The concept of electron holes plays a significant role in condensed matter physics. Here we develop the concept of bosonic holes, which exhibit negative particle excitations, in quadratic bosonic systems. Unlike electron holes, the Fock states of bosonic holes are biorthogonal, and their excitation can be interpreted as removing particles from a mean-particle number with a mean field background. Furthermore, we find that quadratic bosonic Hamiltonians related by non unitary and local particle hole transformation possess the same locality structure and spectral properties in different spaces, reflecting the PH duality. Based on this, we study the generation of PH entanglement in two mode cases and the PH Aharonov Bohm effect in the three mode case, which results in a PH chiral flow with time reversal symmetry breaking. Our findings provide a new way to understand and explore unusual physical phenomena in particle non conserving and non Hermitian systems.

6 pages, 3 figures, comments are welcome