Virtual double-well potential for an underdamped oscillator created by a feedback loop

TL;DR

This paper demonstrates the creation of a tunable virtual double-well potential for an underdamped oscillator using a feedback loop, enabling precise control and exploration of stochastic thermodynamics phenomena.

Contribution

It introduces a novel method to implement virtual double-well potentials in underdamped systems, combining Kramer's theory with a new model for barrier switching.

Findings

Successfully created a virtual double-well potential with tunable parameters.

Analyzed the impact of feedback delay and hysteresis on system behavior.

Demonstrated the virtual potential's statistical indistinguishability from a physical one.

Abstract

Virtual potentials are a very elegant, precise and flexible tool to manipulate small systems and explore fundamental questions in stochastic thermodynamics. In particular double-well potentials have applications in information processing, such as the demonstration of Landauer's principle. Nevertheless, virtual double-well potentials had never been implemented in underdamped systems. In this article, we detail how to face the experimental challenge of creating a feedback loop for an underdamped system (exploring its potential energy landscape much faster than its over-damped counterpart), in order to build a tunable virtual double-well potential. To properly describe the system behavior in the feedback trap, we express the switching time in the double-well for all barrier heights, combining for the first time Kramer's description, valid at high barriers, with an adjusted model for lower ones. We show that a small hysteresis or delay of the feedback loop in the switches between the two wells results in a modified velocity distribution, interpreted as a cooling of the kinetic temperature of the system. We successfully address all issues to create experimentally a virtual potential that is statistically indistinguishable from a physical one, with a tunable barrier height and energy step between the two wells.