Analytical solution for optimal squeezing of wave packet of a trapped quantum particle

TL;DR

This paper presents an analytical solution for optimally squeezing the wave packet of a trapped quantum particle using adiabatic approximation, enhancing localization for applications like atom lithography.

Contribution

It provides the first analytical solution for wave packet squeezing in an infinite well potential using adiabatic control methods.

Findings

Achieves highly localized quantum states

Analytical approach simplifies control design

Potential applications in atom lithography

Abstract

Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final state is presented for a case of an infinite well trapping potential. The presented solution may be applied to increase the resolution of atom lithography.