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arXiv:1502.02742 · New Journal of Physics

Cancellation of collisional frequency shifts in optical lattice clocks with Rabi spectroscopy

Sangkyung Lee, Chang Yong Park, Won-Kyu Lee, Dai-Hyuk Yu

Published Mar 18, 2016• 15 citations
arXivHTMLPDF

Abstract

We analyze both the s- and p -wave collision induced frequency shifts and propose an over- π pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a function of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over- π pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of 10 −18 in both Sr and Yb optical lattice clocks by canceling the collisional frequency shift.

DOI
10.1088/1367-2630/18/3/033030

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We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ(1). The fermion shift instead depends strongly on the second pulse area θ(2). It allows the shift to be canceled, nominally at θ(2)=π/2, but correlations perturb the null to slightly larger θ(2). The frequency shift is relevant for optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally larger at optical frequencies.
We report the realization of closed-loop operation of an optical lattice clock based on 171 Yb atoms. We interrogate the 1 S 0 → 3 P 0 clock transition using single Rabi pulses of 578 nm laser light. The two π-transitions from m F = ± 1 / 2 ground states are alternatively interrogated, and the clock laser frequency is locked to the center of the two resonances. The in-loop error signal stability of the clock reaches 3 × 10 − 17 for an average time of 3500 s. We also perform interleaved operations of the clock with two independent servo loops, and the fractional frequency difference averages down to 2 × 10 − 16 in 7200 s.
We have investigated the frequency shifts caused by inhomogeneous excitation in a 171Yb optical lattice clock. The dependences of the inhomogeneity on the temperature of the cold ytterbium atoms and the misaligning angle between the lattice laser and the clock laser are analyzed by numerical calculations. The dependence of the fractional collisional frequency shift on the ground state fraction under different cold atom temperatures, atom numbers, lattice trap depths and unequal transverse and longitudinal temperatures are also shown. The results show that the uncertainty of the ytterbium clocks, contributed by the inhomogeneous excitation, can be reduced to be 10−19 or even lower with certain conditions.
Optical lattice clocks with extremely stable frequency are possible when many atoms are interrogated simultaneously, but this precision may come at the cost of systematic inaccuracy resulting from atomic interactions. Density-dependent frequency shifts can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation. However, sufficiently strong interactions can suppress collisional shifts in lattice sites containing more than one atom. We demonstrated the effectiveness of this approach with a strontium lattice clock by reducing both the collisional frequency shift and its uncertainty to the level of 10(-17). This result eliminates the compromise between precision and accuracy in a many-particle system; both will continue to improve as the number of particles increases.
We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock on the highly forbidden transition (1)S(0)-(3)P(0) at 698 nm with bosonic (88)Sr. We were able to distinguish two loss channels: inelastic collisions between atoms in the upper and lower clock state and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with (88)Sr shows no degradation due to collisions on the fractional uncertainty level of 10(-16).