  Topological edge-reconstruction occurs in hole-conjugate states of the
fractional quantum Hall effect. The frequently studied polarized state of
filling factor v=2/3 was originally proposed to harbor two counter-propagating
edge modes: a downstream v=1 and an upstream v=1/3. However, charge
equilibration between these two modes always led to an observed downstream
v=2/3 charge mode accompanied by an upstream neutral mode (preventing an
observation of the original proposal). Here, we present a new approach to
synthetize the v=2/3 edge mode from its basic counter-propagating charged
constituents, allowing a controlled equilibration between the two
counter-propagating charge modes. This novel platform is based on a carefully
designed double-quantum-well, which hosts two populated electronic sub-bands
(lower and upper), with corresponding filling factors, vl & vu. By separating
the 2D plane to two gated intersecting halves, each with different fillings,
counter-propagating chiral modes can be formed along the intersection line.
Equilibration between these modes can be controlled with the top gates' voltage
and the magnetic field. Our measurements of the two-terminal conductance G2T
and the presence of a neutral mode allowed following the transition from the
non-equilibrated charged modes, manifested by G2T=(4/3)e2/h, to the fully
equilibrated modes, with a downstream charge mode with G2T=(2/3)e2/h
accompanied by an upstream neutral mode.
