Particle dynamics in a virtual harmonic potential

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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