The answer depends on what you mean by "touch". There are three possible meanings of touch at the atomic level: 1) two objects influence each other, 2) two objects influence each other significantly, or 3) two objects reside in the exact same location. Note that the everday concept of touch (i.e the hard boundaries of two objects exist at the same location) makes no sense at the atomic level because atoms don't have hard boundaries. Atoms are not really solid spheres. They are fuzzy quantum probability clouds filled with electrons spread out into waving cloud-like shapes called "orbitals". Like a cloud in the sky, an atom can have a shape and a location without having a hard boundary. This is possible because the atom has regions of high density and regions of low density. When we say that an atom is sitting at point A, what we really mean is that the high-density portion of the atom's probability cloud is located at point A. If you put an electron in a box (as is done in quantum dot lasers), that electron is only mostly in the box. Part of the electron's wavefunction leaks through the walls of the box and out to infinity. This makes possible the effect of quantum tunneling, which is used in scanning tunneling microscopes. With the non-solid nature of atoms in mind, let us look at each of the possible meanings of touching.