Feedback traps for virtual potentials

Abstract

Feedback traps are tools for trapping and manipulating single charged objects, such as molecules in solution. An alternative to optical tweezers and other single-molecule techniques, they use feedback to counteract the Brownian motion of a molecule of interest. The trap first acquires information about a molecule's position and then applies an electric feedback force to move the molecule. Since electric forces are stronger than optical forces at small scales, feedback traps are the best way to trap single molecules without "touching" them. Feedback traps can do more than trap molecules: They can also subject a target object to forces that are calculated to be the gradient of a desired potential function U(x). If the feedback loop is fast enough, it creates a virtual potential whose dynamics will be very close to those of a particle in an actual potential U(x). But because the dynamics are entirely a result of the feedback loop--absent the feedback, there is only an object diffusing in a fluid--we are free to specify and then manipulate in time an arbitrary potential U(x,t). Here, we review recent applications of feedback traps to studies on the fundamental connections between information and thermodynamics, a topic where feedback plays an even more-fundamental role. We discuss how recursive maximum likelihood techniques allow continuous calibration, to compensate for drifts in experiments that last for days. We consider ways to estimate work and heat to a precision of 0.03 kT over these long experiments. Finally, we compare work and heat measurements of the costs of information erasure, the Landauer limit of kT ln2 per bit of information erased. We argue that when you want to know the average heat transferred to a bath in a long protocol, you should measure instead the average work and then infer the heat using the first law of thermodynamics.