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The XENON1T experiment aims for the direct detection of dark matter in acryostat filled with 3.3 tons of liquid xenon. In order to achieve the desiredsensitivity, the background induced by radioactive decays inside the detectorhas to be sufficiently low. One major contributor is the $\beta$-emitter$^{85}$Kr which is an intrinsic contamination of the xenon. For the XENON1Texperiment a concentration of natural krypton in xenon $\rm{^{nat}}$Kr/Xe < 200ppq (parts per quadrillion, 1 ppq = 10$^{-15}$ mol/mol) is required. In thiswork, the design of a novel cryogenic distillation column using the commonMcCabe-Thiele approach is described. The system demonstrated a kryptonreduction factor of 6.4$\cdot$10$^5$ with thermodynamic stability at processspeeds above 3 kg/h. The resulting concentration of $\rm{^{nat}}$Kr/Xe < 26 ppqis the lowest ever achieved, almost one order of magnitude below therequirements for XENON1T and even sufficient for future dark matter experimentsusing liquid xenon, such as XENONnT and DARWIN.

Removing krypton from xenon by cryogenic distillation to the ppq level