  Quantum measurement remains a puzzle through its stormy history from the
birth of quantum mechanics to state-of-the-art quantum technologies. Two
complementary measurement schemes have been widely investigated in a variety of
quantum systems: von Neumann's projective 'strong' measurement and Aharonov's
weak measurement. Here, we report the observation of a weak-to-strong
measurement transition in a single trapped $40Ca^+$ ion system. The transition
is realized by tuning the interaction strength between the ion's internal
electronic state and its vibrational motion, which play the roles of the
measured system and the measuring pointer, respectively. By pre- and
post-selecting the internal state, a pointer state composed of two of the ion's
motional wavepackets is obtained, and its central-position shift, which
corresponds to the measurement outcome, demonstrates the transition from the
weak-value asymptotes to the expected-value asymptotes. Quantitatively, the
weak-to-strong measurement transition is characterized by a universal
transition factor $e^{-\Gamma^2}$, where $\Gamma$ is a dimensionless parameter
related to the system-apparatus coupling. This transition, which continuously
connects weak measurements and strong measurements, may open new experimental
possibilities to test quantum foundations and prompt us to re-examine and
improve the measurement schemes of related quantum technologies.
