Squeezed Coherent States of Motion for Ions Confined in Quadrupole and Octupole Ion Traps

TL;DR

This paper develops a method to derive classical Hamiltonian functions from quantum descriptions of ions in quadrupole and octupole traps using squeezed coherent states, enabling better understanding of ion dynamics.

Contribution

It introduces a dequantization algorithm that obtains classical Hamiltonians from quantum models of ions in complex traps using squeezed coherent states.

Findings

Derived classical Hamiltonian functions for specific ion traps.

Formulated classical equations of motion for ions in these traps.

Established a link between quantum states and classical dynamics.

Abstract

Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) and radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for a combined and for a RF trap, with axial symmetry and a RF anharmonic electric potential. We also build the classical Hamiltonian functions for the particular traps we considered, and find the classical equations of motion.