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

Morag Am-Shallem, Ronnie Kosloff, Nimrod Moiseyev

Published 2014-11-24Version 1

The dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator ${\cal L}$. The eigenvalues of ${\cal L}$ are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining ${\cal L}$, non-hermitian degeneracies emerge, i.e. exceptional points ($EP$). We study the implications of such points in the open system dynamics of a two-level-system described by the Bloch equation. This open system has become the paradigm of diverse fields in physics, from NMR to quantum information and elementary particles. We find as a function of detuning and driving amplitude a continuous line of exceptional points merging into two cusps of triple degeneracy. The dynamical signature of these $EP$ points is a unique time evolution. This unique feature can be employed experimentally to locate the $EP$ points and thereby to determine the intrinsic system parameters for any desired accuracy.