  Single-step Coulomb excitation of $^{46,48,49,50}$Ti is presented. A complete
set of $E2$ matrix elements for the quintuplet of states in $^{49}$Ti, centered
on the $2^+$ core excitation, was measured for the first time. A total of nine
$E2$ matrix elements are reported, four of which were previously unknown.
$^{49}_{22}$Ti$_{27}$ shows a $20\%$ quenching in electric quadrupole
transition strength as compared to its semi-magic $^{50}_{22}$Ti$_{28}$
neighbour. This $20\%$ quenching, while empirically unprecedented, can be
explained with a remarkably simple two-state mixing model, which is also
consistent with other ground-state properties such as the magnetic dipole
moment and electric quadrupole moment. A connection to nucleon transfer data
and the quenching of single-particle strength is also demonstrated. The
simplicity of the $^{49}$Ti-$^{50}$Ti pair (i.e., approximate single-$j$
$0f_{7/2}$ valence space and isolation of yrast states from non-yrast states)
provides a unique opportunity to disentangle otherwise competing effects in the
ground-state properties of atomic nuclei, the emergence of collectivity, and
the role of proton-neutron interactions.
