Fig. 4: Persistence of strong boundary clustering \({\bar{P}}_{11}\) from interaction-induced caging, even for initial state (4,4) outside a x0 = 3 cage.
From: Non-Hermitian strong bosonic clustering through interaction-induced caging
Snapshots of the time-smoothed (Δt = 2) two-boson correlation probability \({\bar{P}}_{11}\) (Eq. (6)) for (a1) non-interacting and (a2) interacting cases. The bosons still gradually penetrate the L-shaped cage due to the NHSE towards (1,1), and remain trapped in it after that (t = 3, 8) (See Supplementary Video 2). (b1) Eventually, \({\bar{P}}_{11}(t)\) is ultra-enhanced only for the non-Hermitian interacting case (red), with (b2) negligible enhancement of boundary localization by U in the single-boson case, similar to (b1,b2) of Fig. 3. (c1)--(c3) Time-averaged two-boson probability \({\bar{P}}_{{{\rm{cage}}}}\) within the x0 × x0 cage as a function of hopping asymmetry r. For initial states (2, 2) and (4, 4) with coincident bosons, the U = 1 cases exhibit much larger \({\bar{P}}_{{{\rm{cage}}}}\) due to interaction-induced caging. But for (2, 4), non-coincident initial bosons do not interact appreciably and the effect of interactions is negligible.
