Influence of the electron spin resonance saturation on the power sensitivity of cryogenic sapphire resonators

Abstract

Here, we study the paramagnetic ions behavior in presence of a strong microwave electromagnetic field sustained inside a cryogenic sapphire whispering gallery mode resonator. The high frequency measurement resolution that can be now achieved by comparing two CSOs permit for the first time to observe clearly the non-linearity of the resonator power sensitivity. These observations that in turn allow us to optimize the CSO operation, are well explained by the Electron Spin Resonance (ESR) saturation of the paramagnetic impurities contained in the sapphire crystal.

Tests of Sapphire Crystals Manufactured With Different Growth Processes for Ultra-Stable Microwave Oscillators

“…The resulting Allan standard deviation is given in the figure 7. The apparent flicker floor obtained with the Kyropoulos resonator is ∼ 5 × 10 −16 whereas it was 3 × 10 −16 with an optimized HEMEX CSO [16]. Such a difference can be attributed to the lower Q-factor of the Kyropoulos resonator.…”

“…The LSF provides a way of quantifying the overall effect of the noise associated with the oscillator's electronics. Considering the best experimental results obtained to date [3,12,16], we assume LSF ≈ 2.5×10 −7 , which is a conservative value. Thus, to get a stability of 1×10 −15 , the minimum resonator unloaded Q-factor is:…”

“…Equation 4 was used to compute ν(T ), the susceptibility χ (ν) being the summation of the contribution of all ion species: Cr 3+ , Fe 3+ and Mo 3+ . As explained in [16], the individual dc-susceptibilities χ 0 have been evaluated with the Van Vleck equation [32]. Indeed the Curie law has been derived for a free system of spin S, which consists in 2S + 1 levels equally spaced.…”

“…At a signal power higher than typically 100 µW, the resonator sensitivity is of the order of 1×10 −8/ W. At a lower power this sensitivity is affected by the paramagnetic impurities for modes laying nearby or in the ESR bandwidth. It has been recently demonstrated that for a mode near 10 GHz there exists a value P 0 of the injected power specific to each resonator at which the effect of ESR saturation on the mode frequency compensates the impact of the radiation pressure [16]. Thus the mode sensitivity nulls to the first order, greatly relaxing the specification on the signal power stabilisation.…”

“…Black bullets: one of the CSOs is equiped with a Kyropoulos crystal from PST, the other one incorporates an HEMEX grad sapphire crystal. Bold line: the best stability we obtained with a HEMEX resonator[16]. Dashed line: instrument noise floor.…”