Restoring number conservation in quadratic bosonic Hamiltonians with dualities

• URL: http://arxiv.org/abs/2004.07850v2
• Date: Tue, 8 Sep 2020 15:37:44 GMT
• Title: Restoring number conservation in quadratic bosonic Hamiltonians with dualities
• Authors: Vincent P. Flynn, Emilio Cobanera, Lorenza Viola
• Abstract summary: Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. We show that as long as dynamical stability holds, one may always construct a non-trivial dual (unitarily equivalent) number-conserving bosonic Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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