Observing a topological transition in weak-measurement-induced geometric phases

Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements, in particular through their back action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement-induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g., braiding) that are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.

Automated summary

Measurement plays a crucial role in controlling quantum systems. Weak measurements, through their back action on the system, can enable coherent control and induce topological transitions in geometric phases. This connection reveals subtle topological features in measurement-based manipulation of quantum systems and opens up new avenues for measurement-enabled quantum control of many-body topological states.