Topological protection of multiparticle dissipative transport

Abstract

Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

Topologically protected colloidal transport above a square magnetic lattice

“…The colloidal transport is fully determined by the topology of the manifold , which is unique for each type of magnetic pattern. For example, the stationary manifold of a hexagonal pattern is a genus 7 surface [13]. There, the modulation loops in  that induce transport of colloids must cross the fences in , which are lines instead of points as in the present study.…”

“…From an experimental view point, it is possible to use magnetic bubble lattices [14] or lithographic patterns [15] to generate the pattern. Possible methods to levitate the colloids above the pattern consists of using a ferrofluid solvent [13] and the deposition of a polymer layer [16] on the magnetic pattern.…”

“…If the dynamics depends only on a topological invariant it is possible to have total control over the colloidal motion, independently of the intrinsic characteristics of the particles. Recently, we have studied the motion of magnetic colloids above a hexagonal magnetic pattern [13]. The system is driven by an external magnetic field.…”

Edge transport at the boundary between topologically equivalent lattices

“…In Refs. [3,4,5] we demonstrated how the bulk transport of colloidal particles above magnetic lattices with different symmetries is topologically protected. We summarize here the main aspects of the transport in square lattices and refer the reader to Refs.…”

Custom flow in overdamped Brownian dynamics

“…which is the exact external force field for the case of an ideal gas. Prescribing (12) allows to sample F (0) int in BD, and then use f (0) int as the required input for iteration step k = 1 in (11). This completes the description the functional inversion.…”