Fig. 1: Casimir interaction between three optomechanical resonators.

a Three modified cantilevers with resonant frequencies ω₁, ω₂ and ω₃ experience Casimir force between each two nearby surfaces. The vibration amplitudes of three cantilevers are denoted as A₁, A₂ and A₃. Additional parametric modulations are applied on the center cantilever to couple them by the Casimir effect. We can switch on and off the Casimir coupling between cantilever 1 and cantilever 3 by controlling the parametric modulations. In addition, we can amplify the energy transfer through Casimir effect by adding an extra gain to cantilever 2. b Measured Casimir force gradient on cantilever 2 (center) as a function of its position when the other two surfaces are fixed such that d₁ + d₂ = 760 nm. The blue circles are experimental measurements and the red solid line are the theoretical prediction. c The measured Casimir force on cantilever 2 is shown as a function of d₂. d Measured Casimir force gradient experienced by cantilever 2 as a function of d₁ when d₂ is fixed at 310 nm. The red diamonds are the total force gradient \(-\frac{1}{R}\frac{dF}{dx}\) measured from cantilever 2. The blue circles are the force gradient contributed from cantilever 1. The red solid curve is the theoretical prediction of the interaction between cantilever 1 and 2. The gray dashed line is the theoretical prediction of the interaction between cantilever 2 and 3 and hence it is independent of d₁ under additivity approximation. e Measured Casimir force gradient on cantilever 2 as a function of d₂ when d₁ is fixed at 276 nm.