Frequency comparison of optical lattice clocks beyond the Dick limit

Xiaotong Lu, Chihua Zhou, Ting Li +2 more

We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between |mF|=9/2 and |mF|=7/2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.

Darrick E. Chang, Jun Ye, Mikhail D. Lukin

Xiaohua Hu, Xiaotong Lu, Xiao-Fei Zhang +1 more

Precision measurement of the density shift caused by the interaction among neutral atoms trapped in an optical lattice has important applications in the study of multi-body interaction and the realization of high-performance optical lattice clocks. The common methods of measuring the density are the self-comparison technique and frequency comparison between two optical lattice clocks. Both methods are based on the identical density shift coefficient and should interrelatedly operate the clock at high- and low-density state, respectively. The precision of self-comparison method is limited by the Dick effect. The synchronous frequency comparison between two optical lattice clocks can realize the precision beyond the Dick limit. However, both methods can only obtain the average density shift and ignore the fact that the magnitude of the density shift is different over the lattice sites as inhomogeneous density distribution in the lattice. In this paper, the synchronous frequency comparison technique based on in situ imaging is used to accurately measure the density shift coefficient of optical lattice clock. Atoms in the optical lattice are simultaneously and independently excited by the same clock laser beam, and the clock transition probability of 11 uncorrelated regions of the optical lattice is simultaneously detected by in situ imaging. Thus, the clock laser noise, which is the root cause of the Dick effect, is common-mode rejected as the frequency difference between uncorrelated regions is measured by the clock transition spectrum. Beyond the Dick-noise-limited stability, the stability of synchronous frequency comparison between uncorrelated regions is consistent with the limit resulting from the atom detection noise. Between the center and margin of the lattice, the differential shifts of the black-body radiation shift, lattice AC Stark shift, probe Stark shift, DC Stark shift, and quadratic Zeeman shift are all below 5 × 10–6 Hz, which is three orders of magnitude smaller than the density shift and can be ignored in this experiment. Benefitting from the inhomogeneous distribution of atom number and negligible external field gradient in the optical lattice, the compared frequency shift between uncorrelated regions indicates the density shift. By measuring the relationship between the density shift and atom difference, the density shift coefficient is determined as –0.101(3) Hz/atom/site (with a measurement time of 103 s), and the fractional measurement uncertainty of the mean density shift of our system is 1.5 × 10–17.

Noriaki Horiuchi

Hidetoshi Katori, T. Takano, Masao Takamoto

We demonstrate a synchronous frequency comparison of two optical lattice clocks operated using87Sr and88Sr atoms, whose Allan standard deviation achieved 1 × 10-17in an averaging time of 1,600 s by cancelling out the Dick effect to approach the QPN limit. The scheme manifests an advantage of using a large number N ≈ 2,000 of atoms in optical clocks and paves the way to investigate clocks' inherent uncertainties and relativistic geodesy on a time scale of tens of minutes.

Andrei Derevianko, S. G. Porsev