Isotope effect on the Casimir force

Isotopic dependence of the Casimir force is key to probing new physics and pushing novel technologies at the micro and nanoscale, but is largely unexplored. In 2002, an isotope effect of 10^‑4 was estimated for metals—orders of magnitude beyond the experimental resolution. Here, by employing the Lifshitz theory, we reveal a significant isotope effect of over 10^‑1 for polar dielectrics. This effect arises from the isotope-mass-induced line shift of the zone-center optical phonons and is insensitive to the linewidth. We perform numerical analyses on both the imaginary and real-frequency axes, and derive analytical formulas for predicting the isotope effect. The three-orders-of-magnitude difference between polar dielectrics and metals arises from the distinct isotopic dependence of the phonon and plasma frequencies. Our work opens up a new avenue for engineering forces at small scales and may also facilitate the quest for the fifth force of nature.