Frequency comparison of optical lattice clocks beyond the Dick limit

Abstract

The supreme accuracy of atomic clocks (Rosenband in Science 319:1808, 2008) relies on the universality of atomic transition frequencies. The stability of a clock, meanwhile, measures how quickly the clock's statistical uncertainties are reduced. The ultimate measure of stability is provided by the quantum projection noise (Itano in Phys. Rev. A 47:3554, 1993), which improves as 1/√N by measuring N uncorrelated atoms. Quantum projection noise limited stabilities have been demonstrated in caesium clocks (Santarelli in Phys. Rev. Lett. 82:4619, 1999) and in single-ion optical clocks (Peik et al. in J. Phys. B 39:145, 2006, Chou et al. in Phys. Rev. Lett. 104:070802, 2010), where the quantum noise overwhelms the Dick effect (Santarelli in IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45:887, 1998) attributed to local oscillator noise. Here, we demonstrate a synchronous frequency comparison of two optical lattice clocks using ⁸⁷Sr and ⁸⁸Sr atoms (Akatsuka et al. in Nature Phys. 4:954, 2008), respectively, for which the Allan standard deviation reached 1 × 10⁻¹⁷ in an averaging time of 1,600 s by cancelling out the Dick effect to approach the quantum projection noise limit. The scheme demonstrates the advantage of using a large number (N ≈ 1,000) of atoms in optical clocks and paves the way to investigating the inherent uncertainties of clocks and relativistic geodesy (Chou et al. in Science 329:1630, 2010) on a timescale of tens of minutes.