  Single atom manipulation within doped correlated electron systems would be
highly beneficial to disentangle the influence of dopants, structural defects
and crystallographic characteristics on their local electronic states.
Unfortunately, their high diffusion barrier prevents conventional manipulation
techniques. Here, we demonstrate the possibility to reversibly manipulate
select sites in the optimally doped high temperature superconductor
Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ using the local electric field of the tip.
We show that upon shifting individual Bi atoms at the surface, the spectral gap
associated with superconductivity is seen to reversibly change by as much as 15
meV (~5% of the total gap size). Our toy model that captures all observed
characteristics suggests the field induces lateral movement of point-like
objects that create a local pairing potential in the CuO2 plane.
