Probing quantum effects with classical stochastic analogs

TL;DR

This paper introduces a classical analog model for open quantum systems using trapped particles in potential wells, enabling the simulation of quantum effects like tunneling and correlations through a classical setup.

Contribution

It presents a novel method to emulate quantum phenomena with classical particles by reconstructing the Bohm potential from classical distributions.

Findings

Successfully simulated quantum tunneling and correlations.

Demonstrated the classical analog with micron-sized beads in experiments.

Validated the approach with numerical simulations of single and double wells.

Abstract

We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped. The distribution $n(x,t)$ of the classical positions is used to reconstruct the quantum Bohm potential $V_{\rm Bohm} = -\frac{\hbar^2}{2 m} \frac{\Delta \sqrt{n}}{\sqrt{n}}$, which in turn acts on the shape of the potential wells. As a result, the classical particles experience an effective "quantum" force. This protocol is tested with numerical simulations using single- and double-well potentials, evidencing typical quantum effects such as long-lasting correlations and quantum tunneling. For harmonic confinement, the analogy is implemented experimentally using micron-sized dielectric beads optically trapped by a laser beam.