From elastic to inelastic deformation of a dipolar supersolid

Due to its peculiar superfluid-crystal duality feature, the supersolid has received great research interest. Recently, researchers have paid much attention to its elastic response properties; however, the inelastic deformation has barely been explored. In this work, we study the transition from elastic to inelastic deformation of a dipolar supersolid Bose-Einstein condensate trapped in a box potential (i.e., a dipolar supersolid with finite size). We obtain the stationary supersolid states (both ground and excited) of the system and examine the relation between the supersolid size and the number of unit cells it can accommodate, which can essentially help us to understand the dynamical responses of the supersolid during a dilation or compression process. We found that within a certain dilation or compression extent, the supersolid can retain its original crystal structure, that is, it endures an elastic deformation; however, when the extent exceeds a critical threshold, the original crystal structure of the supersolid will be disrupted, which signifies an inelastic deformation. Furthermore, we both analytically and numerically determine the critical point of the transition from elastic to inelastic deformation and map out a phase diagram. These results open up new territory in the research of supersolid mechanical properties and may find applications in quantum material science and quantum-based technologies.