Paper detail

Quantum Bowling: Particle-hole transmutation in one-dimensional strongly interacting lattice models

We study the scattering of a soliton-like propagating particle with a wall of bound particles, in several strongly interacting one-dimensional lattice models with discrete degrees of freedom. We consider spin-polarized fermions (anisotropic Heisenberg spin chain), the fermionic Hubbard model, and the Bose Hubbard model, using precise numerical time dependent Density Matrix Renormalization Group techniques. We show that in all integrable models studied, there is no reflection. Instead, an incoming particle experiences particle-hole transmutation upon entry and exit of the wall, and travels inside the wall as a hole, analoguous to Klein tunneling, even though the dispersion is highly nonlinear and there is no external potential. {\em Two} particles are added to the wall on the incoming side and removed on the opposite side. For spin-polarized fermions a single transmitted particle thus shifts the wall by two lattice sites, in complete contrast to classical physics. For both Hubbard models, the wall shifts by one doubly occupied single site. In the nonintegrable models studied, the same process occurs in linear superposition with backscattering events. We demonstrate a corresponding fermionic quantum Newton's cradle and a metamaterial with "tachyonic" modes travelling faster than in an empty system. We present a possible atomic scale signal counter for spintronics. Our scenario should be realizable in future cold atom experiments.