Combined error signal in Ramsey spectroscopy of clock transitions

V I Yudin,J Kitching,A V Taichenachev,T E Mehlstäubler,R Boudot,J W Pollock,T Zanon-Willette,M Yu Basalaev,E A Donley,M Shuker

doi:10.1088/1367-2630/aaf47c

Abstract

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.

Highlights

Atomic clocks based on high-precision spectroscopy of isolated quantum systems are currently the most precise scientific instruments, with fractional frequency instabilities and accuracies at the 10−18 level [1, 2, 3, 4, 5]
The combined error signal (CES) protocol is applicable to optical atomic clocks as well as to microwave atomic clocks based on coherent population trapping (CPT) Ramsey spectroscopy and pulsed optical pumping (POP) clocks
In the case of usual Ramsey spectroscopy and hyper-Ramsey methods [27, 28, 5, 29, 31, 34, 35], these technical causes can lead to an additional shift of the stabilized clock frequency ω, while the CES method is insensitive to these non-idealities

Summary

Introduction

Atomic clocks based on high-precision spectroscopy of isolated quantum systems are currently the most precise scientific instruments, with fractional frequency instabilities and accuracies at the 10−18 level [1, 2, 3, 4, 5]. For ABRS, in addition to the stabilization of the clock frequency ω, a second loop controls a variable second (concomitant) parameter ξ, which is an adjustable property of the first and/or second Ramsey pulses While both of these two-loop methods [33, 37, 38] are robust and can perfectly suppress probe-induced shifts of the measurement of the clock frequency, their implementation can be complex due to the two-loop architecture. We have found a universal protocol to construct a combined error signal (CES), which allows for perfect suppression of probe-induced shifts with the use of only one feedback loop. The CES protocol is applicable to optical atomic clocks as well as to microwave atomic clocks based on CPT Ramsey spectroscopy and POP clocks

Theoretical model

CES protocol

CES for different Ramsey sequences

Generalized CES and the procedure for frequency stabilization

CES technique for CPT Ramsey spectroscopy

Conclusion