  Waveguide lattices offer a compact and stable platform for a range of
applications, including quantum walks, topological effects, condensed matter
system simulation, and classical and quantum information processing. In such
lattices, the Hamiltonian's hopping and on-site terms determine the optical
evolution, which can be engineered using waveguide spacing and refractive index
profile. While waveguide lattices have been realized in various photonic
platforms, these devices have always been static and designed for specific
applications. We present a programmable waveguide array in which the
Hamiltonian terms can be electro-optically tuned to implement various
Hamiltonian continuous-time evolutions on a single device. We used a single
array with 11 waveguides in lithium niobate, controlled via 22 electrodes, to
perform a range of experiments that realized the Su-Schriffer-Heeger model, the
Aubrey-Andre model, and Anderson localization, which is equivalent to over 2500
static devices. Our architecture's micron-scale local electric fields
independently control waveguide coupling coefficients and effective indices,
which overcomes cross-talk limitations of thermo-optic phase shifters in other
platforms such as silicon, silicon-nitride, and silica. Electro-optic control
allows for ultra-fast and more precise reconfigurability with lower power
consumption, and with quantum input states, our platform can enable the study
of multiple condensed matter quantum dynamics with a single device.
