Topological protection of coherence in a dissipative environment
One-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 nontrivial topological phase displays surface states with exponentially long lifetimes. 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 qubit'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 nontrivial unitary. For W = 2 this results in Rabi-like oscillations of the qubit's coherence measure.