Unraveling the topology of dissipative quantum 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 [Gneiting et al., Phys. Rev. A 104, 062212 (2021)]. 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 jump-time 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, $\mathcal{PT}$, or time-reversal-symmetric Hamiltonians.