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We describe the operation of a laser cooled cesium fountain clock in the quantum limited regime. An ultrastable cryogenic sapphire oscillator is used to measure the short-term frequency stability of the fountain as a function of the number of detected atoms N₀ₓ. For N₀ₓ varying from 410^4 to 610^5 the Allan standard deviation of the frequency fluctuations is in excellent agreement with the N₀ₓ^-1/2 law of atomic projection noise. With 610^5 atoms, the relative frequency stability is 410^-14^-1/2, where is the integration time in seconds. This is the best short-term stability ever reported for primary frequency standards, a factor of 5 improvement over previous results.
Santarelli et al. (Mon,) studied this question.