Separation of Time Scales in a Quantum Newton's Cradle

We provide detailed modeling of the Bragg pulse used in quantum Newton's-cradle-like settings or in Bragg spectroscopy experiments for strongly repulsive bosons in one dimension. We reconstruct the postpulse time evolution and study the time-dependent local density profile and momentum distribution by a combination of exact techniques. We further provide a variety of results for finite interaction strengths using a time-dependent Hartree-Fock analysis and bosonization-refermionization techniques. Our results display a clear separation of time scales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behavior.