Precise wavefunction engineering with magnetic resonance

Controlling quantum fluids at their fundamental length scale will yield superlative quantum simulators, precision sensors, and spintronic devices. This scale is typically below the optical diffraction limit, precluding precise wavefunction engineering using optical potentials alone. We present a protocol to rapidly control the phase and density of a quantum fluid down to the healing length scale using strong time-dependent coupling between internal states of the fluid in a magnetic field gradient. We demonstrate this protocol by simulating the creation of a single stationary soliton and double soliton states in a Bose-Einstein condensate with control over the individual soliton positions and trajectories, using experimentally feasible parameters. Such states are yet to be realized experimentally, and are a path towards engineering soliton gases and exotic topological excitations.