Topological Protection of Coherence in a Dissipative Environment

Abstract

One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases 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.

10 pages, 10 figures

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Cited by in corpus (15)

• New topological invariants in non-Hermitian systems
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Parity-time-symmetric topological superconductor
• Dynamical quantum phase transitions in non-Hermitian lattices
• Hall Conductance of a Non-Hermitian Chern Insulator
• Topologically Protected Quantum Coherence in a Superatom
• Towards Dynamic Simulations of Materials on Quantum Computers
• Unraveling the topology of dissipative quantum systems
• Topological transport in the steady state of a quantum particle with dissipation
• Number of steady states of quantum evolutions
• Topological Protection of Coherence in Noisy Open Quantum Systems
• Lindbladians with multiple steady states: theory and applications
• Microtubules as electron-based topological insulators
• Quantum enhancement of qutrit dynamics through driving field and photonic band-gap crystal
• Simulating monitoring-induced topological phase transitions with small systems