  We propose an experiment to demonstrate spontaneous ordering and symmetry
breaking of kinesin-driven microtubules confined to an optical trap.
Calculations involving the feasibility of such an experiment are first
performed which analyze the power needed to confine microtubules and address
heating concerns. We then present the results of first-principles simulations
of active microtubules confined in such a trap and analyze the types of motion
observed by the microtubules as well as the velocity of the surrounding fluid,
both near the trap and in the far-field. We find three distinct phases
characterized by breaking of distinct symmetries and also analyze the power
spectrum of the angular momenta of polymers to further quantify the differences
between these phases. Under the correct conditions, microtubules were found to
spontaneously align with one another and circle the trap in one direction.
