Spectroscopic Signatures of a Liouvillian Exceptional Spectral Phase in a Collective Spin

TL;DR

This paper explores how non-Hermitian degeneracies in Lindblad generators create distinctive spectral features in a collective spin system, providing a way to detect many-body Liouvillian exceptional phases through spectroscopy.

Contribution

It introduces the concept of an exceptional spectral phase in collective spins and demonstrates how spectral signatures depend on initial states, offering a new diagnostic tool.

Findings

Exceptional spectral phase causes super-Lorentzian spectral features.

Signatures are suppressed in steady-state fluorescence but visible with generic initial states.

Spectroscopic diagnostics can identify many-body Liouvillian exceptional phases.

Abstract

Non-Hermitian degeneracies of Lindblad generators (Liouvillian exceptional points) can induce non-exponential relaxation and higher-order poles in dynamical response functions. A collective spin coupled to a polarized Markovian bath exhibits an \emph{exceptional spectral phase} in which defective Liouvillian modes imprint super-Lorentzian features in frequency-resolved spectra. We compute the emission spectrum via the Liouvillian resolvent, identify symmetry-sector selection rules, and demonstrate that exceptional-point signatures are strongly state-dependent: they are suppressed in steady-state fluorescence yet become unambiguous for generic (infinite-temperature or random) initial states. Our results provide an experimentally accessible spectroscopic diagnostic of many-body Liouvillian exceptional phases and clarify when steady-state emission can (and cannot) reveal them.