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arXiv · 2004.07850

Restoring number conservation in quadratic bosonic Hamiltonians with dualities

Vincent P. Flynn·Emilio Cobanera·Lorenza Viola
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Abstract

Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built in to these Hamiltonians, we show that as long as dynamical stability holds, one may always construct a non-trivial dual (unitarily equivalent) number-conserving quadratic bosonic Hamiltonian. We exemplify this construction for a gapped harmonic chain and 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 $\mathcal{P}\mathcal{T}$-symmetric dynamics in non-dissipative number-conserving bosonic systems. Implications for computing topological invariants are addressed.

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Vincent P. Flynn, Emilio Cobanera, Lorenza Viola. 2020-04-16. Restoring number conservation in quadratic bosonic Hamiltonians with dualities. https://doi.org/10.1209/0295-5075/131/40006

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