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# Improved Tracking of an Atomic-Clock Resonance Transition

- Created: Sunday, 01 August 2010

### The resonance frequency is repeatedly estimated from sequences of three measurements.

An improved method of making an electronic oscillator track the frequency of an atomic-clock resonance transition is based on fitting a theoretical nonlinear curve to measurements at three oscillator frequencies within the operational frequency band of the transition (in other words, at three points within the resonance peak). In the measurement process, the frequency of a microwave oscillator is repeatedly set at various offsets from the nominal resonance frequency, the oscillator signal is applied in a square pulse of the oscillator signal having a suitable duration (typically, of the order of a second), and, for each pulse at each frequency offset, fluorescence photons of the transition in question are counted. As described below, the counts are used to determine a new nominal resonance frequency. Thereafter, offsets are determined with respect to the new resonance frequency. The process as described thus far is repeated so as to repeatedly adjust the oscillator to track the most recent estimate of the nominal resonance frequency.

The theoretical nonlinear curve is that of the Rabi equation for the shape of the resonance peak

P(y)= | sin^{2}( Π / 2
√
1+ y2 1+ y2 C(i) = B + AP(y_{1} – ε) where
These Three Plots represent fits of the nonlinear curve to three sets of simulated measurements, each set comprising photon counts at relative frequency offsets ( Repeatedly, for the most recent such set of three measurements (see figure), this set of three equations is inverted to extract
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