Interaction-Endowed PT -Symmetry and its Effects on Decoherence, Einselection, and Non-Markovianity in a Central Spin Model

Research Question and Approach

This study investigates the impact of parity-time (PT) symmetry on the decoherence, einselection, and non-Markovian dynamics of a central spin-1/2 system interacting with a spin bath. By introducing a PT-symmetric interaction Hamiltonian with a tunable hermiticity parameter (gamma), the authors employ the pseudo-Hermitian formalism and a Dyson map to transform the non-Hermitian system into an equivalent Hermitian representation. This allows for a rigorous analysis of how the system's coherence and pointer states evolve as the parameter approaches the PT-transition point.

The researchers found that increasing the hermiticity parameter effectively rescales the coupling energies, leading to a critical slowing down of decoherence. As the parameter approaches unity, the decoherence timescale becomes effectively infinite, indicating that the central spin is shielded from the environment. Furthermore, the study demonstrates that PT-symmetry forces the system to select the eigenstates of the self-Hamiltonian as pointer states, a process known as einselection. The authors also identified a turning point in the system's purity and non-Markovianity (quantified by the Breuer-Laine-Piilo measure), where information backflow reaches a saturation point before declining, marking the onset of environmental shielding.

This work provides a novel theoretical framework for controlling decoherence in open quantum systems. By using PT-symmetric interactions, researchers can potentially extend the coherence times of central spin systems, which are fundamental components in quantum information processing. The ability to tune the interaction to shield a system from its environment offers a promising strategy for mitigating noise and preserving quantum information without requiring traditional dynamical decoupling techniques.