Theory of Cross Phase Modulation for the Vibrational Modes of Trapped Ions

TL;DR

This paper provides an analytical derivation of the nonlinear coupling constant for vibrational modes in trapped ions, demonstrating agreement with experimental data and advancing understanding of Kerr-type interactions in quantum systems.

Contribution

It offers a new analytical expression for the cross phase modulation coupling constant in trapped ions, improving upon previous formulas.

Findings

Derived an analytical expression for the coupling constant.

The new formula closely matches experimental data.

Enhanced understanding of Kerr-type nonlinear interactions in trapped ions.

Abstract

We analyze nonlinear coupling between individual vibrational quanta for trapped ions. The nonlinear Coulomb interaction causes a Kerr-type Hamiltonian, for which we derive an analytical expression for the coupling constant. In contrast to a previously published formula [1], our result is in close agreement with experimental data.