Study on Dynamics of N Level System of Atom by Laser Fields

TL;DR

This paper extends the analysis of multi-level atomic systems interacting with laser fields, providing explicit solutions for three and four-level cases, and discusses potential applications in cavity QED quantum computation.

Contribution

It offers a complete solution for three and four-level atomic systems under laser interactions, advancing the modeling of realistic multi-level atom dynamics.

Findings

Explicit solutions for three and four-level systems obtained

Model applicable to cavity QED quantum computation

Extension of previous two-level system models

Abstract

This paper is an extension of Fujii et al (quant--ph/0307066) and in this one we again treat a model of atom with n energy levels interacting with n(n-1)/2 external laser fields, which is a natural extension of usual two level system. Then the rotating wave approximation (RWA) is assumed from the beginning. To solve the Schr{\" o}dinger equation we set the {\bf consistency condition} in our terminology and reduce it to a matrix equation with symmetric matrix $Q$ consisting of coupling constants. However, to calculate $\exp(-itQ)$ {\bfexplicitly} is not easy. In the case of three and four level systems we determine it in a complete manner, so our model in these levels becomes realistic. In last, we make a comment on Cavity QED quantum computation based on three energy levels of atoms as a forthcoming target.