Yukawa-type interaction obtained in Ref. [53] from the Casimir-less experiment (the short- dashed line) and the constraints obtained in Ref. [24] from the torsion pendulum experiment of Ref. [23] (the long-dashed line). The latter constraints will be discussed in more detail in the next section. As can be seen in Fig. 4, the constraints following from the measurement of the gradient of the Casimir pressure between two parallel plates are not as strong as the constraints obtained from previously performed experiments. 

The experimental configuration of two parallel plates has some potentialities to obtain stronger constraints on the parameters of the Yukawa-type interaction. One evident resource is connected with the increase of precision [i.e.,with the decrease of Δ$_{i}$( ν $^{2}$− ν 2 $_{0}$)]. Furthermore, the replacement of Cr, as the material of metal coating, with an Au layer of the same thickness would lead to stronger constraints shown in Fig. 4 by the grey line marked 1. Moreover, the increase of thicknesses of the metal coating up to Δ$_{Au}$ = 500 nm would lead to even stronger constraints shown in Fig. 4 by the grey line marked 2. This line presents constraints of the same strength as those obtained in Ref. [53] from the Casimir- less experiment. Thus, the configuration of two parallel plates can be further used for obtaining constraints on the Yukawa-type interaction. As to the possibility of replacing a plane plate with a corrugated one, this does not lead to significantly stronger constraints in the experiment with parallel plates because of much larger separation distances between the test bodies. 

## VI. CONSTRAINTS FROM THE MEASUREMENT OF THERMAL CASIMIR-POLDER FORCE 

Measurements of the Casimir-Polder force between an atom and a plate (cavity wall) and the measure of their agreement with theory provides additional opportunities for constraining the Yukawa-type corrections to Newtonian gravity. Up to now no strongest constraints have been obtained in this way, but to a large extent the potentialities of this field remain unexplored. Here, we obtain constraints on the parameters of the Yukawa-type interaction using the measurement data of dynamic experiment demonstrating the thermal Casimir- Polder force between $^{87}$Rb atoms and a SiO$_{2}$ plate [39]. Rubidium atoms belonged to a Bose-Einstein condensate which was produced in a magnetic trap with frequencies equal to ω$_{0}$$_{z}$ = 1438 . 85 rad/s and ω$_{0}$$_{l}$ = 40 . 21 rad/s in the perpendicular and longitudinal directions to 

