Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

Abstract

We demonstrate precision measurement and control of inhomogeneous broadening in a multiion clock consisting of three 176 Lu + ions. Microwave spectroscopy between hyperfine states in the 3 D1 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 ∼ 10 −17 level relative to the 1 S0 ↔ 3 D1 optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10 s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of σ(τ ) = 8.2 × 10 −17 / √ τ .With fractional uncertainties near to ∼ 10 −18 , stateof-the-art optical atomic clocks are among the most accurate scientific artefacts [1]. The two most successful realizations are ensembles of neutral atoms stored in optical lattices [2,3] and ions confined in radio-frequency (RF) traps [4,5]. The latter offers strong confinement such that atoms can be reused for subsequent clock interrogation and measurement. The stability of the current generation of trapped-ion optical clocks is limited by single-ion operation. This has limited the instability of ion-based clocks to ∼ 10 −15 / √ τ , for which averaging times τ of several days or even weeks are required to reach 10 −18 resolution. Modest improvements to stability can be expected as laser technology develops to allow longer interrogation times but ideally this would go hand-in-hand with an increase in the number of ions.Within the standard quantum limit (SQL), clock stability improves with the √ N where N is the number of atoms [6]. With an ensemble of ions, frequency resolution could be further enhanced using entangled states [7][8][9][10][11] or cascaded interrogation schemes [12,13]. From a technological standpoint, extension of clock operation to a small ensemble of ions is an immediate application for devices developed for small-scale quantum information processing (QIP). However, characterizing and maintaining exquisite control over various systematic effects in an ion ensemble is a significant challenge.Multi-ion operation is complicated by electric quadrupole (EQ) shifts arising from the Coulomb fields of neighbouring ions, excess-micromotion (EMM) shifts induced by the radio-frequency (rf) trapping field, and inhomogeneous magnetic fields. Efforts and proposals towards high-accuracy multi-ion optical clocks include (i) precision engineering of the ion trap to suppress EMM shifts [14], (ii) employing clock transitions with a negative differential scalar polarisability, ∆α 0 , to eliminate EMM shifts in a large ion crystal [15,16], and (iii) using dynamic decoupling or rf-dressed states to 646 nm 1 S 0 3 D 1 3 D 2 3 P 0 = 8 = 7 = 6 847.7 nm Hyperfine splitting: ~11.2 GHz 10.5 GHz 3 P 1 1 D 2 622 nm 895 nm 350 nm FIG. 1. Relevant energy level diagram of a 176 Lu + ion showing: the 1 S0 ↔ 3 D1 clock transition at 848 nm, the 3 D1 ↔ 3 ...

Half-minute-scale atomic coherence and high relative stability in a tweezer clock

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“…2 transition in a two-ion crystal of 138 Ba + , similar to previous work [2]. Specifically, Ramsey spectroscopy is performed on both ions for a duration longer than the optical coherence time of the individuals ions, which is limited by the common mode magnetic field noise.…”

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“…Thus, in lattice clocks spin squeezing can only provide an advantage with significant improvements in dead time and phase noise of next generation clock lasers. In contrast, in atomic clocks based on platforms whose atomic number cannot be easily scaled, such as multi-ion traps [48][49][50][51] or tweezer arrays [52][53][54][55] , spin squeezing can offer a relevant advantage.…”