Exploring the topology induced by non-Markovian Liouvillian exceptional points

TL;DR

This paper investigates the topological properties of non-Markovian Liouvillian exceptional points in quantum systems, revealing novel winding numbers and experimentally demonstrating these phenomena in a superconducting qubit setup.

Contribution

It introduces the concept of topological features of Liouvillian exceptional points in non-Markovian systems, extending the understanding beyond Markovian regimes.

Findings

Two distinct winding numbers can be generated by encircling a twofold LEP2.

Experimental demonstration with a superconducting qubit and a decaying resonator.

Pushes the study of exceptional topology into non-Markovian quantum regimes.

Abstract

Non-Hermitian (NH) systems can display exotic topological phenomena without Hermitian counterparts, enabled by exceptional points (EPs). So far, investigations of NH topology have been restricted to EPs of the NH Hamiltonian, which governs the system dynamics conditional upon no quantum jumps occurring. The Liouvillian superoperator, which combines the effects of quantum jumps with NH Hamiltonian dynamics, possesses EPs (LEPs) that are significantly different from those of the corresponding NH Hamiltonian. We here study the topological features of the LEPs in the system consisting of a qubit coupled to a non-Markovian reservoir. We find that two distinct winding numbers can be simultaneously produced by executing a single closed path encircling the twofold LEP2, formed by two coinciding LEP2s, each involving a pair of coalescing eigenvectors of the extended Liouvillian superoperator. We experimentally demonstrate this purely non-Markovian phenomenon with a circuit, where a superconducting qubit is coupled to a decaying resonator which acts as a reservoir with memory effects. The results push the exploration of exceptional topology from the Markovian to non-Markovian regime.