Restoring number conservation in quadratic bosonic Hamiltonians with dualities

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.

arXiv comment7 pages, 3 figures, uses epl2.cls

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• Interaction induced topological Bogoliubov excitations in a spin-orbit coupled Bose-Einstein condensate
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians
• Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
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