Unraveling the topology of dissipative quantum systems

TL;DR

This paper explores the topological properties of dissipative quantum systems through quantum trajectories, revealing how dark states induce nontrivial topology and lead to observable topological phase transitions in jump-time dynamics.

Contribution

It introduces a topological framework for dissipative quantum systems based on quantum trajectories and dark states, highlighting new topological phase transitions in jump-time dynamics.

Findings

Dark states induce nontrivial topology in Hamiltonian space

Topological phase transitions manifest in transport behavior

Topological features are evident in chiral, PT, and time-reversal symmetric systems

Abstract

We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum trajectories at the occurrence of quantum jumps, i.e., the jump times, gives rise to a discrete, deterministic evolution which is highly sensitive to the presence of dark states. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians, which is also reflected by the corresponding jumptime dynamics. The topological character of the latter can then be observed, for instance, in the transport behavior, exposing an infinite hierarchy of topological phase transitions. We develop our theory for one- and two-dimensional two-band Hamiltonians and show that the topological behavior is directly manifest for chiral, PT, or time reversal-symmetric Hamiltonians.