Restoring number conservation in quadratic bosonic Hamiltonians with dualities: Applications for quantum simulation and topological classification.

The breaking of number conservation in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built into these Hamiltonians, we show that as long as dynamical stability holds, one may always construct a non-trivial dual (unitarily equivalent) quadratic bosonic Hamiltonian, where only number-conserving hopping terms are present. In particular, we exemplify this construction for a bosonic analogue to Kitaev’s Majorana chain. Our duality may be used to identify local number-conserving models that approximate stable bosonic Hamiltonians without the need for parametric amplification and to implement non-Hermitian PT-symmetric dynamics in non-dissipative number-conserving bosonic systems. We describe how our approach may be useful for achieving analog quantum simulation of PT-symmetric Hamiltonians with significantly less experimental demand and increased robustness. We further discuss the implications of our duality transformation for computing topological invariants and classifying free bosonic Hamiltonians.