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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

The sensitivity function: a new tool for the evaluation of frequency shifts in atomic spectroscopy

P. Lemonde, Giorgio Santarelli, Philippe Laurent, Franck Pereira dos Santos, Andr  Clairon, Ch Salomon

Published Nov 27, 2002• 16 citations
Publisher

Abstract

We have proposed to use the sensitivity function to account for frequency shifts in atomic spectroscopy. This method applies to all interrogation schemes and is of particular interest when the atomic evolution cannot be calculated analytically. We have proposed a simple method to experimentally measure the sensitivity function and tested it in the case of a multi-Rabi interrogation (TE/sub 013/ cavity). The results, in good agreement with numerical simulations, give a clear explanation of the frequency shift observed on our frequency standard.

DOI
10.1109/freq.1998.717890

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We have proposed to use the sensitivity function to account for frequency shifts in atomic spectroscopy. This method applies to all interrogation schemes and is of particular interest when the atomic evolution cannot be calculated analytically. We have proposed a simple method to experimentally measure the sensitivity function and tested it in the case of a multi-Rabi interrogation (TE/sub 013/ cavity). The results, in good agreement with numerical simulations, give a clear explanation of the frequency shift observed on our frequency standard.
In certain triple-loop atomic beam experiments reported in the literature, a shift in the resonance frequency was observed on reversing the direction of the CCC field. This shift is explained by assuming that the rf field changes in direction along the transition region, which causes the moving atom to experience a frequency different from that of the basic oscillatory frequency. All the observed properties of the shift can be accounted for by the explanation given.
We analyze both the s- and p -wave collision induced frequency shifts and propose an over- π pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a function of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over- π pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of 10 −18 in both Sr and Yb optical lattice clocks by canceling the collisional frequency shift.
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.
In this paper we describe key aspects of the conceptual design of the microwave interrogation structure in the laser-cooled cesium frequency standard that is part of the primary atomic reference clock in space (PARCS) experiment. The PARCS standard uses balls of cold atoms launched in a pulsed beam configuration. The microwave interrogation will take place in two independent high-Q (/spl sim/20,000) cavities operated in the TE/sub 011/ mode. The cavities will be operated off resonance by several linewidths, with a resonant coupling structure delivering the microwave to the two cavities. One persistent problem related to the end-to-end phase shift has been the extreme temperature sensitivity of the phase of inside the cavities to that just outside the cavities. The end-to-end phase shift must ultimately be known to around 3 microradians, and stable long enough to allow measurement of the shift as well as to allow normal clock operation. Operating the cavities off resonance reduces this sensitivity more strongly than reducing the cavity Q.