Measurement of Berry's Phase in Microscopic -Triaxial Cracking Excitations

Many intractable systems can be reduced to a system of interacting spins. Here, we introduce a system of artificial acoustic spins which are manipulated with ultrasound excitations from microcracking sources with three control parameters in a 3D inhomogeneous confined stress field. We evaluate the evolution of the order parameter visualized as dancing strings constructed from time series collected using multi-array ultrasound sensors. We study the adiabatic cyclic change of the order parameter of the system due to rotation of the pseudo-stress field. We show that the order parameter acquires a geometric phase factor in addition to the dynamic phase known as Berry's phase. We demonstrated the accumulation of a geometric phase in the ``k-chains'' and show that the system can be manipulated geometrically by means of microscopic ultrasound radiation of cracking excitations and observed the real-time accumulated phase. We found that the observed geometric phase is an excellent agreement with Berry's predictions. The introduced acoustic-spin system opens new horizon to study other aspects of spin-systems including different time characteristics of relaxation phases, topological phases induced by driving and stress-quenched induced defects.