Calcium optical frequency standard with ultracold atoms: Approaching 10⁻¹⁵ relative uncertainty

An optical frequency standard based on an ensemble of neutral calcium atoms laser-cooled to 12 μK 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 nm was referenced to the caesium fountain clock of PTB utilizing a femtosecond comb generator with a fractional uncertainty of 1.2×10⁻¹⁴. The transition frequency was determined to be (455 986 240 494 144±5.3) Hz, making the calcium clock transition one of the most accurately known optical transitions. A frequency stability of 3×10⁻¹⁵ at 100 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.