A practical model of quartz crystal microbalance (QCM) is presented, which considers both the Gaussian distribution characteristic of mass sensitivity and the influence of electrodes on the mass sensitivity. The equivalent mass sensitivity of 5 MHz and 10 MHz AT-cut QCMs with different sized electrodes were calculated according to this practical model. The equivalent mass sensitivity of this practical model is different from the Sauerbrey’s mass sensitivity, and the error between them increases sharply as the electrode radius decreases. A series of experiments which plate rigid gold film onto QCMs were carried out and the experimental results proved this practical model is more valid and correct rather than the classical Sauerbrey equation. The practical model based on the equivalent mass sensitivity is convenient and accurate in actual measurements.

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In this letter, an atom-based approach for measuring the microwave (MW) cavity response (including cavity frequency and Q-factor) is presented, which utilizes a MW magnetic field detection technique based on atomic Rabi resonances. We first identify the Rabi resonances on seven π transitions in Cs atoms and demonstrate their uses in continuously frequency-tunable field detectors. With the atom-based field detectors, we then indicate the possibility of reconstructing the MW cavity response by measuring the MW frequency-dependent Rabi frequency (i.e., MW field strength) inside the cavity. To demonstrate this approach, we measured the response curves of a 9.2-GHz cavity and a cavity resonating at 8.3 GHz and 9.7 GHz using π transitions and σ transitions, respectively. We compared the results measured by our approach with those measured by Vector Networker Analyzer and obtained good agreement. From such atom-based, SI-traceable measurements, the MW cavity response can be linked directly to the Rabi frequency, which could be referred to an atomic clock.

After the advent of the quartz crystal microbalance (QCM) technology, various QCM-based sensing systems have got certain applications in many science and technology fields and resulted in dramatic progress in these fields. The core advantage of QCM is its high mass sensitivity which leads to high accuracy and low detection limit. For a QCM, the mass sensitivity is determined by the diameter and thickness of the electrode to a certain extent when the frequency of the quartz wafer is already determined. Theoretical approximate calculation reveals that there is an optimum electrode diameter corresponding to the maximum sensitivity. This is different from the traditional opinion that the smaller the electrode, the higher the mass sensitivity. A plating experiment was carried out using 28 QCMs with different electrode diameters, and the experimental results verified the existence of the optimum diameter. This study is helpful to obtain higher mass sensitivity by optimizing electrode parameters.