Manifolds of exceptional points and effective Zeno limit of an open two-qubit system

TL;DR

This paper analytically explores the structure of Liouvillian exceptional points in a two-qubit open system, revealing complex topologies and phase diagrams that relate to Zeno transitions and relaxation dynamics.

Contribution

It introduces an analytical framework for understanding Liouvillian exceptional point manifolds in a two-qubit system, highlighting their topology and relation to Zeno effects.

Findings

Identification of two planar LEPMs and a multi-sheet topology.

Phase diagram for effective Zeno transitions at small dissipation.

Fastest relaxation occurs on LEPMs linked to Zeno regime transition.

Abstract

We analytically investigate the Liouvillian exceptional point manifolds (LEPMs) of a two-qubit open system, where one qubit is coupled to a dissipative polarization bath. Exploiting a Z_2 symmetry, we block-diagonalize the Liouvillian and show that one symmetry block yields two planar LEPMs while the other one exhibits a more intricate, multi-sheet topology. The intersection curves of these manifolds provide a phase diagram for effective Zeno transitions at small dissipation. These results are consistent with a perturbative extrapolation from the strong Zeno regime. Interestingly, we find that the fastest relaxation to the non-equilibrium steady state occurs on LEPMs associated with the transition to the effective Zeno regime.