Focusing on a quantum-limit behavior, we study a single vortex in a cl
ean s-wave type-II superconductor by self-consistently solving the Bog
oliubov-de Gennes equation. The discrete energy levels of the vortex b
ound states in the quantum limit are discussed. The vortex core radius
shrinks monotonically up to an atomic-scale length on lowering the te
mperature T, and the shrinkage stops to saturate at a lower T. The pai
r potential, supercurrent, and local density of states around the vort
ex exhibit Friedel-like oscillations. The local density of states has
particle-hole asymmetry induced by the vortex. These are potentially o
bserved directly by scanning tunneling microscopy.