Topological transitions in quantum jump dynamics: Hidden exceptional points

TL;DR

This paper reveals hidden exceptional points in the full counting statistics of monitored quantum systems, linking topological transitions to observable quantum jump distributions, and offers a new way to experimentally detect these phenomena.

Contribution

It introduces the concept of hidden EPs in Lindbladian spectra, accessible via counting fields, and connects them to topological transitions characterized by braid theory.

Findings

Identifies hidden EPs in monitored three-level quantum systems.

Shows hidden EPs correspond to topological class transitions.

Demonstrates experimental detection of these EPs through quantum jump statistics.

Abstract

Complex spectra of dissipative quantum systems may exhibit degeneracies known as exceptional points (EPs). At these points the systems' dynamics may undergo drastic changes. Phenomena associated with EPs and their applications have been extensively studied in relation to various experimental platforms, including, i.a., the superconducting circuits. While most of the studies focus on EPs appearing due to the variation of the system's physical parameters, we focus on EPs emerging in the full counting statistics of the system. We consider a monitored three level system and find multiple EPs in the Lindbladian eigenvalues considered as functions of a counting field. These "hidden" EPs are not accessible without the insertion of the counting field into the Linbladian, i.e., if only the density matrix of the system is studied. Nevertheless, we show that the "hidden" EPs are accessible experimentally. We demonstrate that these EPs signify transitions between different topological classes which are rigorously characterized in terms of the braid theory. Furthermore, we identify dynamical observables affected by these transitions and demonstrate how experimentally measured quantum jump distributions can be used to spot transitions between different topological regimes. Additionally, we establish a duality between the conventional Lindbladian EPs (zero counting field) and some of the "hidden" ones. Our findings allow for easier experimental observations of the EP transitions, normally concealed by the Lindbladian steady state, without applying postselection schemes. These results can be directly generalized to any monitored open system as long as it is described within the Lindbladian formalism.