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arXiv:0910.5948 · Physical Review A

Hyper-Ramsey spectroscopy of optical clock transitions

Valeriy I. Yudin, А. В. Тайченачев, Chris W. Oates, Zeb W. Barber, N. Lemke, Andrew D. Ludlow, Uwe Sterr, Christian Lisdat, F. Riehle

Published Jul 22, 2010• 139 citations
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Abstract

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 $10$${}^{\ensuremath{-}17}$. Moreover, our approach opens the door for high-precision optical clocks based on direct frequency comb spectroscopy.

DOI
10.1103/physreva.82.011804

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•Feb 21, 2017•2 citations
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 10$${}^{\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.
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.
Probing an atomic resonance without disturbing it is an ubiquitous issue in physics. This problem is critical in high-accuracy spectroscopy or for the next generation of atomic optical clocks. Ultra-high resolution frequency metrology requires sophisticated interrogation schemes and robust protocols handling pulse length errors and residual frequency detuning offsets. This review reports recent progress and perspective in such schemes, using sequences of composite laser-pulses tailored in pulse duration, frequency and phase, inspired by NMR techniques and quantum information processing. After a short presentation of Rabi technique and NMR-like composite pulses allowing efficient compensation of electromagnetic field perturbations to achieve robust population transfers, composite laser-pulses are investigated within Ramsey's method of separated oscillating fields in order to generate non-linear compensation of probe-induced frequency shifts. Laser-pulses protocols such as hyper-Ramsey, modified hyper-Ramsey, generalized hyper-Ramsey and hybrid schemes as auto-balanced Ramsey spectroscopy are reviewed. These techniques provide excellent protection against both probe induced light-shift perturbations and laser intensity variations. More sophisticated schemes generating synthetic frequency-shifts are presented. They allow to reduce or completely eliminate imperfect correction of probe-induced frequency-shifts even in presence of decoherence due to the laser line-width. Finally, two universal protocols are presented which provide complete elimination of probe-induced frequency shifts in the general case where both decoherence and relaxation dissipation effects are present by using exact analytic expressions for phase-shifts and the clock frequency detuning. These techniques might be applied to atomic, molecular and nuclear frequency metrology, Ramsey-type mass spectrometry as well as precision spectroscopy.
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.
Optical clock interrogation protocols, based on laser-pulse spectroscopy, suffer from probe-induced frequency shifts and their variations induced by laser power. The original hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by the laser probe by deriving the exact canonical form of a multipulse generalized hyper-Ramsey resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulse spectroscopy with phase modulation eliminating probe-induced frequency shifts at all orders in the presence of various dissipative processes. Unlike frequency shift extrapolation based methods, a universal interrogation protocol based on $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/4$ and $\ifmmode\pm\else\textpm\fi{}3\ensuremath{\pi}/4$ phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultrarobust error signal gradient in the presence of substantial uncompensated ac Stark shifts. Such a scheme can be implemented in two flavors: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular, and nuclear frequency metrology, mass spectrometry, and the field of precision spectroscopy. It might be designed using magic-wave-induced transitions, two-photon excitation, and magnetically induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement.
Optical clock interrogation protocols, based on laser-pulse spectroscopy, are suffering from probe-induced frequency shifts and their variations induced by laser power. Original Hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by laser probe by deriving the exact canonical form of a multi-pulse generalized Hyper-Ramsey (GHR) resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulses spectroscopy with phase-modulation eliminating probe-induced frequency shifts at all orders in presence of various dissipative processes. Unlike frequency shifts extrapolation-based methods, a universal interrogation protocol based on ±π/4\pm\pi/4±π/4 and ±3π/4\pm3\pi/4±3π/4 phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultra-robust error signal gradient in presence of substantial uncompensated ac Stark-shifts. Such a scheme can be implemented in two flavours: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular and nuclear frequency metrology, mass spectrometry and to the field of precision spectroscopy. It might be designed using magic-wave induced transitions, two-photon excitation and magnetically-induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement.