A research team from the Innovation Academy for Precision Measurement Science and Technology (APM) of the Chinese Academy of Sciences, in collaboration with the National University of Defense Technology and other institutions, has experimentally observed the transition behavior between two types of exceptional points in non-Hermitian quantum systems for the first time, using an ion-trap chip independently developed by APM.

The team has dubbed the observed singularities "Lindblad exceptional points," which simultaneously exhibit the characteristics of both second-order and third-order exceptional points. The study reveals that these two types of exceptional points can recombine to form hybrid Lindblad exceptional points that migrate within the observable parameter space.

The findings were recently published in Nature Communications.

Quantum exceptional points constructed on the basis of the Liouvillian matrix are known as Liouvillian exceptional points (LEPs). At such points, both the eigenvalues and eigenstates of a non-Hermitian quantum system undergo simultaneous collapse and degeneracy, giving rise to a host of novel physical properties in the vicinity of the exceptional point.

Real open quantum systems are described by the Lindblad master equation, which incorporates both dissipation and decoherence processes. However, existing experiments on LEPs have only been built around dissipative physical processes, entirely neglecting decoherence effects.

To tackle this long-standing challenge, the team for the first time integrated decoherence processes into the study of LEPs. To differentiate the non-Hermitian phenomena generated by these two physical mechanisms, the researchers classified them as dissipation-based Lindblad exceptional points and decoherence-based Lindblad exceptional points, respectively.

Beginning with dissipation-based Lindblad exceptional points, the researchers gradually decreased dissipation while strengthening decoherence. Under these conditions, the hybrid Lindblad exceptional points continuously shift toward the region where total dissipation approaches infinity. When dissipation and decoherence reach equal intensity, the hybrid Lindblad exceptional point vanishes entirely into the infinite parameter space.

As decoherence further becomes dominant, the hybrid Lindblad exceptional point transforms into a decoherence-based Lindblad exceptional point and migrates back to its original parameter location.

These phenomena stem from the non-commutativity between the two categories of Liouvillian operators corresponding to pure dissipation and pure decoherence, uncovering a more fundamental interplay between dissipation and decoherence in open quantum systems.

In addition, the team observed that higher-order exceptional points induced by the quantum jump effect also display mobile behavior. This higher-order singularity is a third-order exceptional point, formed by the intersection of two singular lines derived from second-order exceptional points. Its physical origin lies in the extra Hilbert space dimensions introduced by environmental quantum jump terms.

This discovery offers new technological routes for precision measurement and quantum manipulation based on higher-order exceptional points, and opens fresh avenues for controlling the topological properties and chiral dynamics of single-qubit systems.

The research was supported by the National Key Research and Development Program of China and the National Natural Science Foundation of China.