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Usually, when investigating exceptional points (EPs) of an open Markovianbosonic system, one deals with spectral degeneracies of a non-HermitianHamiltonian (NHH), which can correctly describe the system dynamics only in thesemiclassical regime. A recently proposed quantum Liouvillian framework enablesto completely determine the dynamical properties of such systems and their EPs(referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking intoaccount the effects of quantum jumps, which are ignored in the NHH formalism.Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part ofmuch larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspaceof the LEPs. Here we show that once an NHH of a dissipative linear bosonicsystem exhibits an EP of a certain finite order $n$, it immediately impliesthat the corresponding LEP can become of any higher order $m\geq n$, defined inthe infinite Hilbert space. Most importantly, these higher-order LEPs can beidentified by the coherence and spectral functions at the steady state. Thecoherence functions can offer a convenient tool to probe extreme systemsensitivity to external perturbations in the vicinity of higher-order LEPs. Asan example, we study a linear bosonic system of a bimodal cavity withincoherent mode coupling to reveal its higher-order LEPs; particularly, ofsecond and third order via first- and second-order coherence functions,respectively. Accordingly, these LEPs can be additionally revealed by squaredand cubic Lorentzian spectral lineshapes in the power and intensity-fluctuationspectra. Moreover, we demonstrate that these EPs can also be associated withspontaneous parity-time (${\cal PT}$) and anti-${\cal PT}$-symmetry breaking inthe system studied.

physical review. a/physical review, a

Liouvillian exceptional points of any order in dissipative linear  bosonic systems: Coherence functions and switching between ${\cal PT}$ and  anti-${\cal PT}$ symmetries