  The process of quantum measurement has been a long standing source of debate.
A measurement is postulated to collapse a wavefunction onto one of the states
of a predetermined set - the measurement basis. This basis origin is not
specified within quantum mechanics. According to the theory of decohernce, a
measurement basis is singled out by the nature of coupling of a quantum system
to its environment. Here we show how a measurement basis emerges in the
evolution of the electronic spin of a single trapped atomic ion due to
spontaneous photon scattering. Using quantum process tomography we visualize
the projection of all spin directions, onto this basis, as a photon is
scattered. These basis spin states are found to be aligned with the scattered
photon propagation direction. In accordance with decohernce theory, they are
subjected to a minimal increase in entropy due to the photon scattering, while,
orthogonal states become fully mixed and their entropy is maximally increased.
Moreover, we show that detection of the scattered photon polarization measures
the spin state of the ion, in the emerging basis, with high fidelity. Lastly,
we show that while photon scattering entangles all superpositions of pointer
states with the scattered photon polarization, the measurement-basis states
themselves remain classically correlated with it. Our findings show that photon
scattering by atomic spin superpositions fulfils all the requirements from a
quantum measurement process.
