A theory of enhancing thermally induced effects on atomic force microscope cantilevers with respect to the input power is proposed. An optical microcavity is used to increase the absorbed power and radiation pressure on thin films. We show that the response to the input power is enhanced up to an order of magnitude for cantilevers of ∼200 µm in length and ∼0.5 µm in thickness. A decrease in the absorbed power in the presence of cantilever deflection increases system endurability with respect to the input power. The study gives methods for amplifying and tuning vibration amplitudes in amplitude modulation modes with high sensitivity and low controlling input power.

Bimaterial cantilevers have recently been used in, for example, the calorimetric analysis with picowatt resolution in microscopic space based on state-of-the-art atomic force microscopes. However, thermally induced effects usually change physical properties of the cantilevers, such as the resonance frequency, which reduce the accuracy of the measurements. Here, we propose an approach to circumvent this problem that uses an optical microcavity formed between a metallic layer coated on the back of the cantilever and one coated at the end of an optical fiber irradiating the cantilever. In addition to increasing the sensitivity, the optical rigidity of this system diminishes the thermally induced frequency shift. For a coating thickness of several tens of nanometers, the input power is 5–10 μW. These values can be evaluated from parameters derived by directly irradiating the cantilever in the absence of the microcavity. The system has the potential of using the cantilever both as a thermometer without frequency shifting and as a sensor with nanometer-controlled accuracy.

We theoretically study the dynamics of an atomic force microscope cantilever under various irradiation configurations of a laser. By conveying a stream of photons and its momenta, the laser beam whose geometrical intensity profile has a Gaussian form will exert a nonuniform radiation pressure on the cantilever surface and modify its vibration. The dependences of cantilever modeshapes on the laser spot position and waist reveal a possibility of diminishing or exciting a specific eigenmode. For cantilevers of ∼200 µm length, the vibration amplitude of higher-order eigenmodes can be increased 4–5 times. This implies the change in cantilever effective mass once the interaction with the ambient is taken into account. The study gives a deeper understanding of soft cantilever dynamics in liquids and can be applied in the modern measurement configuration where high frequencies are required.

The thermodynamic functions of ideal Bose gases are important in fundamental physics and have been widely studied via both analytical and numerical methods. Studying these functions is important for undergraduates as it is the first step for exploring ultracold physics and quantum phenomena. However, the accuracy of the calculations is usually limited owing to the discontinuity of the functions at critical points. In this study, we present an analytical procedure for deriving the chemical potential, the total energy, and the heat capacity as functions of the absolute temperature. The approximated analytical results are compared with values obtained using the numerical method to evaluate their accuracy and to determine the applicable range of the procedure. Moreover, a correction for the chemical potential calculated around the critical temperature was proposed to reduce the deviation between the approximated and numerical approaches.