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 (e.g. by putting them in a small box or attaching them to a tether). 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 functionU(x). If the feedback loop is fast enough, it creates avirtual potentialwhose dynamics will be very close to those of a particle in an actual potentialU(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 potentialU(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, using them to measure fluctuating energies to a precision of ±0.03kTover these long experiments. Finally, we compare work and heat measurements of the costs of information erasure, theLandauer limitofkTln 2 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.This article is part of the themed issue ‘Horizons of cybernetical physics’.

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

“…In earlier work, we developed a recursive, real-time calibration technique [73] that allows us to measure accurately the stochastic work done by a changing potential 6 on a particle. Using an improved setup with higher feedback loop rates [74], we explored erasure in asymmetric memories [75], tested subtle forms of reversibility [76], and compared different estimators of heat transfer [77].…”

“…This protocol is repeated for several different cycle times τ , where, for each τ , we recorded multiple trajectories over a thirty-minute period. The uncertainty in the estimate of average work values depends only on the total time of data collection, not on the cycle time τ directly [77]. …”

“…The beads sink to the bottom of the chamber (top of the coverslip) under gravity, which confines them in the vertical (z) direction. Two pairs of electrodes near the bottom of the chamber create an electric field (∼ 10 V/cm) whose value is updated every time step to move a bead in the horizontal (xy) plane [75][76][77]. The control software analyzes images in real time using a centroid algorithm [79].…”

“…In earlier work, we developed a recursive, real-time calibration technique [73] that allows us to measure accurately the stochastic work done by a changing potential 6 on a particle. Using an improved setup with higher feedback loop rates [74], we explored erasure in asymmetric memories [75], tested subtle forms of reversibility [76], and compared different estimators of heat transfer [77].The experimental setup for our feedback trap has three major segments: the imaging system, the trapping chamber, and the control software. The imaging system consists of an inverted, home-built, dark-field, frontillumination microscope with a 60x Olympus NA=0.95 air objective [74,78].…”

Horizons of cybernetical physics

“…Further advances and real high precision experiments were based on the notion of feedback trap [86]. In the paper by Momčilo Gavrilov & John Bechhoefer [87], the results of [86] are improved and extended. It makes the bridge between control theory and thermodynamics stronger.…”