Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of ${}^{87}\mathrm{Rb}$ by applying the recently discovered spin self-rephasing [C. Deutsch et al., Phys. Rev. Lett. 105, 020401 (2010)]. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a stability of $2.4\times {10}^{-11}{\tau }^{-1/2}$, where $\tau$ is the integration time in seconds. Based on a set of technical improvements, the presented frequency standard is predicted to rival the stability of microwave fountain clocks in a potentially much more compact setup.

• Received 11 March 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.240801