Analytic solutions for a three-level system in a time-dependent field

TL;DR

This paper derives analytic solutions for a three-level quantum system driven by a time-dependent elliptic field, enabling analysis of arbitrary initial states and revealing beat phenomena due to non-linear driving.

Contribution

It extends known solutions to include elliptic functions as driving fields and provides a complete basis set for arbitrary initial conditions.

Findings

Analytic solutions for three-level systems with elliptic driving fields.

Observation of beating phenomena caused by non-linear time-dependent fields.

Framework for analyzing arbitrary initial states in such systems.

Abstract

This paper generalizes some known solitary solutions of a time-dependent Hamiltonian in two ways: The time-dependent field can be an elliptic function, and the time evolution is obtained for a complete set of basis vectors. The latter makes it feasible to consider arbitrary initial conditions. The former makes it possible to observe a beating caused by the non-linearity of the driving field.