  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.
