Exceptional points for parameter estimation in open quantum systems: Analysis of the Bloch equations

Abstract

Wesuggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: the dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator L. The eigenvalues of L are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining L, non-Hermitian degeneracies emerge, i.e. exceptional points (EP). The dynamical signature of these EPs corresponds to a unique time evolution. This unique feature can be employed experimentally to locate the EPs and thereby to determine the intrinsic system parameters with a high accuracy. This way we turn the disadvantage of the dissipation into an advantage.Wedemonstrate this method in the open system dynamics of a two-level system described by the Bloch equation, which has become the paradigm of diverse fields in physics, from NMRto quantum information and elementary particles.