Probing quantum effects with classical stochastic analogs

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_{Bohm}=−ℏ^{2}/2mΔsqrt[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.