The 3D optical tweezer traps an atom in a cylindrically-symmetric Gaussian beam. This simulator exploits that symmetry exactly: it restricts the atom to the meridional plane y=0 through the beam axis, so the transverse coordinate x plays the role of the radial distance ρ. Since the potential and force have no y-component when y=0, this is not an approximation or a flattened view — it is an exact 2-DOF reduction of the same physics:
U(x,z) = -U₀ · A(z) · exp(-2x²A(z)/w₀²), A(z) = 1/(1+(z/z_R)²)
z_R = π w₀² / λ, ω_r = √(4U₀/m w₀²), ω_z = √(2U₀/m z_R²)
The left field renders U(x,z) as a live heatmap on a 2D grid — dark blue is the deep well at the focus, fading to black at the beam periphery — with the atom's real trajectory integrated by m dv/dt = -∇U(x,z) plotted on top of it. The inset renders the same motion as a radial phase-space portrait (x vs vx): a bound atom traces a closed loop whose area is set by its energy; releasing the trap turns the loop into an outward-spiralling ballistic streak.
- Trap depth / waist sliders — set U₀ and w₀, which fix ω_r, ω_z and z_R exactly as in the 3D experiment.
- Temperature slider — sets the thermal velocity drawn independently on x and z from a Maxwell–Boltzmann distribution (⟨v²⟩ per axis = k_BT/m).
- Release & Recapture — switches the trap off for trel, then re-evaluates the same criterion as the 3D lab: the atom is recaptured only if its mechanical energy E = ½mv² + U(x,z) is still negative when the trap turns back on.