Higgs and anomalous phase modes in non-Hermitian superfluids

Abstract

The Higgs and Goldstone modes are hallmarks of superconducting and superfluid order. Extending these systems into the non-Hermitian regime reveals qualitatively new behaviors absent in Hermitian settings. We study a driven BCS-like Hamiltonian with a complex pairing interaction, employing a metricized formulation to generalize the Anderson pseudospin formalism to non-Hermitian systems. We uncover both amplitude and phase oscillations of the order parameter, in contrast to the purely amplitude response of the Hermitian limit. This non-Hermitian phase oscillation is distinct from the conventional Goldstone mode, and is notably gapped even for neutral superfluids. The obtained collective oscillations also show sensitivity to the phase of the equilibrium non-Hermitian order parameter.