Probing beyond the laser coherence time in optical clock comparisons

Hume, David; Leibrandt, David R.

doi:10.1103/physreva.93.032138

Cited by 45 publications

(61 citation statements)

References 42 publications

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“…This is roughly an order of magnitude reduction in the shift and a factor of 50 reduction in the uncertainty due to secular motion time-dilation in comparison with −(16.3 ± 5.0) × 10 −18 reported in the previous 27 Al + optical clock [8]. Extending the clock interrogation time to 1 s [28][29][30][31], the fractional time-dilation shift due to secular motion is estimated to be −(5.7 ± 0.3) × 10 −18 .…”

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confidence: 74%

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

et al. 2017

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We report on Raman sideband cooling of 25 Mg + to sympathetically cool the secular modes of motion in a 25 Mg + -27 Al + two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of −(1.9 ± 0.1) × 10 −18 for an 27 Al + clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous 27 Al + clocks. Trapped and laser-cooled ions are useful for many applications in quantum information processing and quantum metrology because of their isolation from the ambient environment and mutual Coulomb interaction [1][2][3][4][5][6]. The Coulomb interaction establishes normal modes of motion, called secular modes, which enable information exchange and entanglement between ions. For many operations in quantum information processing and metrology, these secular modes should ideally be prepared in their ground state. For example, in state-of-the-art trapped-ion optical clocks [7], uncertainty in the Doppler shift due to the residual excitation of these modes is a dominant contribution to the total clock uncertainty [8][9][10].All trapped-ion optical clocks to date have been operated with the ions' motion near the Doppler cooling limit [7][8][9][10]. For clocks based on quantum-logic spectroscopy of the 1 S 0 ↔ 3 P 0 transition in 27 Al + [11], the smallest uncertainty has been achieved by performing continuous sympathetic Doppler cooling on the logic ion ( 25 Mg + ) during the clock interrogation [8]. Due to the difficulty of performing accurate temperature measurements of trapped ions near the Doppler cooling limit, the uncertainty of the secular motion temperature was limited to 30 % [8].To reduce the secular motion time-dilation shift and its uncertainty, sub-Doppler cooling techniques can be employed [12][13][14][15][16][17]. These schemes have not previously been implemented in ion-based clock experiments due to high ambient motional heating rates, the need for extra cooling laser beams, and the difficulty of characterizing the resulting motional state distribution, which can be nonthermal [8,10,18]. For example, in sideband cooling, a non-thermal distribution can result from zero-crossings in the cooling transition Rabi rate as a function of the Fock state [19,20] and from cooling durations insufficient to reach equilibrium. Although sideband cooling can reach extremely low energies, a small non-thermal component of the distribution may contribute more than 90 % of the total energy [21], rendering the temperature measurement technique using motional sideband ratios unsuitable for determining the energy [12,13].Here we demonstrate sympathetic cooling of a 25 Mg + -27 ...

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confidence: 74%

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

et al. 2017

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“…One of the many potential applications of the proposed scheme is a cascaded clock [75][76][77] in which a clock laser is first stabilized to an ensemble of Ca + ions to improve its phase coherence time and thus allow extended probing times [24,25] in a high-accuracy single-ion clock (e.g. Al + or Yb + ).…”

Section: Applicationsmentioning

confidence: 99%

“…Al + or Yb + ). To bridge the difference in clock transition frequencies, a transfer scheme using a frequency comb would be employed [77][78][79]. Table 1 shows the achievable instabilities of an Al + clock for different initial clock laser instabilities.…”

Section: Applicationsmentioning

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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“…This is roughly an order of magnitude reduction in the shift and a factor of 50 reduction in the uncertainty due to secular motion time dilation in comparison with −ð16.3 AE 5.0Þ × 10 −18 , reported in the previous 27 Al þ optical clock [8]. Extending the clock interrogation time to 1 s [33][34][35][36], the fractional time-dilation shift due to secular motion is estimated to be −ð5.7 AE 0.3Þ × 10 −18 .…”

Section: Prl 118 053002 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 89%

Trapped Ions Stopped Cold

Huntemann

2017

Physics

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We report on Raman sideband cooling of 25 Mg þ to sympathetically cool the secular modes of motion in a 25 Mg þ -27 Al þ two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of −ð1.9 AE 0.1Þ × 10 −18 for an 27 Al þ clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous 27 Al þ clocks. DOI: 10.1103/PhysRevLett.118.053002 Trapped and laser-cooled ions are useful for many applications in quantum information processing and quantum metrology because of their isolation from the ambient environment and the mutual Coulomb interaction [1][2][3][4][5][6]. The Coulomb interaction establishes normal modes of motion, called secular modes, which enable information exchange and entanglement between ions. For many operations in quantum information processing and metrology, these secular modes should, ideally, be prepared in their ground state. For example, in state-of-the-art trappedion optical clocks [7], uncertainty in the Doppler shift due to the residual excitation of these modes is a dominant contribution to the total clock uncertainty [8][9][10].All trapped-ion optical clocks to date have been operated with the ions' motion near the Doppler cooling limit [7][8][9][10]. For clocks based on quantum-logic spectroscopy of the 1 S 0 ↔ 3 P 0 transition in 27 Al þ [11], the smallest uncertainty has been achieved by performing continuous sympathetic Doppler cooling on the logic ion ( 25 Mg þ ) during the clock interrogation [8]. Because of the difficulty of performing accurate temperature measurements of trapped ions near the Doppler cooling limit, the uncertainty of the secular motion temperature was limited to 30% [8].To reduce the secular motion time-dilation shift and its uncertainty, sub-Doppler cooling techniques can be employed [12][13][14][15][16][17]. These schemes have not previously been implemented in ion-based clock experiments due to high ambient motional heating rates, the need for extra cooling laser beams, and the difficulty of characterizing the resulting motional state distribution, which can be nonthermal [8,10,18]. For example, in sideband cooling, a nonthermal distribution can result from zero crossings in the cooling transition Rabi rate as a function of the Fock state [19,20] and from cooling durations insufficient to reach equilibrium. Although sideband cooling can reach extremely low energies, a small nonthermal component of the distribution may contribute more than 90% of the total energy [21], rendering the temperature measurement technique using motional sideband ratios unsuitable for determining the energy [12,13].Here, we dem...

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Probing beyond the laser coherence time in optical clock comparisons

Cited by 45 publications

References 42 publications

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

Robust optical clock transitions in trapped ions using dynamical decoupling

Trapped Ions Stopped Cold

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