Emergent $\mathcal{PT}$-symmetry breaking of collective modes with topological critical phenomena

Abstract

The spontaneous breaking of parity-time ($\mathcal{PT}$) symmetry yields rich critical behavior in non-Hermitian systems, and has stimulated much interest, albeit most previous studies were performed within the single-particle or mean-field framework. Here, by studying the collective excitations of a Fermi superfluid with $\mathcal{PT}$-symmetric spin-orbit coupling, we uncover an emergent $\mathcal{PT}$-symmetry breaking in the Anderson-Bogoliubov (AB) collective modes, even as 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, which derives from the coalescence and annihilation of the AB mode and its hole partner, reminiscent of the particle-antiparticle annihilation. The system consequently becomes immune to low-frequency external perturbations at the critical point, a phenomenon associated with the spectral topology of the complex quasiparticle dispersion. This critical phenomenon offers a fascinating route toward perturbation-free quantum states.