Sympathetic cooling of a trapped proton mediated by an LC circuit

Efficient cooling of trapped charged particles is essential to many fundamental physics experiments^1,2, to high-precision metrology^3,4 and to quantum technology^5,6. Until now, sympathetic cooling has required close-range Coulomb interactions^7,8, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps^5,9,10, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be⁺ ions in spatially separated Penning traps. The traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We also demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environmental temperature. Notably, as this technique uses only image-current interactions, it can be easily applied to an experiment with antiprotons¹, facilitating improved precision in matter-antimatter comparisons¹¹ and dark matter searches^12,13.