  While engineered quantum systems are a general route to the manipulation of
multipartite quantum states, access in a physical system to a continuous
quantum phase transition under sufficient control offers the possibility of an
intrinsic source of entangled states. To this end we realize the quantum
version of the linear-zigzag structural transition for arrays of up to five
ground state-cooled ions held in a linear Paul trap and we demonstrate several
of the control requirements towards entangled-state interferometry near the
critical point. Using in-situ spectroscopy we probe the energy level structure
and occupation of the soft mode associated with the structural transition, and
show a stable critical point and majority ground state occupation crossing the
transition. We resolve biases arising from trap electrode asymmetries that
change the nature of the transition, show that they can be suppressed by
varying the ion number, and demonstrate control of the transition bias using
optical dipole forces.
