We report precision measurements of the gradient of the Casimir force between an Au-coated sphere and graphene sheet deposited on a silica plate. The measurement data are compared with exact theory using the polarization tensor found in the framework of the Dirac model including effects of the nonzero chemical potential and energy gap of the graphene sample with no fitting parameters. The very good agreement between experiment and theory demonstrates the unusually big thermal effect at separations below $1\mu \mathrm{m}$ which has never been observed for conventional 3D materials. Thus, it is confirmed experimentally that for graphene the effective temperature is determined by the Fermi velocity rather than by the speed of light.

We performed measurements of the gradient of the Casimir force between Au-coated surfaces of a sphere and a plate by means of a significantly upgraded dynamic atomic force microscope (AFM)-based technique. By introducing a combined cleaning procedure of interior surfaces of the vacuum chamber and the test bodies by means of UV light and Ar ions, we reached higher vacuum and eliminated the role of electrostatic patches. Furthermore, the use of a much softer cantilever allowed a sixfold decrease of the systematic error in measuring the force gradient. The experimental data are compared with the theoretical predictions of the Lifshitz theory taking into account corrections due to the inaccuracy of the proximity force approximation and that due to surface roughness. It is shown that the theoretical approach accounting for the relaxation properties of free electrons is excluded by the data up to a larger than previous sphere-plate separation of 820 nm, whereas an alternative approach is found in very good agreement with the data. The importance of these results in connection with the foundations of quantum statistical physics is discussed.

We report precision measurements of the Casimir interaction at larger separation distances between the Au-coated surfaces of a sphere and a plate in ultrahigh vacuum using a much softer cantilever of the dynamic atomic-force-microscope-based setup and two-step cleaning procedure of the vacuum chamber and test body surfaces by means of UV light and Ar-ion bombardment. Compared to the previously performed experiment, two more measurement sets for the gradient of the Casimir force are provided, which confirmed and slightly improved the results. Next, additional measurements have been performed with a factor-of-two larger oscillation amplitude of the cantilever. This allowed the obtainment of meaningful results at much larger separation distances. The comparison of the measurement data with theoretical predictions of the Lifshitz theory using the dissipative Drude model to describe the response of Au to the low-frequency electromagnetic field fluctuations shows that this theoretical approach is experimentally excluded over the distances from 250 to 1100 nm (i.e., a major step forward compared to the previous work where it was excluded up to only 820 nm). The theoretical approach using the dissipationless plasma model at low frequencies is shown to be consistent with the data over the entire measurement range from 250 to 1300 nm. The possibilities to explain these puzzling results are discussed.