{"product_id":"trimera-efimov-states-physics-t-shirt","title":"Trimera – Efimov States Physics T-Shirt","description":"\u003cp\u003eTrimera 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.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn 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\u003csup\u003eπ\/s₀\u003c\/sup\u003e ≈ 22.7 times larger than the one before, and its binding energy is about 22.7² ≈ 515 times smaller.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ee\u003csup\u003eπ\/s₀\u003c\/sup\u003e ≈ 22.7     E\u003csub\u003en+1\u003c\/sub\u003e \/ E\u003csub\u003en\u003c\/sub\u003e → e\u003csup\u003e−2π\/s₀\u003c\/sup\u003e ≈ 1\/515\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003es₀ ≈ 1.00624: the solution of s₀ cosh(πs₀\/2) = (8\/√3) sinh(πs₀\/6), for three identical bosons\u003c\/li\u003e\n\u003cli\u003ea: two-body scattering length; |a| → ∞ is the unitarity limit\u003c\/li\u003e\n\u003cli\u003eE\u003csub\u003en\u003c\/sub\u003e: binding energy of the n-th trimer\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe 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).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e 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.\u003c\/p\u003e\u003cp\u003eRings 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.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: 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.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50963509739623,"sku":"29625925767914236920","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50963509772391,"sku":"76087652820441934122","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50963509805159,"sku":"29057855628622290993","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50963509837927,"sku":"64525474505752716029","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50963509870695,"sku":"24777189472912058091","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50963509903463,"sku":"16497419594951164130","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50963509936231,"sku":"33865890961517755224","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50963509968999,"sku":"24889774391205741302","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50963510001767,"sku":"30240688888266626703","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50963510034535,"sku":"33977737390117439120","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50963510067303,"sku":"55456724872768407024","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50963510100071,"sku":"32830306250970546234","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50963510132839,"sku":"13150527290162749176","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50963510165607,"sku":"20695485789900422701","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50963510198375,"sku":"27876214442587554139","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50963510231143,"sku":"14459508008178771624","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/3116549644530107613_2048.jpg?v=1793648535","url":"https:\/\/pixelatedphysics.com\/es\/products\/trimera-efimov-states-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}