  We present a Shortcut To Adiabaticity (STA) protocol applicable to 3D unitary
Fermi gases and 2D weakly-interacting Bose gases containing defects such as
vortices or solitons. Our protocol relies on a new class of exact scaling
solutions in the presence of anisotropic time-dependent harmonic traps. It
connects stationary states in initial and final traps having the same frequency
ratios. The resulting scaling laws exhibit a universal form and also apply to
the classical Boltzmann gas. The duration of the STA can be made very short so
as to realize a quantum quench from one stationary state to another. When
applied to an anisotropically trapped superfluid gas, the STA conserves the
shape of the quantum defects hosted by the cloud, thereby acting like a perfect
microscope, which sharply constrasts with their strong distortion occurring
during the free expansion of the cloud.
