Control of atomic Bose - Einstein condensate with interferometric feedback probing

We consider the problem of decoherence in a Bose - Einstein condensate (BEC) of noninteracting atoms during interferometric probing with a classical monochromatic external field. The condensate is located in one of the arms of the Mach - Zehnder interferometer, while part of the radiation from the interferometer output is fed back to the input, thereby closing the coherent feedback loop. A more general setting of the problem is also considered, in which the condensate is located in a system of interferometers 'nested' into each other, while part of the output radiation of each of them is also fed back to its input, closing the so-called multiloop feedback. The possibility of effective control of decoherence rates of various matrix elements is shown. The application of feedback of the proposed type to BEC in a double-well potential is investigated. It is found that this feedback allows efficient control of the distribution of atoms between the wells.