We have built an information engine that can transport a bead in a desired direction by using favorable fluctuations from the thermal bath. However, in its original formulation, the information engine generates a fluctuating velocity and cannot control the position of the bead. Here, we introduce a feedback algorithm that can control the bead’s position, to follow a desired trajectory. The bead can track the path if the maximum desired velocity is below the engine’s maximum average velocity. Measuring the range of frequency that the feedback algorithm can track, we find a bandwidth that is slightly lower than the corner frequency of the bead in the trap.
Feedback traps can manipulate particles arbitrarily. In a feedback trap, a position detector detects the particle’s position, a computer calculates the necessary force to be applied based on the position in the “virtual potential,” which is applied to the particle. The process is repeated with as fast a loop rate as practical. Previous feedback traps have used electrokinetic or hydrodynamic forces to manipulate particles. Here, an optical trap creates the force used by the feedback trap to impose arbitrary potentials. We create feedback forces on optically trapped particles by moving the trap position rapidly in response to observed fluctuations with the help of an acoustooptic deflector (AOD). In preliminary experiments, we have confined a 1.5 μm silica bead in a virtual potential that is 35-40 times stiffer than the underlying optical trap, whose laser power is kept constant. We also create a virtual double-well potential with independent control over the well separation and barrier height, which is impossible to do with time-sharing optical tweezers.
Feedback traps are tools for trapping single charged objects in solution. They periodically measure an object’s position and apply a feedback force to counteract Brownian motion. The feedback force can be calculated as a gradient of a potential function, effectively creating a “virtual potential.” Its flexibility regarding the choice of form of the potential gives an opportunity to explore various fundamental questions in stochastic thermodynamics. Here, we review the theory behind feedback traps and apply it to measuring the average work required to erase a fraction of a bit of information. The results agree with predictions based on the nonequilibrium system entropy. With this example, we also show how a feedback trap can easily implement the complex erasure protocols required to reach ultimate thermodynamic limits.
Feedback traps can create arbitrary virtual potentials for exploring the dynamics of small Brownian particles. In a feedback trap, the particle position is measured periodically and, after each measurement, one applies the force that would be produced by the gradient of the “virtual potential,” at the particle location. Virtual potentials differ from real ones in that the feedback loop introduces dynamical effects not present in ordinary potentials. These dynamical effects are caused by small time scales associated with the feedback, including the delay between the measurement of a particle’s position and the feedback response, the feedback response that is applied for a finite update time, and the finite camera exposure from integrating motion. Here, we characterize the relevant experimental parameters and compare to theory the observed power spectra and variance for a particle in a virtual harmonic potential. We show that deviations from the dynamics expected of a continuous potential are measured by the ratio of these small time scales to the relaxation time scale of the virtual potential.
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