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.
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 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.
We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems whose dynamics can be effectively described by a non-Hermitian Hamiltonian. We derive a timescale for the degree of mixedness for an input state undergoing non-Hermitian dynamics and specialize these results in the case of a driven-dissipative two-level system. Next, we derive a timescale for the growth of mixedness for bipartite quantum systems that depends on the effective non-Hermitian Hamiltonian. In the Hermitian limit, this result recovers the perturbative expansion for coherence loss in Hermitian systems, while it provides an entanglement timescale for initial pure and uncorrelated states. To illustrate these findings, we consider the many-body transverse-field XY Hamiltonian coupled to an imaginary all-to-all Ising model. We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states. Overall, each timescale depends on minimal ingredients such as the probe state and the non-Hermitian Hamiltonian of the system, and its evaluation requires low computational cost. Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and
PT-symmetric quantum field theory.