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

We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter $\gamma$. Using the pseudo-Hermitian formalism, we applied a Dyson map to transform the non-Hermitian Hamiltonian to its Hermitian representation. We have found that the decoherence slows down as $\gamma$ increases, eventually ceasing at $\gamma=1$. We define a pseudo-Hermitian observable that commutes with the metric operator to add as the self-Hamiltonian. Einselection gradually forced the system to select the eigenstates of the self-Hamiltonian as $\gamma\rightarrow1$. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as $\gamma$ increases. However, a turning point (minimum) corresponding to a maximum information dissipation to the spin bath is found. Finally, the Breuer-Laine-Piilo (BLP) measure, which is used to quantify the non-Markovianity of a quantum system, was evaluated for a finite time. The BLP measure in the strong environment regime exhibited similar turning point behavior, which means that the information backflow reaches a saturation point before declining. This decline signifies the point where PT-symmetry starts shielding the central spin from the environment.