Abstract
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.
Highlights
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport
A photonic simulator of the Hubbard model can map the dynamics of two correlated particles hopping on a onedimensional (1D) lattice into the motion of a single particle in a 2D lattice with engineered defects[22,23], thereby offering the possibility to visualize the effect under simulation, but requiring a high level of control of the photonic structure
Lattice driven by an external force. This model is more accurate than the standard BH model as it accounts for higher-order processes whose magnitude is comparable with the one of second-order tunnelling26. given by H 1⁄4 H extended Bose–Hubbard (EBH) þ H F, wThheereHHa^mF i1⁄4ltoFndiaPn l of ln^l the system is describes the effect of the external constant force F (d is the lattice period) and
Summary
The oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. We report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose–Hubbard Hamiltonian. With the advent of semiconductor superlattices and ultracold atoms, BO have been observed for matter waves[3,4,5,6] In their essence, BO are a wave phenomenon. A photonic simulator of the Hubbard model can map the dynamics of two correlated particles hopping on a onedimensional (1D) lattice into the motion of a single particle in a 2D lattice with engineered defects[22,23], thereby offering the possibility to visualize the effect under simulation, but requiring a high level of control of the photonic structure. We report on the first observation of fractional BO using a photonic lattice as a model system of a few-particle extended Bose–Hubbard Hamiltonian, which is the most appropriate theoretical framework to consistently describe fractional BO
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