Quantum Projection Noise in an Atomic Fountain: A High Stability Cesium Frequency Standard

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 $N_{\mathrm{at}}$. For $N_{\mathrm{at}}$ varying from $4\times {10}^4$ to $6\times {10}^5$ the Allan standard deviation of the frequency fluctuations is in excellent agreement with the $N_{\mathrm{at}}^{-1/2\mathrm{}}$ law of atomic projection noise. With $6\times {10}^5$ atoms, the relative frequency stability is $4\times {10}^{-14\mathrm{}}{\tau }^{-1/2\mathrm{}}$, where τ 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.