  A controlled quantum system can alter its environment by feedback, leading to
reduced-entropy states of the environment and to improved system coherence.
Here, using a quantum dot electron spin as control and probe, we prepare the
quantum dot nuclei under the feedback of coherent population trapping and
measure the evolution from a thermal to a reduced-entropy state, with the
immediate consequence of extended qubit coherence. Via Ramsey interferometry on
the electron spin, we directly access the nuclear distribution following its
preparation, and measure the emergence and decay of correlations within the
nuclear ensemble. Under optimal feedback, the inhomogeneous dephasing time of
the electron, $T_2^*$, is extended by an order of magnitude to $39$~ns. Our
results can be readily exploited in quantum information protocols utilizing
spin-photon entanglement, and represent a step towards creating quantum
many-body states in a mesoscopic nuclear spin ensemble.
