Bosonic Holes in Quadratic Bosonic Systems
Abstract
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 CPT 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 C-parity is shown to label PH conjugate eigenspaces. Building on this duality, we demonstrate the PH Bogoliubov quasiparticles in APT symmetric Hamiltonians, investigate the dynamical generation of PH entanglement, and predict Hermitian PH Aharonov-Bohm interference in non-Hermitian QBSs.