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Confinement can have a dramatic effect on the behavior of all sorts ofparticulate systems and it therefore is an important phenomenon in manydifferent areas of physics and technology. Here, we investigate the role playedby the softness of the confining potential. Using grand canonical Monte Carlosimulations, we determine the phase diagram of three-dimensional hard spheresthat in one dimension are constrained to a plane by a harmonic potential. Thephase behavior depends strongly on the density and on the stiffness of theharmonic confinement. Whilst we find the familiar sequence of confinedhexagonal and square-symmetric packings, we do not observe any of the usualintervening ordered phases. Instead, the system phase separates under strongconfinement, or forms a layered re-entrant liquid phase under weakerconfinement. It is plausible that this behavior is due to the larger positionalfreedom in a soft confining potential and to the contribution that theconfinement energy makes to the total free energy. The fact that specificstructures can be induced or suppressed by simply changing the confinementconditions (e.g. in a dielectrophoretic trap) is important for applicationsthat involve self-assembled structures of colloidal particles.

Layering, freezing and re-entrant melting of hard spheres in soft confinement