Simulating monitoring-induced topological phase transitions with small systems

TL;DR

This paper introduces methods to simulate and observe topological phase transitions in small quantum systems by emulating larger lattice models and using auxiliary systems to access jump-time averaged states, simplifying experimental requirements.

Contribution

The authors propose two key simplifications: emulating topology in small systems' phase space and using auxiliary systems to measure jump-time averaged states without continuous monitoring.

Findings

Emulation of topological properties in small quantum systems.

Access to jump-time averaged states via auxiliary systems.

Application demonstrated on a 1D Su-Schrieffer-Heeger model.

Abstract

The topological properties of open quantum lattice systems have attracted much attention, due to their fundamental significance and potential applications. However, experimental demonstrations with large-scale lattice models remain challenging. On top of that, formulations of topology in terms of quantum trajectories require monitoring along with the detection of quantum jumps. This is particularly the case for the dark state-induced topology that relies on averaging quantum trajectories at their jump times. Here, we propose two significant simplifications to ease the experimental burden to demonstrate dark-state induced topological phase transitions: First, we emulate the topology in the phase space of small systems, where the effective size of the system is reflected by the accessible parameter range. Second, we develop a method how to, by augmenting the system with an auxiliary system, access the jump-time averaged state through standard wall-time averaging, which effectively substitutes the monitoring along with the counting of quantum jumps. While these simplifications are applicable to general lattice systems, we demonstrate them with a one-dimensional Su-Schrieeffer-Heeger model. In this case, the lattice system is emulated by a four-level system, while the jump-time averaged state up to the second jump is accessed through a three-level auxiliary system.