Coherent control of the gap function in superconductors on the nanoscale

•Optimal control with the help of a time-dependent external field may result in the spatial localization of quasiparticles.•The localization occurs on the spatial scale much less than the control field wavelength.•The localization of quasiparticles is periodic in time.•The quasiparticle density inside the target volume increases, while the density outside the target volume decreases.

We propose a nonequilibrium mechanism of the gap function enhancement in nanoscale superconductors. The mechanism is based on coherent control and localization of the spatial distribution of Bogoliubov quasiparticles on the scale much less than the wavelength of the control field.