  Multielectron semiconductor quantum dots (QDs) provide a novel platform to
study the role of Coulomb correlations in finite quantum systems and their
impact on many-body energy spectra. An example is the formation of
interaction-driven, spatially localized electron states of Wigner molecules
(WMs). Although Wigner molecularization has been confirmed by real-space
imaging and coherent spectroscopy, the open system dynamics of the
strongly-correlated states with the environment are not yet well understood.
Here, we demonstrate efficient control of spin transfer between an artificial
three-electron WM and the nuclear environment in a GaAs double QD. A
Landau-Zener sweep-based polarization sequence and low-lying anti-crossings of
spin multiplet states enabled by Wigner molecularization are utilized. An
efficient polarization rate of 2.58 $h \cdotp kHz \cdotp (g^* \cdotp
\mu_B)^{-1}$ per electron spin flip and, consequently, programmable nuclear
polarization by controlled single-electron tunneling are achieved. Combined
with coherent control of spin states, we achieve control of magnitude,
polarity, and site dependence of the nuclear field. It is demonstrated that the
same level of control cannot be achieved in the non-interacting regime. Thus,
we confirm the multiplet spin structure of a WM, paving the way for active
control of newly emerging correlated electron states for application in
mesoscopic environment engineering.
