Quadrupole Shift Cancellation Using Dynamic Decoupling

Shaniv, Ravid; Akerman, Nitzan; Manovitz, Tom; Shapira, Yotam; Ozeri, Roee

doi:10.1103/physrevlett.122.223204

Cited by 21 publications

(27 citation statements)

References 27 publications

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“…Our scheme is applicable to other atomic species and experimental setups, paving the way for dynamically-decoupled Coulomb crystal clocks as references with high stability. We would like to note that during the preparation of this manuscript we became aware of a related independent work by Shaniv et al [85].…”

Section: Discussionmentioning

confidence: 99%

Robust optical clock transitions in trapped ions using dynamical decoupling

et al. 2019

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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 field 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 Ca 40 + , Sr 88 + , Ba 138 + and Lu 176 + . Taking a spherically symmetric Coulomb crystal formed by 400 Ca 40 + 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 twoorder-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 2.9×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 Al 27 + clock.- [3,22,23]. The statistical uncertainty can be improved by probing for longer times, ultimately limited by the excited clock state lifetime or the laser coherence time [24,25]. Alternatively, the number of probed ions can be increased.Recently, multi-ion clock schemes have been proposed to address this issue [26][27][28][29]. However, several challenges have to be overcome to maintain and transfer the small and very well characterizable systematic shifts achievable with single trapped ions to larger ion crystals. The oscillating rf field in Paul traps results in ac Stark and second order Doppler shifts through micromotion [30][31][32]. Furthermore, electric field gradients from the trapping fields and the surrounding ions couple to atomic quadrupole moments, resulting in an electric quadrupole shift (QPS). The effects of micromotion can be avoided by trapping strings of ions in a precisionmachined linear Paul trap with negligible excess micromotion from trap imperfections [28,33]. The QPS in such Q 0 m J J J m , J j å = =-[67]. Such an average will also eliminate the linear Zeeman shift, assuming the field does not change between the frequency measurements contributing to the average. We propose a novel dynamical decoupling scheme in which robustness to this type of shifts is achieved by the application of a detuned driving field, mixing all m J states to form dressed states with effective Q 0 J m , j = . While the cancellation scheme is general and applies to tensor shifts of arbitrary electronic states, we consider in the following the Hamiltonian of the D 2 5 2 states of e.g.Ca + ions 2 1 , 1 0 J J 2

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Section: Discussionmentioning

confidence: 99%

Robust optical clock transitions in trapped ions using dynamical decoupling

et al. 2019

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“…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 P0 transition at 646 nm used for Doppler cooling and detection, and optical pumping transitions at 350 nm, 622 nm, and 895 nm to initialize population to the 3 D1 level.suppress EQ shifts [17,18]. All three approaches are readily adaptable to 176 Lu + although the first approach requires EQ shifts to be mitigated in a linear ion crystal.In this work, high resolution microwave spectroscopy is used to characterize the effects of neighbouring ions in a three-ion crystal.…”

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confidence: 99%

“…suppress EQ shifts [17,18]. All three approaches are readily adaptable to 176 Lu + although the first approach requires EQ shifts to be mitigated in a linear ion crystal.…”

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confidence: 99%

Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

et al. 2019

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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 ...

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“…Dynamic decoupling is an attractive approach to suppressing inhomogeneous broadening, as it also reduces the sensitivity of the clock frequency to electromagnetic fields, and simplifies the averaging by eliminating the need to probe multiple transitions. However, the recent demonstration in 88 Sr + [12] is not directly applicable to 176 Lu + . Instead we use a simple scheme in which population is transferred between hyperfine states during a Ramsey interrogation so that each upper state is sampled for an equal duration of time.…”

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confidence: 98%

“…Hence, broadening mechanisms must be well characterized and controlled, which can be a significant challenge in an ensemble of ions. Nevertheless progress towards multi-ion operation has been made: precision engineering of the ion trap has allowed the control of excess-micromotion (EMM) shifts to the 10 −19 level over millimeter length scales [15]; precise alignment of the magnetic field has demonstrated suppression of tensor shifts [8]; and dynamic decoupling during interrogation has also demonstrated suppression of inhomogeneous broadening [12].…”

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Hyperfine Averaging by Dynamic Decoupling in a Multi-Ion Lutetium Clock

et al. 2020

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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 1 S0 ↔ 3 D1 clock transition in a three-ion Lu + clock. From the demonstration we are able to provide a measurement of the 3 D1 quadrupole moment, Θ( 3 D1) = 0.634(9)ea 2 0 .

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Quadrupole Shift Cancellation Using Dynamic Decoupling

Cited by 21 publications

References 27 publications

Robust optical clock transitions in trapped ions using dynamical decoupling

Robust optical clock transitions in trapped ions using dynamical decoupling

Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

Hyperfine Averaging by Dynamic Decoupling in a Multi-Ion Lutetium Clock

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