Optical Lattice Clock — Magic Wavelength Cancellation

Optical lattice clocks trap thousands of atoms in a standing-wave laser to probe an ultra-narrow clock transition for seconds at a time, but the trapping light itself shifts the very transition it's meant to hold still for. This simulator renders a 1D optical lattice with atoms sitting in each well and shows their ground- and excited-state energy levels as a pair of colored "sticks" whose separation is the AC Stark (light) shift. Detune the trap laser away from the magic wavelength — 813.4 nm for strontium's ¹S₀→³P₀ clock transition — and the ground and excited polarizabilities stop cancelling, so the sticks split apart and the live differential light-shift and fractional-frequency readouts move off zero; land exactly on the magic wavelength and they collapse back together. A Gaussian trap-intensity profile makes atoms at the edge of the cloud shift less than atoms at the center, and an optional hyperpolarizability toggle reveals the small higher-order residual shift that survives even exactly at the magic point in very deep traps.