Constraining New Forces in the Casimir Regime Using the Isoelectronic Technique

We report the first isoelectronic differential force measurements between an Au-coated probe and two Au-coated films, made out of Au and Ge. These measurements, performed at submicron separations using soft microelectromechanical torsional oscillators, eliminate the need for a detailed understanding of the probe-film Casimir interaction. The observed differential signal is directly converted into limits on the parameters $\alpha$ and $\lambda$ which characterize Yukawa-like deviations from Newtonian gravity. We find $\alpha \lesssim {10}^{12}$ for $\lambda \sim 200\mathrm{nm}$, an improvement of $\sim 10$ over previous limits.

Figure 1

(a) Scanning electron microscope image of the MTO with the composite sample deposited on it. The coordinate system used in the Letter is indicated. Inset: schematic of the sample deposited on the MTO. The thickness of the different layers are (in order of deposition): $d_{\mathrm{Ti}}=1\mathrm{nm}$, $d_{\mathrm{Ge}}=200\mathrm{nm}$, $d_{\mathrm{Pt}}=1\mathrm{nm}$, and $d_{\mathrm{Au}}^p=150\mathrm{nm}$. The thickness of the layers deposited on the sphere (not shown) are: $d_{\mathrm{Cr}}=1\mathrm{nm}$ and $d_{\mathrm{Au}}^s=200\mathrm{nm}$. (b) Experimental setup. The red dotted line indicates where AFM line cuts were taken. Inset: AFM profile of the sample interface.

Figure 2

(a) Dependence of ${\mathcal{F}}_d(t_i)$ on $\tau$ at $z_{mo}=300\mathrm{nm}$. Data at $\tau =0.1\mathrm{s}$ are scaled by $A=20$. The dotted line is the reference signal at ${\omega }_r$, adjusted to fit on the same scale. (b)–(d) ${\mathcal{F}}_p$ and ${\mathcal{F}}_q$ at $\tau =2\mathrm{s}$ ($N=300$), 200 s ($N=30$), and 2000 s ($N=6$), respectively. Each point is a repetition of the experiment. The circles in (b) and (c) are centered at $({\overline{\mathcal{F}}}_p,{\overline{\mathcal{F}}}_q)$ and have a radius given by the calculated thermal noise over the relevant $\tau$. The measured noise exceeds the thermal noise by $\sim 20\%$. (d) Results for all samples. Different symbols and colors have been used for each case.

Figure 3

Dependence of the peak-to-peak ${\overline{\mathcal{F}}}_T$ on $z_{mo}$. Colors and symbols are the same as in Fig. 2d. The shaded regions, representing values of hypothetical forces excluded by our experiments, are defined by the points with minimum absolute value of $\overline{\mathcal{F}}$.

Figure 4

Values in the $\{\lambda ,\alpha \}$ space excluded by experiments. The red curve represents limits obtained in this work. Curves 1 to 5 were obtained by Mohideen’s group [7], our group [1], Lamoreaux [6], Kapitulnik’s group [8], and Price’s group [5], respectively. Also shown are theoretical predictions [21].