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Accord et stabilité de fréquence
A very high frequency stability is required to preserve the phase coherence of the stored field over the cavity lifteime. At the same time, the cavity mode frequency must be adjusted easily.
The precise shape and thickness of the cavity mirrors is inferred from measurements at room temperature. The finite precision of the cavity assembly and of the thermal contraction measurements results in an uncertainty of a few MHz of the final cavity frequency.
We perform the cavity frequency tuning with the help of four piezo-electric tubes separating the two mirrors holders (see photograph above). The efficiency of PZT’s drops with temperature, but we still obtain a 
5 MHz tuning range, which is able to compensate for the cavity frequency imprecision in most cases. These piezos are fed with a high stability voltage source. The tunnig precision and stabilty are both below the spectral linewidth of the cavity mode (1.22 Hz at 0.8 K).
Planned experiments on Schrödinger cat states and non-classical fields Wigner function require an excellent phase stability of the stored field. A drift of a few Hertz of the cavity mode frequency induces a few tens of degrees phase shift over the cavity lifetime.
Since a translation of the mirrors by 500 fm corresponds to a 1 Hz shift, the microphonic noises and slow mechanical drifts are thus a major concern for the cavity stability. We have devoted considerable efforts to their control. The whole cryostat is on a bench isolated from the laboratory ground by air vibration isolators. All cables and pipes feeding the cryostat are clamped to large masses ’floating’ on rubber foam blocks. All a.c. power supplies have been removed from the bench.
The final stability is inferred from the cavity resonance spectrum. We check that the mode linewidth is consistent with the cavity lifetime. We also measure the amplitude of the sidebands due to fast vibrations of the cavity structure. The main sidebands are at 100 Hz (magnetostriction a.c. noise... in Europe) and 1.5 kHz (first oscillation mode of the structure). These sidebands are at least 30 dB below the carrier. We infer that the phase of the stored field should not drift by more than a few degrees over the cavity lifetime.
We are now coping with slow cavity frequency drifts due to a change in the pressure in the helium reservoir. An active stabilization of this presssure shoudl allow us to reach a regime in which cavity stability is good enough for all the experiments we have in mind.
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