Experimental demonstration of elastic Wannier-Stark Ladders and Bloch oscillations in 1D granular crystals

We numerically investigate and experimentally demonstrate the existence of elastic Wannier-Stark Ladders (WSLs) and Bloch oscillations (BOs) in a highly tunable 1D granular crystal consisting of cylindrical particles. These WSLs are obtained by introducing a gradient in contact stiffness along the chain so that it resembles the analogous physics of an electron under a uniform external electric field. We perform direct velocity measurements using Laser Doppler Vibrometer to detect the existence of time-resolved BOs, which are spatially localized elastic vibrations in the system. Experimental findings agree well with the numerical simulation results. We also show that this system can be easily tuned further to tailor the spatial and temporal properties of the Bloch oscillations, including localization length, position, and period. We envision that such tunable systems could be potentially used for vibration energy harvesting purposes as they promise a great degree of control over energy localization in a system.