We demonstrate the creation of vortices in the electronic probability density of an atom subject to short electric field pulses, how these vortices evolve and can be manipulated by varying the applied pulses, and that they persist to macroscopic distances in the spectrum of ejected electrons. This opens the possibility to use practical femtosecond or shorter laser pulses to create and manipulate these vortex quasiparticles at the atomic scale and observe them in the laboratory. Within a hydrodynamic interpretation we also show, since the Schrödinger equation is a particular instance of the Navier-Stokes equations, that for compressible fluids vortices can appear spontaneously and with a certain time delay, which is not expected to occur from the conventional point of view, illustrating applicability of the present study to vortex formation more broadly.