Ultracold atoms have demonstrated great prospects for both technological and fundamental science applications. In order to fully exploit their potential, a precise control of the atomic cloud that can manipulate the quantum features and harness quantum resources is required. The proposed research aims to develop a robust method for measurement and control of the atom number in an ultracold atomic ensemble with precision better than the atom shot noise level. The measurement is based on the Faraday paramagnetic effect: off-resonant light, when traveling through a polarized atomic cloud, experiences optical rotation at an angle that is proportional to the number of atoms. The proposed measurement does not destroy quantum coherences and has an insignificant effect on the atomic temperature, so that it can be used to perform quantum-enhanced measurements and prepare the atomic state at the start of an interferometer sequence.
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