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European Frequency and Time Forum

Microwave field amplitude stabilization using Ramsey spectroscopy signal

Michele Gozzelino, Aldo Godone, Salvatore Micalizio, Filippo Levi, Claudio Eligio Calosso

Published Apr 1, 2018• 0 citations
Publisher

Abstract

We present a method to actively stabilize the amplitude of the microwave field which constitutes the probe for many state-of-the-art compact atomic clocks. The method applies to clocks working in pulsed operation, specifically with a Ramsey scheme. The proposed technique relies on information directly extracted from the clock atomic signal, as it computes the gradient in the two variables (amplitude and frequency) characterizing the probe field, instead of differentiating solely the frequency response, as in usual operation. Magnetic field sensing based on spectroscopy has proven to be a valuable tool for metrology and precise measurement field. We demonstrate the advantage of using the spectroscopic signal to stabilize the microwave field amplitude, in order to reach 10-15stability with compact clocks, by mitigating cavity-pulling shift effects.

DOI
10.1109/eftf.2018.8409002

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We present a method to actively stabilize the amplitude of the microwave field which constitutes the probe for many state-of-the-art compact atomic clocks. The method applies to clocks working in pulsed operation, specifically with a Ramsey scheme. The proposed technique relies on information directly extracted from the clock atomic signal, as it computes the gradient in the two variables (amplitude and frequency) characterizing the probe field, instead of differentiating solely the frequency response, as in usual operation. Magnetic field sensing based on spectroscopy has proven to be a valuable tool for metrology and precise measurement field. We demonstrate the advantage of using the spectroscopic signal to stabilize the microwave field amplitude, in order to reach 10-15stability with compact clocks, by mitigating cavity-pulling shift effects.
We describe a method to stabilize the amplitude of the interrogating microwave field in compact atomic clocks working in a Ramsey approach. In this technique, we take advantage of the pulsed regime to use the atoms themselves as microwave amplitude discriminators. Specifically, in addition to the dependence on the microwave detuning, the atomic signal after the Ramsey interrogation acquires a dependence on the microwave pulse area (amplitude times duration) that can be exploited to implement an active stabilization of the microwave field amplitude, in a similar way in which the Ramsey clock signal is used to lock the local oscillator frequency to the atomic reference. This stabilization results in a reduced sensitivity of the clock frequency to microwave amplitude fluctuations that are transferred to the atoms through the cavity-pulling effect. The proposed technique is then effective to improve the clock stability and drift on medium and long term. We demonstrate the method for a vapor-cell clock working with a hot sample of atoms but it can be extended to cold-atom compact clocks.
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 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.
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.
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.
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.