Wave-particle duality is a key part of quantum mechanics. All matter appears to be particulate at the microscopic level, yet it can also behave like waves. Just like ripples on a pond can overlap to form patterns having peaks and valleys, the wave description of quantum mechanics allows quantum objects like atoms to be in superposition states. In order to observe wave-like behavior of atoms, physicists cool them down to near-absolute zero temperature. At these temperatures the deBroglie wavelength of each particle in a typical dilute atomic gas is long compared to the spacing between the atoms. The atom waves, like water waves, can interfere to create ripples and patterns. One of the neat aspects of this is that the interference is a single-particle effect--the atoms themselves are not interacting.
An atom interferometer is device or experiment in which atom waves are made to interfere with each other.
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