  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.
