content_image/362903.jpg
grey line. The best constraints in the interaction range λ ≤ 80 nm were obtained from Ξ$_{P}$ = 3 . 30 mPa at a = 200 nm [21, 36]. For the interaction range from 80 to 140 nm and from 140 to 250 nm the constraints shown by the grey line were obtained from Ξ$_{P}$ = 0 . 84 and 0.57 mPa, as occurs at a = 300 and 350 nm, respectively. For comparison purposes in the same figure the long-dashed line reproduces constraints following from the experiment of Ref. [28] and reobtained in Refs. [36, 37] at a 95% confidence level. The short-dashed line shows constraints following from the so-called Casimir-less experiment [53] where the contribution of the Casimir force is subtracted due to the advantages of the dynamic measurement scheme. As can be seen in Fig. 3, the strengthening of constraints on the parameters of Yukawa- type interaction due to the use of corrugated plate is up to one order of magnitude. The largest strengthening (in 10 times) is achieved at λ = 18 . 6 nm. If we compare with the static experiment proposed in Sec. III, the use of a plate covered with sinusoidal corrugations turns out to be not so promising (one order of magnitude strengthening of constraints instead of a factor of 4 . 5 × 10 4 strengthening). This can be explained by the fact that the measurement technique using a micromachined oscillator is workable only in the region where this oscillator is linear, i.e., starting from at least two times larger separations than using an AFM. Here, the shortest separation between a corrugated plate and a smooth sphere is equal to 114.6 nm (compare with 22 nm and 14.6 nm in Secs. II and III, respectively). 

## V. GRADIENT OF THE YUKAWA PRESSURE BETWEEN TWO PARALLEL PLATES IN THE DYNAMIC REGIME 

The only recent experiment on measuring the Casimir force which used the configuration of two parallel plates was performed in the dynamic regime [40]. The immediately measured quantity was the oscillator frequency shift due to the Casimir pressure between the plates. This frequency shift is proportional to the gradient of the Casimir pressure 

<img src='content_image/362903.jpg'>

where the coefficient is equal to β ≈ 0 . 0479 m $^{2}$/ kg. Until the present time the constraints on the Yukawa-type interaction following from this experiment have not been published. Be- cause of this, here we derive these constraints and discuss the possibilities of their strength- ening. 

