Are there any companies that use atom interferometers in aircraft? If so, are they used for navigation? If not, is it possible to assemble it?
The 2012 paper Advances in Atomic Gyroscopes: A View from Inertial Navigation Applications* states in the abstract that "there are still lots of problems that need to be overcome to meet the requirements of inertial navigation systems." Even once atomic inferometer gyroscopes are able to meet the basic requirements of inertial navigation systems, it will take years of testing and certification before they will actually be used in production aircraft.
I highly suggest reading that paper if atomic physics is your thing, but for us the conclusion is gold:
Recent progress on atomic gyroscopes has demonstrated that AIG is an ultra-high precision gyroscope for strategic grade inertial navigation in the future, and ASG is a high performance gyroscope which features both high precision and compact size. There are still lots of problems that need to be overcome when considering the atomic gyroscope for inertial navigation applications, however with the technologies available in the near future, the AIG could be used in space for fundamental physics research, the ASG based on comagnetometer can be used in strategic grade gimbaled INS, and the navigation grade ASG based on NMR can be demonstrated on chip-scale size. Furthermore, with the development of new theories and technologies for atomic manipulation, the future of high performance inertial navigation applications using AIG and ASG is indeed bright.
I would be slightly more cynical about time scales than this paper. This intro to INS notes on page 5 that it took 18 years for ring laser systems to reach maturity. No current atomic gyroscope system can meet the performance of ring laser systems, and the highest-performance AIG systems are on the order of a cubic meter. Chip-scale ASG systems have been produced, but their performance is dreadful compared to mechanical or ring laser systems.
*Note: I'm not sure how much to trust this article. It's published in a peer-reviewed journal, but there are clear copyediting errors. I don't have a better source, though, so I'll trust it for the purposes of this question. Also, note that this paper does not only have aviation users in mind; there are a lot of references to strategic INS, which I think refers to submarines, and it also talks about INS in the context of satellites.