9705058 Lukens Experiments will be undertaken to explore the quantum mechanical behavior of a macroscopic variable---in this case, the magnetic flux through a ring. A particular focus of this work will be to understand the effect of the environment (damping and temperature) on the evolution of the flux from purely classical to quantum. The system to be studied is a superconducting loop containing a Josephson junction (SQUID) which undergoes transitions between two fluxoid states by tunneling through a potential barrier between potential wells. The system energy is quantized within each fluxoid well as has recently been confirmed using macroscopic resonant tunneling. At low temperatures only the lowest state in a well is occupied, giving a model two state system. These states differ in magnetic moment by about 10^10 Bohr magnetons---a very macroscopic quantity. The primary goal of this work is to attempt an observation of macroscopic quantum coherence (MQC) between these two states and to understand the role of the environment in determining the extent of such coherence. %%% Quantum mechanics predicts many `strange' phenomena which are very much at odds with our everyday experience. This was illustrated rather vividly in the early years of the field by Schroedinger -- one of the founders of quantum mechanics -- through a thought experiment in which he postulated his cat in a state where it oscillated between being dead and alive. We are usually spared the consequences of these paradoxes since they tend to only arise in atomic scale systems: interactions with the rest of the world prevent them from occurring in the sort of macroscopic objects we encounter in our everyday lives. Recent advances in experimental technology are, however, predicted to make it possible to observe such effects (called macroscopic quantum coherence (MQC)) in a superconducting system known as a SQ UID, which generates a magnetic field (or magnetic moment as it is more correctly known) about 10 billion times greater than that of an atom. In our experiments, which must be performed a few thousandths of a degree above absolute zero, we hope to be able to observe this system in a coherent superposition of states with the magnetic moment pointing up and down. ***