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Register a new userSuppressing inhomogeneous broadening in a lutetium multi-ion optical clock
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We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three $^{176}$Lu$^+$ ions. Microwave spectroscopy between hyperfine states in the $^3D_1$ level is used to characterise differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the $sim 10^{-17}$ level relative to the $^1S_0leftrightarrow{}^3D_1$ optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of $sigma(tau)=8.2times 10^{-17}/sqrt{tau}$
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We measure the dynamic differential scalar polarizabilities at 10.6 $mu$m for two candidate clock transitions in $^{176}mathrm{Lu}^+$. The fractional black body radiation (BBR) shifts at 300 K for the $^1S_0 leftrightarrow {^3D_1}$ and $^1S_0 leftrightarrow {^3D_2}$ transitions are evaluated to be $-1.36,(9) times 10^{-18}$ and $2.70 ,(21) times10^{-17}$, respectively. The former is the lowest of any established optical atomic clock.
We propose and experimentally demonstrate a scheme which effects hyperfine averaging during a Ramsey interrogation of a clock transition. The method eliminates the need to average over multiple optical transitions, reduces the sensitivity of the clock to its environment, and reduces inhomogeneous broadening in a multi-ion clock. The method is compatible with auto-balanced Ramsey spectroscopy, which facilitates elimination of residual shifts due to imperfect implementation and ac Stark shifts from the optical probe. We demonstrate the scheme using correlation spectroscopy of the $^1S_0$-to-$^3D_1$ clock transition in a three-ion Lu+ clock. From the demonstration we are able to provide a measurement of the $^3D_1$ quadrupole moment, $Theta(^3D_1)=0.634(9)ea_0^2$.
We consider hyperfine-mediated effects for clock transitions in $^{176}$Lu$^+$. Mixing of fine structure levels due to the hyperfine interaction bring about modifications to Lande $g$-factors and the quadrupole moment for a given state. Explicit expressions are derived for both $g$-factor and quadrupole corrections, for which leading order terms arise from the nuclear magnetic dipole coupling. High accuracy measurements of the $g$-factors for the $^1S_0$ and $^3D_1$ hyperfine levels are carried out, which provide an experimental determination of the leading order correction terms.
We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions, such as $^{40}mathrm{Ca}^{+}$, $^{88}mathrm{Sr}^{+}$, $^{138}mathrm{Ba}^{+}$ and $^{176}mathrm{Lu}^{+}$. Taking a spherically symmetric Coulomb crystal formed by 400 $^{40}mathrm{Ca}^{+}$ ions as an example, we show through numerical simulations that the inhomogeneous linewidth of tens of Hertz in such a crystal together with linear Zeeman shifts of order 10~MHz are reduced to form a linewidth of around 1~Hz. We estimate a two-order-of-magnitude reduction in averaging time compared to state-of-the art single ion frequency references, assuming a probe laser fractional instability of $10^{-15}$. Furthermore, a statistical uncertainty reaching $2.9times 10^{-16}$ in 1~s is estimated for a cascaded clock scheme in which the dynamically decoupled Coulomb crystal clock stabilizes the interrogation laser for an $^{27}mathrm{Al}^{+}$ clock.
Optical frequency comparison of the 40Ca+ clock transition u_{Ca} (2S1/2-2D5/2, 729nm) against the 87Sr optical lattice clock transition u_{Sr}(1S0-3P0, 698nm) has resulted in a frequency ratio u_{Ca} / u_{Sr} = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio u_{Ca} / u_{Sr} to reach 1x10-15 in only 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of u_{Ca} using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical comparison (free from microwave link uncertainties) is smaller than that obtained using absolute frequency measurement, demonstrating the advantage of optical frequency evaluation. We report the absolute frequency of ^{40}Ca+ with a systematic uncertainty 14 times smaller than our previous measurement [1].
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