Short-Range Force Detection Using Optically Cooled Levitated Microspheres

We propose an experiment using optically trapped and cooled dielectric micro-spheres for the detection of short-range forces. The center-of-mass motion of a microsphere trapped in vacuum can experience extremely low dissipation and quality factors of ${10}^{12}$, leading to yoctonewton force sensitivity. Trapping the sphere in an optical field enables positioning at less than $1\mu \mathrm{m}$ from a surface, a regime where exotic new forces may exist. We expect that the proposed system could advance the search for non-Newtonian gravity forces via an enhanced sensitivity of ${10}^5–{10}^7$ over current experiments at the $1\mu \mathrm{m}$ length scale. Moreover, our system may be useful for characterizing other short-range physics such as Casimir forces.

Figure 1

(a) Proposed experimental geometry. A subwavelength dielectric microsphere of radius $a$ is trapped with light in an optical cavity. The sphere is positioned at an antinode occurring at distance $z$ from a gold-coated SiN membrane. Light of a second wavelength ${\lambda }_{\mathrm{cool}}=2{\lambda }_{\mathrm{trap}}/3$ is used to simultaneously cool and measure the center-of-mass motion of the sphere. The sphere displacement $\delta z$ results in a phase shift $\delta \varphi$ in the cooling light reflected from the cavity. For the short-range gravity measurement, a source mass of thickness $t$ with varying density sections is positioned on a movable element behind the mirror surface that oscillates harmonically with an amplitude $\delta y$. The source mass is coated with a thin layer of gold to provide an equipotential. (b) Displacement spectral density (blue curve) due to thermal noise and shot-noise limited displacement sensitivity (flat line, red) for parameters discussed in the text.

Figure 2

Fractional frequency shift due to Casimir interaction of microspheres of radius $a=150\mathrm{nm}$ at distance $z$ from the gold surface. The PFA is expected to be valid at short distances, while the Casimir-Polder form is expected at large distances, and the transition region is shown as a shaded area. Inset: Optical and Casimir contributions to the cavity trapping potential.

Figure 3

Experimental constraints [23, 24, 25, 26, 27, 28, 29] and theoretical predictions [30] for short-range forces due to an interaction potential of Yukawa form $V=-\frac{G_N{m}_1{m}_2}{r}[1+\alpha e^{-r/\lambda }]$. Lines ($a$) and ($b$) denote the projected improved search reach for microspheres of radius $a=150\mathrm{nm}$ and $a=1500\mathrm{nm}$, respectively.