Kapitza-Dirac scattering is an effect that occurs when particles (in our case 87Rb atoms) are scattered by a short-duration optical lattice. In contrast to Bragg scattering, Kapitza-Dirac scattering happens in a regime where the duration of the optical lattice is so short that the atoms can be considered stationary. The result is scattering into several high order components, with momentum given by 2n of the recoil momentum of the optical lattice. The number of atoms in each component is given by the Bessel functions.
Our BEC is in a magnetic trap, so if we split it into multiple orders with different momentum, those orders will begin to move differently in the trap. If we apply a second Kapitza-Dirac scattering pulse, we split each order into several orders.
As can be seen in the above diagram, we now have several components with similar momenta; however, because they have been given time to evolve in the trap, they are not identical. Thus, they can interfere with each other. This technique not only works for BECs, it even works for cold thermal gas clouds!
The above picture shows what happens to a thermal gas cloud with increasingly long delays between the two pulses. By the bottom picture, with a 400 microsecond delay, the different components have been left along so long that the components with high-momentum have been slowed down a significant amount by the trap. When the second pulse splits them again, they're no longer very similar to the newly split components of the formerly stationary part. Now the interference fringes are so small we can barely see them.
Luckily, our magnetic trap is approximately a harmonic oscillator, so all we have to do is wait a half oscillation for the components to move away from the center and come back, now with as much momentum as they started with. If we apply our second pulse now, we get interference again, although due to imperfections in the setup these fringes can only be easily seen with a BEC:
For more about our Kapitza-Dirac atom interferometers, see our paper: