Speaker: Vincent Flynn
Affiliation: Dartmouth College (New Hampshire, USA)
Date: Monday, 11 September 2023 at 15:00
Location: Online seminar
Unlike their fermionic counterparts, systems of non-interacting bosons appear to lack any ability to support symmetry-protected topological (SPT) phases. In this talk, we report the emergence of non-trivial signatures of genuine SPT physics in metastable Markovian bosonic systems. Beginning with the closed-system setting, we discuss the main obstructions towards realizing SPT physics with non-interacting bosons and place a specific emphasis on the key differences with well-known examples of topological bosonic band structures, e.g., in photonic arrays. We then take the plunge into the open (Markovian) system setting in the hope to circumvent these obstructions and uncover convincing SPT signatures. Inspired by topological free fermions, we precisely characterize the properties any bosonic SPT signature must have, and consequentially, determine the class of bosonic dynamics that can support them: namely, those generated by topologically metastable quadratic bosonic Lindbladians. Such systems are shown to support tight analogues of Majorana fermions, which we deem “Majorana bosons”, and, when number symmetry is present, their U(1)-symmetric counterparts. Along the way, we discuss the subtle distinction between symmetry generators and conserved quantities in dissipative settings and present a nontrivial correspondence between these objects for non-interacting bosons. We further explore several models exemplifying they realm of potential realizations of these signatures and explore connections with topological amplification, the non-Hermitian skin effect, and non-reciprocal transport. Finally, we discuss observable consequences of topological metastability in the form of zero-frequency power-spectral peaks and long-lived, macroscopically separated (in space), quantum correlations.