Bosonic Holes in Quadratic Bosonic Systems

Hole degrees of freedom play a central role in the exact solution of quadratic (mean-field) systems. Although a variety of experiments have suggested the existence of bosonic holes, a consistent and complete theory has long been hindered by the ghost problems. Here, we resolve the ghost problem and establish a unified theoretical framework for bosonic holes by introducing the $\mathcal{C}\mathcal{P}\mathcal{T}$ theory and bosonic particle-hole (PH) transformation. The bosonic analogs of the Fermi surface' and Fermi level’ are proposed. Furthermore, a PH duality between Hermitian and non-Hermitian quadratic bosonic systems (QBSs) is revealed. In both distinct QBSs, the $\mathcal{C}$-parity is shown to label PH conjugate eigenspaces. Building on this duality, we demonstrate the PH Bogoliubov quasiparticles in $\mathcal{A}\mathcal{P}\mathcal{T}$ symmetric Hamiltonians, investigate the dynamical generation of PH entanglement, and predict Hermitian PH Aharonov-Bohm interference in non-Hermitian QBSs.