Abstract
Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization(1), where increasing the randomness induces a metal-insulator transition. The introduction of topology in condensed-matter physics(2-4) lead to the discovery of topological phase transitions and materials as topological insulators(5). Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy(6) and new topological phases(7-9). Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition(10). Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal-insulator), a topological and parity-time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops(11). Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled.