Calcium optical frequency standard with ultracold atoms: Approaching10−15relative uncertainty

An optical frequency standard based on an ensemble of neutral calcium atoms laser-cooled to $12\mu \mathrm{K}$ has been realized. By using ultracold atoms, one major previous source of uncertainty, the residual Doppler effect, was reduced. We show that cold collisions contribute a negligible amount to the uncertainty. The influence of a temporal evolution of the phase of the laser pulses used to interrogate the clock transition was measured and corrected for. The frequency of the clock transition at $657\mathrm{nm}$ was referenced to the caesium fountain clock of PTB utilizing a femtosecond comb generator with a fractional uncertainty of $1.2\times {10}^{-14}$. The transition frequency was determined to be $(455986240494144\pm 5.3)\mathrm{Hz}$, making the calcium clock transition one of the most accurately known optical transitions. A frequency stability of $3\times {10}^{-15}$ at $100\mathrm{s}$ averaging time was achieved and the noise contributions that limit to the observed stability were analyzed in detail. Additionally, the natural linewidth of the clock transition has been determined.