  In a recent, modified double-pinhole diffraction experiment the existence of
an interference pattern was established indirectly along with a near-perfect
imaging of the double pinhole. Our theoretical analysis shows that the
experiment constitutes a preparation of a quantum state that is, to a good
approximation, a joint eigenstate of commuting functions of position and
momentum. Gaining information about the momentum distribution by means of the
particular experimental setup is thus possible with negligible impact on the
position distribution. Furthermore, we construct explicitly a class of states
simultaneously localised on periodic sets in position and momentum space, which
are therefore eigenstates of the observables being measured jointly (to a good
approximation) in multi-slit interferometry. Finally, we show that with an
appropriate change of settings the experiment demonstrates the mutual
disturbance of position and momentum measurements.

Quantum Physics