Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps

TL;DR

This paper explores how quantum jumps influence spectral singularities in atomic vapors, demonstrating that the Liouvillian approach is essential for accurately capturing the system's spectral properties and exceptional points.

Contribution

It reveals the limitations of the non-Hermitian Hamiltonian method and emphasizes the importance of the Liouvillian formalism in describing spectral features and exceptional points in atomic systems.

Findings

Quantum jumps significantly alter spectral degeneracies.

Liouvillian formalism provides a complete spectral description.

NHH approach may be insufficient for accurate predictions.

Abstract

We investigate spectral singularities in an alkali-metal atomic vapor modeled using four and effectively three hyperfine states. By comparing the eigenvalue spectra of a non-Hermitian Hamiltonian (NHH) and a Liouvillian superoperator, we analyze the emergence and characteristics of both semiclassical and quantum exceptional points. Our results reveal that, for atomic systems, the NHH approach alone may be insufficient to fully capture the system's spectral properties. While NHHs can yield accurate predictions in certain regimes, a comprehensive description typically requires the Liouvillian formalism, which governs the Lindblad master equation and explicitly incorporates quantum jump processes responsible for repopulation dynamics. We demonstrate that the inclusion of quantum jumps fundamentally alters the spectral structure of the system. In particular, we present examples in which the existence, location in parameter space, or even the order of spectral degeneracies differ significantly between the two approaches, thereby highlighting the impact of quantum jumps and the limitations of the NHH method. Finally, using the hybrid-Liouvillian formalism, we show how quantum jumps reshape spectral features initially predicted by the NHH, ultimately determining the full Liouvillian spectrum.