From a superfluid to a Mott insulator
(a) In the superfluid state of a Bose-Einstein condensate the underlying atoms can be described as a giant macroscopic matter wave. When such a condensate is released from the periodic potential, a multiple matter-wave interference pattern is formed due to the phase coherence between the atomic wavefunctions on different lattice sites. In this case the phase of the macroscopic matter wave is well defined. However, the number of atoms at each lattice site fluctuates. (b) In the limit of a Mott insulating state each lattice site is filled with a fixed number of atoms, but the phase of the matter-wave field remains uncertain. As a result, no matter-wave interference pattern can be seen when the quantum gases are released from the lattice potential.