Optical clock comparison for Lorentz symmetry testing.

Questioning basic assumptions about the structure of space and time has greatly enhanced our understanding of nature. State-of-the-art atomic clocks1-3 make it possible to precisely test fundamental symmetry properties of spacetime and search for physics beyond the standard model at low energies of just a few electronvolts4. Modern tests of Einstein's theory of relativity try to measure so-far-undetected violations of Lorentz symmetry5; accurately comparing the frequencies of optical clocks is a promising route to further improving such tests6. Here we experimentally demonstrate agreement between two single-ion optical clocks at the 10-18 level, directly validating their uncertainty budgets, over a six-month comparison period. The ytterbium ions of the two clocks are confined in separate ion traps with quantization axes aligned along non-parallel directions. Hypothetical Lorentz symmetry violations5-7 would lead to periodic modulations of the frequency offset as the Earth rotates and orbits the Sun. From the absence of such modulations at the 10-19 level we deduce stringent limits of the order of 10-21 on Lorentz symmetry violation parameters for electrons, improving previous limits8-10 by two orders of magnitude. Such levels of precision will be essential for low-energy tests of future quantum gravity theories describing dynamics at the Planck scale4, which are expected to predict the magnitude of residual symmetry violations.

Autobalanced Ramsey Spectroscopy.

We devise a perturbation-immune version of Ramsey's method of separated oscillatory fields. Spectroscopy of an atomic clock transition without compromising the clock's accuracy is accomplished by actively balancing the spectroscopic responses from phase-congruent Ramsey probe cycles of unequal durations. Our simple and universal approach eliminates a wide variety of interrogation-induced line shifts often encountered in high precision spectroscopy, among them, in particular, light shifts, phase chirps, and transient Zeeman shifts. We experimentally demonstrate autobalanced Ramsey spectroscopy on the light shift prone ^{171}Yb^{+} electric octupole optical clock transition and show that interrogation defects are not turned into clock errors. This opens up frequency accuracy perspectives below the 10^{-18} level for the Yb^{+} system and for other types of optical clocks.

Frequency Comparison of [Formula: see text] Ion Optical Clocks at PTB and NPL via GPS PPP.

We used precise point positioning, a well-established GPS carrier-phase frequency transfer method to perform a direct remote comparison of two optical frequency standards based on single laser-cooled [Formula: see text] ions operated at the National Physical Laboratory (NPL), U.K. and the Physikalisch-Technische Bundesanstalt (PTB), Germany. At both institutes, an active hydrogen maser serves as a flywheel oscillator which is connected to a GPS receiver as an external frequency reference and compared simultaneously to a realization of the unperturbed frequency of the (2)S1/2(F=0)-(2)D3/2(F=2) electric quadrupole transition in [Formula: see text] via an optical femtosecond frequency comb. To profit from long coherent GPS-link measurements, we extrapolate the fractional frequency difference over the various data gaps in the optical clock to maser comparisons which introduces maser noise to the frequency comparison but improves the uncertainty from the GPS-link instability. We determined the total statistical uncertainty consisting of the GPS-link uncertainty and the extrapolation uncertainties for several extrapolation schemes. Using the extrapolation scheme with the smallest combined uncertainty, we find a fractional frequency difference [Formula: see text] of -1.3×10(-15) with a combined uncertainty of 1.2×10(-15) for a total measurement time of 67 h. This result is consistent with an agreement of the frequencies realized by both optical clocks and with recent absolute frequency measurements against caesium fountain clocks within the corresponding uncertainties.

Ultraprecise measurement of optical frequency ratios.

We developed a novel technique for frequency measurement and synthesis, based on the operation of a femtosecond comb generator as transfer oscillator. The technique can be used to measure frequency ratios of any optical signals throughout the visible and near-infrared part of the spectrum. Relative uncertainties of 10(-18) for averaging times of 100 s are possible. Using a Nd:YAG laser in combination with a nonlinear crystal we measured the frequency ratio of the second harmonic nu(SH) at 532 nm to the fundamental nu(0) at 1064 nm, nu(SH)/nu(0) = 2.000 000 000 000 000 001x (1 +/- 7x10(-19)).