Abstract
The sorting of objects into groups is a fundamental operation, critical in the preparation and purification of populations of cells, crystals, beads, or droplets, necessary for research and applications in biology, chemistry, and materials science. Most of the efforts exploring such purification have focused on two areas: the degree of separation and the measurement precision required for effective separation. Conventionally, achieving good separation ultimately requires that the objects are considered one by one (which can be both slow and expensive), and the ability to measure the sorted objects by increasing sensitivity as well as reducing sorting errors. Here we present an approach to sorting that addresses both critical limitations with a scheme that allows us to approach the theoretical limit for the accuracy of sorting decisions. Rather than sorting individual objects, we sort the objects in ensembles, via a set of registers which are then in turn sorted themselves into a second symmetric set of registers in a lossless manner. By repeating this process, we can arrive at high sorting purity with a low set of constraints. We demonstrate both the theory behind this idea and identify the critical parameters (ensemble population and sorting time), and show the utility and robustness of our method with simulations and experimental systems spanning several orders of scale, sorting populations of macroscopic beads and microfluidic droplets. Our method is general in nature and simplifies the sorting process, and thus stands to enhance many different areas of science, such as purification, enrichment of rare objects, and separation of dynamic populations.