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.Comment: 8+ pages, 3 figures; revised parameters and added section about
optimisation of adiabatic, finite-duration pulses and analytic resolution
limi