Free-falling nanoparticles help to detect tiny forces

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A miniature mechanical sensor works by repeatedly dropping and catching the particles.

Free-fall experiments are the stuff of scientific legend. Galileo is said to have dropped cannonballs from the Leaning Tower of Pisa to demonstrate to his students that gravitational acceleration is independent of mass. And Isaac Newton often recounted the tale of the falling apple that inspired him to think about gravitational forces over longer distances. (There’s no evidence, however, that the apple landed on his head.)

Now Erik Hebestreit, his PhD adviser Lukas Novotny, and their colleagues at ETH Zürich have miniaturized the apple drop to create a technique for measuring gravitational and other static forces on nanoparticles. The principle of the scheme, illustrated in the figure, is simple to state. A nanoparticle is held in the center of a harmonic optical trap. The trap is turned off for a fraction of a millisecond, during which time the particle moves under the static force F. When the trap is reactivated, the particle is no longer near the center, and it oscillates with a large amplitude, which the researchers measure with high precision.

Free-falling nanoparticles help to detect tiny forces

The final oscillation energy E depends on both F and the fall duration τ. It also depends, however, on the particle’s small but unpredictable initial velocity at the moment the trap is turned off. To minimize that source of uncertainty, the researchers repeat the drop-and-catch process thousands of times for several values of τ. By fitting the average E as a function of τ, they can extract F for forces as small as 10 attonewtons—half the gravitational force on a silica particle with a radius of 58 nm. By endowing the particle with a single extra electron, they show that their technique also works to measure electrostatic forces.

The ETH Zürich researchers’ nanoparticles aren’t the smallest objects to have been observed in free fall. Steven Chu and colleagues studied falling atoms two decades ago. But nanoparticles occupy a size scale of particular interest in many contexts. For example, the Casimir force (see the article by Steve Lamoreaux, Physics Today, February 2007, page 40) between submicron objects at submicron separations is still largely unexplored. (E. Hebestreit et al., Phys. Rev. Lett. 121, 063602, 2018.)

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