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European Frequency and Time Forum

Two-loop frequency stabilization using concomitant parameter

Valeriy I. Yudin, A. V. Taǐchenachev, M. Yu. Basalaev, T. Zanon-Willette, J. W. Pollock, M. Shuker, Elizabeth A. Donley, John E. Kitching

Published Apr 1, 2018• 0 citations
Publisher

Abstract

When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. This includes precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized auto-balanced Ramsey spectroscopy (GABRS) is proposed. Here, the usual local oscillator frequency control loop is supplemented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different Ramsey period. This second loop feeds back to a secondary clock variable and ultimately compensates for the perturbation of the clock frequency caused by the measurements in the first loop. We show that such a two-loop scheme can lead to perfect compensation of measurement-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors that are typical of other hyper-Ramsey schemes.

DOI
10.1109/eftf.2018.8409066

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When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. This includes precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized auto-balanced Ramsey spectroscopy (GABRS) is proposed. Here, the usual local oscillator frequency control loop is supplemented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different Ramsey period. This second loop feeds back to a secondary clock variable and ultimately compensates for the perturbation of the clock frequency caused by the measurements in the first loop. We show that such a two-loop scheme can lead to perfect compensation of measurement-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors that are typical of other hyper-Ramsey schemes.
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 have developed a universal method to form the reference signal for the stabilization of arbitrary atomic clocks based on Ramsey spectroscopy. Our approach uses an interrogation scheme of the atomic system with two different Ramsey periods and a specially constructed combined error signal (CES) computed by subtracting two error signals with the appropriate calibration factor. CES spectroscopy allows for perfect elimination of probe-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors and other imperfections of the interrogation procedure. The method is simpler than recently developed auto-balanced Ramsey spectroscopy techniques (Sanner et al 2018 Phys. Rev. Lett. 120 053602; Yudin et al 2018 Phys. Rev. Appl. 9 054034), because it uses a single error signal that feeds back on the clock frequency. The use of CES is a general technique that can be applied to many applications of precision spectroscopy.
Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, mass spectrometry, and precision spectroscopy.
We present a rigorous justification for the applicability of the recently developed methods of generalized autobalanced Ramsey spectroscopy (GABRS) [V. I. Yudin et al., Phys. Rev. Appl. 9, 054034 (2018)] and combined error signal in Ramsey spectroscopy (CESRS) [ , New J. Phys. 20, 123016 (2018)] for resonances of coherent population trapping (CPT). A protocol of modified combined error signal for CPT resonances is also proposed, in which two successive interrogations of atoms under different times of free evolution are integrated in one cycle. The implementation of the GABRS and CESRS methods in a compact atomic clock based on the CPT effect allows us to significantly suppress the light shift and its fluctuation, which will lead to an improvement in the long-term stability and accuracy of these devices. Moreover, these spectroscopic schemes are insensitive to various distortions of the pulse shape, relaxation processes, errors in the generation of phase jumps, etc., which provides their high reliability and immunity to perturbations.
Abstract Light shifts induced during atom–light interactions significantly affect the medium- and long-term frequency stability of atomic clocks. Here, we employ composite laser pulse sequences to mitigate interrogation-induced light shifts in a cold-atom coherent-population-trapping clock. We obtain the anti-symmetry error signal via modulating the local oscillator phase in the free-evolution time of Ramsey interferometry. Utilizing this signal, we employ two feedback loops to simultaneously eliminate light shifts and stabilize the clock frequency using the auto-balanced Ramsey (ABR) spectroscopy scheme. Our experimental results demonstrate that this approach can reduce the clock frequency’s sensitivity to variations in light shifts by implementing four Ramsey sub-sequences. Furthermore, we show that the ABR spectroscopy scheme enhances the long-term frequency stability of the atomic clock when the averaging time τ > 5000 s.
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.