Probing Time Dilation in Coulomb Crystals in a High-Precision Ion Trap

Keller, Jonas; Kalincev, D.; Burgermeister, T.; Kulosa, A. P.; Alexandre, Didier; Nordmann, T.; Kiethe, Jan

doi:10.1103/physrevapplied.11.011002

Cited by 34 publications

(40 citation statements)

References 46 publications

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“…In contrast to neutral atom lattice clocks, which are typically probed with hundreds to thousands of atoms, single ion clocks are currently limited in their statistical uncertainty by quantum projection noise [21] to levels of a few parts in 10 15 t chains can be avoided by choosing an ion species with negligible differential electric quadrupole moment between the clock states, such as In + or Al + , or by employing ring traps in which the QPS is the same for all ions [29]. A high-accuracy multi-ion clock based on ion chains containing on the order of tens of ions in a linear quadrupole trap has been proposed and is expected to achieve trap-induced fractional systematic uncertainties at the 10 −19 level [26].…”

Section: Introductionmentioning

confidence: 99%

“…We demonstrate the basic principle, which is illustrated in figure 1, on the S 2 1 2 « D 2 5 2 clock transition in Ca 40 + , but the scheme is directly applicable to other systems as well. It therefore allows the operation of a multi-ion clock [26] using ion species whose clock transitions have a non-vanishing differential electric quadrupole moment. One of the many possible applications of such a multi-ion frequency reference is the phase stabilization of a probe laser for a single ion clock to allow nearlifetime-limited probe times and correspondingly reduced statistical uncertainties [24,25].…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

“…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.…”

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confidence: 99%

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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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Robust optical clock transitions in trapped ions using dynamical decoupling

et al. 2019

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“…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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confidence: 99%

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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Prospects and challenges for squeezing-enhanced optical atomic clocks

et al. 2020

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Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.

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Probing Time Dilation in Coulomb Crystals in a High-Precision Ion Trap

Cited by 34 publications

References 46 publications

Robust optical clock transitions in trapped ions using dynamical decoupling

Robust optical clock transitions in trapped ions using dynamical decoupling

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

Prospects and challenges for squeezing-enhanced optical atomic clocks

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