Emergent $\mathcal{PT}$-symmetry breaking of Anderson-Bogoliubov modes in Fermi superfluids

The spontaneous breaking of parity-time ($\mathcal{PT}$) symmetry, which yields rich critical behavior in non-Hermitian systems, has stimulated much interest. Whereas most previous studies were performed within the single-particle or mean-field framework, exploring the interplay between $\mathcal{PT}$ symmetry and quantum fluctuations in a many-body setting is a burgeoning frontier. Here, by studying the collective excitations of a Fermi superfluid under an imaginary spin-orbit coupling, we uncover an emergent $\mathcal{PT}$-symmetry breaking in the Anderson-Bogoliubov (AB) modes, whose quasiparticle spectra undergo a transition from being completely real to completely imaginary, even though the superfluid ground state retains an unbroken $\mathcal{PT}$ symmetry. The critical point of the transition is marked by a non-analytic kink in the speed of sound, as the latter completely vanishes at the critical point where the system is immune to low-frequency perturbations.These critical phenomena derive from the presence of a spectral point gap in the complex quasiparticle dispersion, and are therefore topological in origin.