Liouvillian exceptional points and their relation to non-Hermitian Hamiltonians and quantum trajectories

Exceptional points (EPs) are spectral degeneracies of open systems that are attracting much interest in optics, plasmonics, and condensed matter physics. In the classical and semiclassical approaches, Hamiltonian EPs (HEPs) are degeneracies of non-Hermitian Hamiltonians such that at least two eigenfrequencies and the corresponding eigenstates coalesce. We argue that quantum jumps should be included in a fully quantum approach, e.g., that of the Lindblad master-equation approach. Thus, we define EPs via degeneracies of a Liouvillian superoperator (including quantum jumps, LEPs), and we clarify the relations between HEPs and LEPs [1]. The Liouvillian approach can be easily generalized to account for postselection of certain quantum jump trajectories [2]. The resulting hybrid-Liouvillian superoperator describes a new type of EPs, and can characterize experiments in the presence of finite-efficiency detectors[3].

[1] F. Minganti, A. Miranowicz, R. W. Chhajlany & F. Nori, Phys. Rev. A 100, 062131 (2019)
[2] M. Naghiloo, M. Abbasi, Yogesh N. Joglekar & K. W. Murch, Nat. Phys. 15, 1232 (2019)
[3] F. Minganti, A. Miranowicz, R. W. Chhajlany, Ievgen I. Arkhipov & F. Nori, Phys. Rev. A 101, 062112 (2020)