Volume 131, Number 4, August 2020
|Number of page(s)||7|
|Published online||07 September 2020|
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
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.
PACS: 05.30.-d – Quantum statistical mechanics / 05.30.Jp – Boson systems / 45.30.+s – General linear dynamical systems
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