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Journal of Physics Conference Series

Synthetic frequency protocol in the Ramsey spectroscopy

Valeriy I. Yudin, M. Yu. Basalaev, А. В. Тайченачев

Published Jan 1, 2017• 1 citation
Publisher

Abstract

We develop an universal method to significantly suppress probe-induced shifts in any types of atomic clocks using the Ramsey spectroscopy. The frequency shifts can be suppressed considerably below a fractional level of 10 −18 practically for any optical atomic clocks.
DOI
10.1088/1742-6596/793/1/012034

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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.
We present nonstandard optical Ramsey schemes that use pulses individually tailored in duration, phase, and frequency to cancel spurious frequency shifts related to the excitation itself. In particular, the field shifts and their uncertainties can be radically suppressed (by two to four orders of magnitude) in comparison with the usual Ramsey method (using two equal pulses) as well as with single-pulse Rabi spectroscopy. Atom interferometers and optical clocks based on two-photon transitions, heavily forbidden transitions, or magnetically induced spectroscopy could significantly benefit from this method. In the latter case, these frequency shifts can be suppressed considerably below a fractional level of 101010${}^{\ensuremath{-}17}$. Moreover, our approach opens the door for high-precision optical clocks based on direct frequency comb spectroscopy.
We develop a method of modified hyper-Ramsey spectroscopy in optical clocks, achieving complete immunity to the frequency shifts induced by the probing fields themselves. Using particular pulse sequences with tailored phases, frequencies, and durations, we can derive an error signal centered exactly at the unperturbed atomic resonance with a steep discriminant which is robust against variations in the probe shift. We experimentally investigate the scheme using the magnetically induced ${}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{0}$ transition in 88Sr^{88}\mathrm{Sr}88Sr, demonstrating automatic suppression of a sizable $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ probe Stark shift to below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ even with very large errors in shift compensation.
During precision measurement, the quantity being measured is often perturbed by the measurement process itself. This includes precision frequency measurements for atomic-clock applications using Ramsey spectroscopy. To eliminate probe-induced perturbations, a generalized method is developed in which the frequency control loop is augmented with a second control loop that feeds back to a secondary clock variable, and can perfectly compensate for perturbations of the clock frequency caused by the measurements in the first loop. This universal technique can be used for atomic clocks, high-resolution molecular spectroscopy, two-photon probing schemes, Ramsey mass spectrometry, and beyond.
We develop a concept of atomic clocks where the blackbody radiation shift and its fluctuations can be suppressed by 1--3 orders of magnitude independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$) which are exposed to the same thermal environment, there exists a ``synthetic'' frequency ${\ensuremath{\nu}}_{\mathrm{syn}}$ $\ensuremath{\propto}$ (${\ensuremath{\nu}}_{1}\ensuremath{-}{\ensuremath{\epsilon}}_{12}{\ensuremath{\nu}}_{2}$) largely immune to the blackbody radiation shift. For example, in the case of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ it is possible to create a synthetic-frequency-based clock in which the fractional blackbody radiation shift can be suppressed to the level of ${10}^{\ensuremath{-}18}$ in a broad interval near room temperature ($300\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{K}$). We also propose a realization of our method with the use of an optical frequency comb generator stabilized to both frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$, where the frequency ${\ensuremath{\nu}}_{\mathrm{syn}}$ is generated as one of the components of the comb spectrum.
We present an interrogation scheme for the next generation of quantum clocks to suppress frequency shifts induced by laser probing fields that are themselves based on generalized hyper-Ramsey resonances. Sequences of composite laser pulses with a specific selection of phases, frequency detunings, and durations are combined to generate a very efficient and robust frequency locking signal with an almost perfect elimination of the light shift from off-resonant states and to decouple the unperturbed frequency measurement from the laser's intensity. The frequency lock point generated from synthesized error signals using either $\ensuremath{\pi}/4$ or $3\ensuremath{\pi}/4$ laser phase steps during the intermediate pulse is tightly protected against large laser-pulse area variations and errors in potentially applied frequency shift compensations. Quantum clocks based on weakly allowed or completely forbidden optical transitions in atoms, ions, molecules, and nuclei will benefit from these hyperstable laser frequency stabilization schemes to reach relative accuracies below the ${10}^{\ensuremath{-}18}$ level.