Tale of Tilted Washboards of Potential Energy

Abstract

Tilted washboard potentials are periodic functions of potential energy whose graphs remind the profiles of inclined washboards for scrubbing clothes. Practically unknown until the 1970, washboard potentials are at present ubiquitous seminal landscapes across diverse physics researches and technologies now receiving significant attention. However, washboard potentials are still rarely presented to science and engineering undergraduates; perhaps they could hear about those when first studying Josephson junctions. Aiming to promote the presentation of such potentials to undergraduates, we here consider cases of washboard potentials in: classical mechanics, quantum physics and optics. The quantum case is the superconducting Josephson junction whose phase quasi-particle has a tilted washboard potential leading to important applications, e.g. the phase qubit in quantum computation. Optical cases are electro-optical potentials generated with laser beams in which thousands of atom electric dipoles may become confined or evolve, potentials being generated either with laser Bessel beams, or with laser standing waves, whose periodic potential profile is implicitly tilted or may be experimentally adjusted to become tilted. Electro-optical potentials are presently used in fast-paced fundamental research, e.g. Brownian particle motors, atom trapping in optical lattices, optical atomic clocks, protein transport in biological cells, and in condensed matter physics to name a few.