AI 中文总结
研究非厄米费米子超流体中的集体模式，基于非厄米量子力度规公式建立赝自旋框架，应用于驱动非厄米BCS哈密顿量，发现新型相位模式，其有能隙、共振谱依赖序参量相位且共振时响应有限，例外点出现时共振消失。
AI 中文摘要
希格斯模式和南布-戈德斯通模式是超导体和超流体中的典型集体激发。这些模式通常在BCS理论的赝自旋公式中分析，其动力学由赝自旋的海森堡运动方程得到。但直接扩展到非厄米系统时该构造变得不一致。本文基于非厄米量子力学的度规公式，为非厄米费米子超流体建立了一致的赝自旋框架。应用此形式体系到具有复配对相互作用的驱动非厄米BCS型哈密顿量并分析其集体激发谱。发现除了传统的希格斯（幅度）模式，系统还有一个在厄米超流体中没有对应物的新型相位模式。该模式即使在没有安德森-希格斯机制时也有能隙，与中性超流体情况相同。此外，共振谱明确依赖于复序参量的初始非规范相位，且在共振时动力学响应保持有限，这与厄米系统的发散特性相反。这些共振在例外点出现时消失。
英文摘要
The Higgs and Nambu-Goldstone modes are paradigmatic collective excitations in superconductors and superfluids. These modes are commonly analyzed within the pseudospin formulation of BCS theory, where the dynamics are obtained from the Heisenberg equations of motion for pseudospins. However, this construction becomes inconsistent when directly extended to non-Hermitian systems. In this work, we develop a consistent pseudospin framework for non-Hermitian fermionic superfluids based on the metricized formulation of non-Hermitian quantum mechanics. We apply this formalism to a driven non-Hermitian BCS-type Hamiltonian with complex pairing interaction and analyze its collective excitation spectrum. We find that, in addition to the conventional Higgs (amplitude) mode, the system hosts a novel phase mode that has no counterpart in Hermitian superfluids. Remarkably, this mode is gapped even in the absence of the Anderson-Higgs mechanism, as is the case in neutral superfluids. Furthermore, the resonance spectrum depends explicitly on the initial nongauge phase of the complex order parameter and the dynamical response remains finite at resonance, in contrast to the divergence characteristic of Hermitian systems. These resonances disappear upon the emergence of exceptional points.
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