Home▸Physics & Mechanics▸The Efimov Effect: An Infinite Ladder of Three-Body Quantum States

🌀 The Efimov Effect: An Infinite Ladder of Three-Body Quantum States

Explore the Efimov effect: how three identical bosons can form an infinite geometric ladder of bound states even when no two of them can bind together at all.

Physics & Mechanics3DModerate60 FPS

The simulator shows how tuning the two-body scattering length toward the unitary limit, where it approaches infinity, causes an infinite geometric ladder of three-body Efimov bound states to appear, with each state's size and binding energy related to its neighbors by the universal scaling factor of about 22.7.

🔬 What It Demonstrates

🎮 How to Use

Adjust the scattering length slider to move the interaction strength toward and through the unitary limit, and watch the Efimov energy ladder populate on the accompanying spectrum plot. Toggle between different mass ratios or particle combinations to see how the geometric scaling factor between successive states changes, and switch on the three-body recombination loss-rate view to see how each Efimov state produces a resonant peak, the same type of signal used in the 2006 cesium discovery experiment.

💡 Did You Know?

Did you know that in the strict theoretical limit of a true zero-range interaction, the Efimov ladder extends infinitely both to larger sizes and to states arbitrarily close to zero binding energy, yet in real ultracold gas experiments only a handful of the largest, most weakly bound rungs, typically two or three, are ever within experimental reach before the finite range of real atomic interactions cuts the pattern off.

⚙ Under the hood

Explore the Efimov effect: how three identical bosons can form an infinite geometric ladder of bound states even when no two of them can bind together at all.

quantum physicsfew-body physicsultracold atomsefimov effectfeshbach resonanceuniversalityatomic physicsscattering theory

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install