Time has always had a special status in physics because of its fundamental role in specifying the regularities of nature and because of the extraordinary precision with which it can be measured. This precision enables tests of fundamental physics and cosmology, as well as practical applications such as satellite navigation. Recently, a regime of operation for atomic clocks based on optical transitions has become possible, promising even higher performance. We report the frequency ratio of two optical atomic clocks with a fractional uncertainty of 5.2 x 10(-17). The ratio of aluminum and mercury single-ion optical clock frequencies nuAl+/nuHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 x 10(-17), and systematic uncertainties of 1.9 x 10(-17) and 2.3 x 10(-17) in the mercury and aluminum frequency standards, respectively. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant alpha of alpha/alpha = (-1.6+/-2.3) x 10(-17)/year.

Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years, finding widespread use in basic scientific studies, communications, and navigation. However, with its higher operating frequency, an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced to the 1.064-petahertz transition of a single trapped 199 Hg ϩ ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional frequency instability of 7 ϫ 10 Ϫ15 is measured in 1 second of averaging-a value substantially better than that of the world's best microwave atomic clocks.

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The evaluation procedure of a new laser-cooled caesium fountain primary frequency standard developed at the National Institute of Standards and Technology (NIST) is described. The new standard, NIST-F1, is described in some detail and typical operational parameters are discussed. Systematic frequency biases for which corrections are made -second-order Zeeman shift, black-body radiation shift, gravitational red shift and spin-exchange shiftare discussed in detail. Numerous other frequency shifts are evaluated, but are so small in this type of standard that corrections are not made for their effects. We also discuss comparisons of this standard both with local frequency standards and with standards at other national laboratories.

With simple optical geometries a separate resonant Fabry-Perot cavity can serve as an optical feedback element that forces a semiconductor laser automatically to lock its frequency optically to the cavity resonance. This method is used to stabilize laser frequencies and reduce linewidths by a factor of 1000 from 20 MHz to approximately 20 kHz.