Trimera

Trimera is three atoms linked in a ring. No two of them can hold together, but all three can. Around her, the rings repeat: every 22.7× bigger, another trio.

The Physics

In 1970 Vitaly Efimov showed that three identical bosons with a resonant pair attraction can form three-body bound states, even where no pair can bind. In the unitarity limit, where the scattering length |a| is much larger than the range of the force, there is an infinite ladder of these trimers. Each one is e^π/s₀ ≈ 22.7 times larger than the one before, and its binding energy is about 22.7² ≈ 515 times smaller.

e^π/s₀ ≈ 22.7 E_n+1 / E_n → e^−2π/s₀ ≈ 1/515

• s₀ ≈ 1.00624: the solution of s₀ cosh(πs₀/2) = (8/√3) sinh(πs₀/6), for three identical bosons
• a: two-body scattering length; |a| → ∞ is the unitarity limit
• E_n: binding energy of the n-th trimer

The first evidence came in 2006 from Innsbruck: a giant three-body loss resonance in an ultracold gas of caesium atoms (Kraemer et al., Nature 440, 315). In 2014 the same lab found the second resonance, with a measured scaling factor of 21.0(1.3), close to the ideal 22.7 (Huang et al., Phys. Rev. Lett. 112, 190401).

Honest caveat: 22.7 is exact only for three identical bosons with zero-range forces at unitarity; other masses and spins give other values. In real atoms |a| and the range of the force are finite, so the ladder stops after a few steps. The 2006 result was a loss signal, not an image of a trimer.

Rings drawn not to scale: each real Efimov trio is about 22.7× larger than the last, too big a step to fit on a shirt.

On the shirt

Front: Trimera, the pixel-art character, with "EFIMOV STATES / THREE CAN BIND WHERE TWO CANNOT" and the slogan "EVERY 22.7× BIGGER, ANOTHER TRIO". Back: the ladder, the 22.7 and 1/515 ratios, the equation for s₀, the unitarity condition, the 2006 and 2014 caesium results and the three papers. Printed on a unisex tee.