Optical Lattice Clock — Magic-Wavelength Parameter Map (2D)

This is the 2D parameter-space counterpart to the 3D optical-lattice-clock simulator. Rather than a spatial view of atoms sitting in lattice wells, it evaluates the exact same differential AC Stark shift formula, Δν(λ, U₀) = [α_e(λ) − α_g(λ)]·I/(2h), at every point of a 2D grid spanning trap-laser wavelength against trap depth, and paints the result as a live heatmap: a genuine computed scalar field, not a flattened camera angle on the 3D scene. The zero-shift band collapses to a hair-thin vertical line at the magic wavelength (813.4 nm for strontium's ¹S₀→³P₀ clock transition) when the trap is shallow and hyperpolarizability is switched off; switching it on tilts that line by a few ten-thousandths of a nanometer per recoil energy of trap depth — small enough that the live "true zero-crossing" readout has to carry six decimal places to show it, exactly matching how real lattice-clock groups report picometer-level magic-wavelength shifts. Click or drag directly on the map to set the wavelength and depth, or use the sliders; a companion strip below re-draws the schematic ground/excited polarizability curves whose crossing produces the field above.