Experimental realization of an optical second with strontium lattice clocks.

Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics. Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2-4 × 10(-16), have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second. Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 × 10(-16). Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 × 10(-16).

Improved tests of local position invariance using 87Rb and 133Cs fountains.

We report tests of local position invariance based on measurements of the ratio of the ground state hyperfine frequencies of 133Cs and 87Rb in laser-cooled atomic fountain clocks. Measurements extending over 14 years set a stringent limit to a possible variation with time of this ratio: d ln(ν(Rb)/ν(Cs))/dt=(-1.39±0.91)×10(-16) yr(-1). This improves by a factor of 7.7 over our previous report [H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003)]. Our measurements also set the first limit to a fractional variation of the Rb/Cs frequency ratio with gravitational potential at the level of c(2)d ln(ν(Rb)/ν(Cs))/dU=(0.11±1.04)×10(-6), providing a new stringent differential redshift test. The above limits equivalently apply to the fractional variation of the quantity α(-0.49)(g(Rb)/g(Cs)), which involves the fine-structure constant α and the ratio of the nuclear g-factors of the two alkalis. The link with variations of the light quark mass is also presented together with a global analysis combining other available highly accurate clock comparisons.

A simple analysis of the Dick effect in terms of phase noise spectral densities.

In cold-atom frequency standards based on the Ramsey double interaction method, the phase noise of the interrogating signal appears as a random "end-to-end phase difference", thereby introducing frequency noise in the loop. This phenomenon is analyzed in this paper in the Fourier frequency domain, using phase noise power spectral densities S(phi)(f). In continuously operated standards, the excess noise thus introduced is servoed out in the long term to become eventually smaller than the atomic shot noise, whereas in standards with pulsed operation the phase noise around even harmonics of the pulse rate is down-converted by aliasing to base band. This latter mechanism is referred to in the literature as Dick effect. In this paper, a model of the frequency control servo system is proposed, in which the input signal is the (known) local oscillator (LO) phase noise S(phi)(f) and the output signal is the (unknown) phase noise S(phi)(f) of the standard in closed loop operation. The level of excess white frequency noise added by aliasing on the stabilized LO through the Dick effect can be related analytically to the characteristics of the free LO phase noise. From this, the stability limitation (with slope tau(-1/2)) typical of the Dick effect can then be obtained by the usual conversion formulas based on the power law model.