Stability of linear and non-linear lambda and tripod systems in the presence of amplitude damping

TL;DR

This paper analyzes the stability of dark states in linear and non-linear lambda and tripod quantum systems during adiabatic passage, considering amplitude damping effects, and identifies a common three-stage eigenvalue evolution.

Contribution

It provides an analytic and numerical stability analysis of dark states in both linear and non-linear systems, revealing a shared three-stage eigenvalue evolution process.

Findings

Eigenvalues' real parts evolve in three distinct stages.

Adiabatic reduction of degrees of freedom is possible during STIRAP.

Stability properties are characterized for systems with amplitude damping.

Abstract

We present the stability analysis of the dark states in the adiabatic passage for the linear and non-linear lambda and tripod systems in the presence of amplitude damping (losses). We perform an analytic evaluation of the real parts of eigenvalues of the corresponding Jacobians, the non-zero eigenvalues of which are found from the quadratic characteristic equations, as well as by the corresponding numerical simulations. For non-linear systems, we evaluate the Jacobians at the dark states. Similarly to the linear systems, here we also find the non-zero eigenvalues from the characteristic quadratic equations. We reveal a common property of all the considered systems showing that the evolution of the real parts of eigenvalues can be split into three stages. In each of them the evolution of the stimulated Raman adiabatic passage (STIRAP) is characterized by different effective dimension. This results in a possible adiabatic reduction of one or two degrees of freedom.