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Quantum Electronics

Effect of trapped-ion heating on generalised Ramsey methods for suppressing frequency shifts caused by a probe field in atomic clocks

S.N. Kuznetsov, А. В. Тайченачев, Valeriy I. Yudin, N. Huntemann, Christian Sanner, K. Tamm, E. Peik

Published May 8, 2019• 4 citations
Publisher

Abstract

Abstract Based on a simple one-dimensional model, we consider the effect of trapped-ion heating on the efficiency of generalised Ramsey methods for the probe-induced frequency shift suppression in optical frequency standards based on single ultracold ions. It is shown that ion heating reduces the efficiency of all previously proposed one-loop generalised Ramsey methods, leading in all cases to the appearance of a linear dependence of the reference frequency shift on the residual field frequency shift. Two versions of the most heating stable generalised Ramsey schemes, for which the proportionality coefficient in this dependence is minimal, are demonstrated.

DOI
10.1070/qel17005

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Abstract Based on a simple one-dimensional model, we consider the effect of trapped-ion heating on the efficiency of generalised Ramsey methods for the probe-induced frequency shift suppression in optical frequency standards based on single ultracold ions. It is shown that ion heating reduces the efficiency of all previously proposed one-loop generalised Ramsey methods, leading in all cases to the appearance of a linear dependence of the reference frequency shift on the residual field frequency shift. Two versions of the most heating stable generalised Ramsey schemes, for which the proportionality coefficient in this dependence is minimal, are demonstrated.
We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40) J m(2)/V(2) and a dynamic correction η(300 K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).
Abstract We study the possibility of suppressing light shifts in Ramsey spectroscopy of coherent population trapping (CPT) using generalised autobalanced Ramsey spectroscopy (GABRS) and combined error signal in Ramsey spectroscopy (CESRS). We consider CPT resonances excited by a coherent bichromatic field in an open Λ-system with a ‘trap’ state. Using a rigorous mathematical proof and numerical calculations, these methods are shown to lead to complete suppression of the light shift and its fluctuations. Implementation of GABRS and CESRS in CPT clocks can markedly improve accuracy and long-term stability of these devices. These methods can also be applied in atomic CPT magnetometers and interferometers.
We develop a universal method to significantly suppress probe-induced shifts in any type of atomic clock using Ramsey spectroscopy. Our approach is based on the adaptation of the synthetic frequency concept [V. I. Yudin et al., Phys. Rev. Lett. 107, 030801 (2011)] (previously developed for blackbody radiation shift suppression) to Ramsey spectroscopy with the use of interrogations with different dark time intervals. The most significant suppression of the shift is obtained in combination with the so-called hyper-Ramsey spectroscopy technique [V. I. Yudin et al., Phys. Rev. A 82, 011804(R) (2010)]. In this case, the probe-induced frequency shifts can be suppressed considerably from metrologically significant levels to below a fractional level of ${10}^{\ensuremath{-}18}$ for practically any optical atomic clocks. The main advantage of our method in comparison with other hyper-Ramsey approaches [R. Hobson et al., Phys. Rev. A 93, 010501(R) (2016); T. Zanon-Willette et al., Phys. Rev. A 93, 042506 (2016)] derives from its much greater efficiency and robustness in the presence of decoherence.
This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.
We perform a theoretical analysis of the Ramsey scheme with pulses of different duration and with a phase step in the second pulse with account for the finite width of laser line. We define optimum features of pulses that correspond to maximum suppression of the field shift and maximum amplitude of resonance for both schemes. Ramsey scheme with a phase step in the second pulse provides effective suppression of the field shift and it is less sensitive to the Rabi frequency fluctuations in comparison with Ramsey scheme with pulses of different duration. First experiments on ytterbium single-ion optical clock (Germany, PTB) confirm theoretical predictions