Fast driving between arbitrary states of a quantum particle by trap deformation

TL;DR

This paper introduces a method to rapidly transform a quantum particle between arbitrary states by deforming the trapping potential, bypassing slow adiabatic processes even in complex scenarios.

Contribution

It provides a simple formula for designing trap deformations that achieve fast state transformations without level crossings or adiabatic constraints.

Findings

Enables quick state changes in quantum traps

Applicable to complex and topologically nontrivial transformations

Demonstrated with harmonic and periodic traps

Abstract

By performing a slow adiabatic change between two traps of a quantum particle, it is possible to transform an eigenstate of the original trap into the corresponding eigenstate of the final trap. If no level crossings are involved, the process can be made faster than adiabatic by setting first the interpolated evolution of the wave function from its initial to its final form and inferring from this evolution the trap deformation. We find a simple and compact formula which gives the trap shape at any time for any interpolation scheme. It is applicable even in complicated scenarios where there is no adiabatic process for the desired state-transformation, e.g., if the state changes its topological properties. We illustrate its use for the expansion of a harmonic trap, for the transformation of a harmonic trap into a linear trap and into an arbitrary number of traps of a periodic structure. Finally, we study the creation of a node exemplified by the passage from the ground state to the first excited state of a harmonic oscillator.