Symmetric Bloch oscillations of matter waves.

Cold atoms in an optical lattice provide an ideal platform for studying Bloch oscillations. Here, we extend Bloch oscillations to two superposed optical lattices that are accelerated away from one another, and for the first time show that these symmetric Bloch oscillations can split, reflect and recombine matter waves coherently. Using the momentum parity-symmetry of the Hamiltonian, we map out the energy band structure of the process and show that superpositions of momentum states are created by adiabatically following the ground state of the Hamiltonian. The relative phase and velocity of the two lattices completely determines the trajectories of different branches of the matter wave. Experimentally, we demonstrate symmetric Bloch oscillations using cold Cesium atoms where we form interferometers with up to $240\hbar k$ momentum splitting, one of the largest coherent momentum splittings achieved to date. This work has applications in macroscopic tests of quantum mechanics, measurements of fundamental constants, and searches for new physics.