Collective modes in non-Hermitian fermionic superfluids

This study investigates the collective excitation modes of non-Hermitian fermionic superfluids. While the Higgs and Nambu-Goldstone modes are well-understood in Hermitian systems, the authors address the inconsistency of applying standard pseudospin formalisms to non-Hermitian systems, which often arise in open quantum systems with gain and loss.

The authors employ a metricized formulation of non-Hermitian quantum mechanics to develop a consistent pseudospin framework. This approach allows for a well-defined Heisenberg picture that remains compatible with the Schrödinger picture, preserving operator commutation relations. By applying this to a driven BCS-type Hamiltonian with a complex pairing interaction, the researchers derive the equations of motion for pseudospin operators and analyze the resulting collective excitation spectrum under external driving.

The analysis reveals that non-Hermitian fermionic superfluids host a novel phase mode that has no counterpart in Hermitian systems. Unlike the gapless Nambu-Goldstone mode, this new phase mode is gapped even in neutral superfluids. Furthermore, the authors find that the resonance spectrum is sensitive to the initial nongauge phase of the complex order parameter. Notably, the dynamical response remains finite at resonance, contrasting with the divergences typically seen in Hermitian systems. These resonances disappear when the system reaches exceptional points, where the eigenvectors of the Bogoliubov-de Gennes Hamiltonian coalesce.

This work provides a robust theoretical foundation for studying collective dynamics in dissipative quantum systems. By identifying a gapped phase mode unique to non-Hermitian physics, the paper expands our understanding of how environmental coupling and non-unitary processes fundamentally alter the collective behavior of superfluids, offering new insights for experiments in ultracold atoms and superconducting circuits.