines.