https://hal-cea.archives-ouvertes.fr/cea-01540332v2Campos Venuti, LorenzoLorenzoCampos VenutiUSC - University of Southern CaliforniaMa, ZhengzhiZhengzhiMaUSC - University of Southern CaliforniaSaleur, HubertHubertSaleurIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueUSC - University of Southern CaliforniaHaas, StephanStephanHaasUSC - University of Southern CaliforniaTopological protection of coherence in a dissipative environmentHAL CCSD2017[PHYS] Physics [physics]Savelli, BrunoThe Hall Plateau Transition and non-unitary Quantum Field Theory - NuQFT - - H20202015-10-01 - 2020-09-30 - 669205 - VALID - 2022-10-21 11:14:492022-12-06 04:09:522022-10-21 11:20:32enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-01540332v2/document10.1103/PhysRevA.96.053858https://hal-cea.archives-ouvertes.fr/cea-01540332v1application/pdf2One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phase to non-Hermitian systems, a finite system in a non-trivial topological phase displays surface states with exponentially long life times. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-particle sector, by a non-Hermitian " Hamiltonian " of the desired form. We then study, both analytically and numerically, one-dimensional geometries with up to three sites per unit cell, and up to a topological winding number $W$ = 2. For finite-size systems the number of edge modes is a complicated function of $W$ and the system size $N$. However we find that there are precisely $W$ modes localized at one end of the chain. In such topological phases the quibt's coherence lifetime is exponentially large in the system size. We verify that, for $W$ > 1, at large times, the Lindbladian evolution is approximately a non-trivial unitary. For $W$ = 2 this results in Rabi-like oscillations of the qubit's coherence measure.