  We have studied the temporal evolution of a quantum system subjected to
strong dissipation at ultra-low temperatures where the system-bath interaction
represents the leading energy scale. In this regime, theory predicts the time
evolution of the system to follow a generalization of the classical
Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting
quantum Brownian motion characteristics. For this purpose, we have investigated
the phase dynamics of a superconducting tunnel junction in the presence of high
damping. We performed current-biased measurements on the small-capacitance
Josephson junction of a scanning tunneling microscope placed in a low impedance
environment at milli-Kelvin temperatures. We can describe our experimental
findings by a quantum diffusion model with high accuracy in agreement with
theoretical predications based on the quantum Smoluchowski equation. In this
way we experimentally demonstrate that quantum systems subjected to strong
dissipation follow quasi-classical dynamics with significant quantum effects as
the leading corrections.
