A well-aimed baseball bat hits its target, causing a sudden change in the direction of the ball’s motion. In introductory physics we refer to the explosive force that the bat exerts on the ball, acting over the brief interval during which bat and ball are in contact, as an impulse. We examine how analogous impulses affect quantum systems. We distinguish between two different flavors of impulses, ordinary and super, which differ in how the impulse’s strength scales with its duration. Super impulses—the main focus of our work—are stronger than ordinary ones.

Under appropriate conditions, a quantum super impulse suddenly deforms a system’s wave function: It translates, stretches, and squeezes various portions of the wave function in a generally nonlinear manner. Mathematically, this deformation is specified by a map of the system’s configuration space onto itself. As our main result, we pose and answer the following question: If we wish to deform a given initial wave function ${\psi }_i$ under a map $\mu$ of our choice, how do we design a super impulse that achieves this goal?

While our paper is self-contained, it draws on theoretical tools from the fields of shortcuts to adiabaticity and optimal transport. To build intuition, we illustrate our results with simple examples for which the super impulse can be obtained analytically. Our results extend to many-body systems, in a mean-field approximation, and potentially open the way to the development of experimental tools for manipulating quantum systems.