Restoring number conservation in quadratic bosonic Hamiltonians with dualities

¹ Department of Physics and Astronomy, Dartmouth College - 6127 Wilder Laboratory, Hanover, NH 03755, USA
² Department of Mathematics and Physics, SUNY Polytechnic Institute - 100 Seymour Ave., Utica, NY 13502, USA

Received: 20 April 2020
Accepted: 9 August 2020

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 -symmetric dynamics in non-dissipative number-conserving bosonic systems. Implications for computing topological invariants are addressed.