There are experiments with cold atom gases in optical traps that deal with matter's essential quantum nature. Cold atom gases' is actually quite a hot field (no pun intended). In an attempt to answer your question, I will try to explain how I understand quantum superposition experiments work in the most general possible way I can.
A superposition state $\left|\Psi\right\rangle$, under this most general description possible, is a linear superposition (that is precisely the reason why they are called that way) of the different quantum states that the system may have:
$$\left|\Psi\right\rangle=\sum_i c_i\left|\tilde{\Psi}_i\right\rangle$$
Where the sum is performed over all possible $\left|\tilde{\Psi}_i\right\rangle$ states in the chosen basis, each one of them weighed by a complex factor $c_i$. The common idea in every experiment dealing with quantum superposition is simple: to have a system whose initial state, which is given by the $c_i$'s, can be prepared and controlled (that is called a coherent state), and in which a certain observable quantity can be measured (associated with an operator branded $\hat{A}$). At the end of the day, the result of every observable measurement can be understood in terms of how the operator $\hat{A}$ acts over the different states in the basis, how each one of these states in the particular basis of choice evolve in time and which are the weights $c_i$.
What happens in the double slit experiment, trying to explain it in these terms without delving into further details, is that the different time evolutions of the (initially coherent) electrons moving through the experimental setup introduce phase factors that keep adding up to the $c_i$'s. When the position of the electrons is recorded on a screen (which constitutes the measurement), the mean value of the position observable has these different phase factors interfering with each other, giving rise to an interference pattern in the screen as a result.
The key idea in these experiments is always the following: To start with a coherent state (or at least as coherent as it can be managed in practice), to let interactions and time evolution make their respective jobs, and later on to see what happens when the system is looked at.
What happens with a macroscopic system? The abridged answer is: 'Way too many things'. For starters, the number of components would be of the order of $N_A=6'022\cdot10^{23}$ when not greater, so the number of states in our basis for a complete, many-body description would be absolutely humongous. On top of that, atoms and electrons are subject to many interactions on a microscopic level, so any coherence that may be momentaneously achieved will be destroyed in a quick, uncontrolled way before any measurement may be performed...
... Unless what we are dealing with is a system of a very particular kind, either with not too many particles (cold atom gases) or some specific interaction which favours the appearance of a coherent state even on a $N_A$-level macroscopic scale (as in conventional superconductivity and superfluidity).
This post imported from StackExchange Physics at 2014-03-22 17:24 (UCT), posted by SE-user user17581
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