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Physical Review A

Generalized Ramsey methods in the spectroscopy of coherent-population-trapping resonances

M. Yu. Basalaev, Valeriy I. Yudin, Д. В. Коваленко, T. Zanon-Willette, А. В. Тайченачев

Published Jul 14, 2020• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.102.013511

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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 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 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.
Light-induced frequency shifts can be a key limiting contribution to the mid- and long-term frequency instabilities in atomic clocks. In this letter, we demonstrate the experimental implementation of the combined error signal interrogation protocol to a cold-atom clock based on coherent population trapping (CPT) and Ramsey spectroscopy. The method uses a single error signal that results from the normalized combination of two error signals extracted from two Ramsey sequences of different dark periods. The single combined error signal is used to stabilize the atomic clock frequency. Compared to the standard Ramsey-CPT interrogation, this method reduces the clock frequency sensitivity to light-shift variations by more than one order of magnitude. This method can be applied in various kinds of Ramsey-based atomic clocks, sensors, and instruments.
Everyone is trying to make frequency measurements as accurate as possible. But what if the measurement process itself becomes a major source of error? This issue is particularly relevant in the context of state-of-the-art atomic clocks where errors at the 18th decimal place are not negligible anymore. In order to spectroscopically interrogate an atomic clock transition without compromising the clock's accuracy, we devise a perturbation-immune version of Ramsey's method of separated oscillatory fields. By actively balancing the spectroscopic responses from phase-congruent Ramsey probe cycles of unequal durations, we eliminate a wide variety of interrogation-induced line shifts often encountered in high precision spectroscopy, among them, in particular, light shifts, phase chirps, and transient Zeeman shifts. We experimentally demonstrate autobalanced Ramsey spectroscopy on the light shift prone171Yb+electric octupole optical clock transition and show that interrogation defects are not turned into clock errors. This opens up frequency accuracy perspectives below the 10-18level for the Yb+system and for other types of optical clocks. Further applications of this simple and universal approach include next generation coherent population trapping clocks and perturbation-immune readout of quantum sensors. Future long-term clock comparisons searching for physics beyond the standard model will also benefit from this technique.
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 brief review of the rapidly growing field of autobalanced Ramsey spectroscopy followed by a detailed discussion and review of two novel techniques that were developed and tested in our laboratory: displaced frequency-jump Ramsey spectroscopy and combined error signal spectroscopy. These two techniques are related to, yet different from autobalanced Ramsey spectroscopy. The use of these techniques in a cold-atom clock based on coherent population trapping has reduced instabilities from variations in light-shift parameters by at least one order of magnitude. In each of these techniques the Ramsey sequence adapts to cancel light shifts and drifts.