Majorana bosons: Searching for symmetry-protected topological phases in quasi-free bosonic systems*

Despite the ubiquity of quasi-free bosonic systems in condensed-matter, atomic, molecular, and optical physics, their ability to exhibit symmetry-protected topological phases remains elusive. While it is well known that such phases are forbidden in closed, stable, bosonic matter, we uncover potential signatures in the form of 'Majorana bosons' in quasi-free systems undergoing Markovian dissipation. By leveraging tools from pseudospectral analysis, we show that Majorana bosons exist over a transient timescale which increases with system size. This 'topological metastability' is unique to bosons and is associated with a robust topological invariant. Each Majorana boson pair consists, in general, of a distinct zero mode and a symmetry generator, reflecting the absence of a Noether-like theorem in open quantum dynamics. We argue that Majorana bosons will result in distinctive zero-frequency peaks in steady-state observable power spectra.