How can quantum confinement be obtained? I have been reading about quantum confined systems. That is, systems of one or two  particles or atoms inside a region of space of radius R where potential energy is, say V(r), for r < R and infinity of r >= R. However, something I cannot find using Google is how one can obtain such space. I mean, if I can isolate two atoms, how can I put these two atoms inside a confined region?
Thanks
 A: The potential you have described is an infinite square well. This is a useful example to understand theoretically, but essentially impossible to create experimentally since it requires discontinuities, infinite energies etc. However, there do exist a large number of techniques for trapping atoms, mostly involving electric or magnetic fields. 
Perhaps the easiest to understand (classically, at least) are ion traps. If the atom is actually ionised, so that it carries an electric charge, it is obvious that you can push it around with electric fields. If you design these electric fields such that the atom is constantly pushed into the middle of the trap, you have successfully confined it. Note that the picture is not quite so simple, because Earnshaw's theorem forbids you from having an electric potential minimum in free space. This is usually circumvented by using oscillating fields, so that the time-averaged potential has a minimum even when the instantaneous potential at any time doesn't.
Neutral atoms can also be trapped by electric or magnetic fields. This is because the field changes the energies of the electron orbitals within the atom. So, for example, in a strong electric field the energy of one atom may be increased by an amount proportional to the square of the field (Stark shift). If you design the electric field so that its magnitude is minimal at a certain position, then the neutral atom will like to stay there. An example is an optical lattice: a standing wave of laser light. The field intensity is minimised at the nodes of the standing wave, so that neutral atoms are confined there. The potential felt by the atom close to the node can usually be well approximated by a harmonic potential. 
