{"product_id":"molassa-the-doppler-cooling-limit-physics-t-shirt","title":"Molassa – The Doppler Cooling Limit Physics T-Shirt","description":"\u003cp\u003eMolassa stands where six laser beams cross, and atoms freeze in her palm. Then they got colder than the rules allowed.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn optical molasses, red-detuned laser beams from every direction slow a moving atom like friction, while random recoils from spontaneous emission heat it. For a simple two-level atom the balance sets a minimum temperature, the Doppler limit, best reached at detuning δ = −Γ\/2. For sodium's D2 line that limit is about 235 μK.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ek_B T_D = ħ Γ \/ 2\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ek_B: Boltzmann constant (J\/K)\u003c\/li\u003e\n\u003cli\u003eT_D: Doppler limit temperature (K)\u003c\/li\u003e\n\u003cli\u003eħ: reduced Planck constant (J·s)\u003c\/li\u003e\n\u003cli\u003eΓ: natural linewidth of the transition (1\/s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eIn 1988 Lett, Phillips and co-workers measured sodium atoms at 43 ± 20 μK, far below the limit; Chu, Cohen-Tannoudji and Phillips shared the 1997 Nobel Prize in Physics.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The Doppler limit is right for two-level atoms. Real atoms have many sublevels, and polarisation-gradient (Sisyphus) cooling beats it.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Molassa, the pixel-art character, with the title. Back: the Doppler limit, the sodium numbers, the 1988 measurement, the Sisyphus explanation and the 1997 Nobel. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936521359463,"sku":"31142184380546792824","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936521392231,"sku":"32776562005637991359","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936521424999,"sku":"28728697985711203624","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936521457767,"sku":"26885848251366182881","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936521490535,"sku":"22420692634641033522","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936521523303,"sku":"20652098104860379075","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936521556071,"sku":"22651187599635485450","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936521588839,"sku":"55016429665537967681","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936521621607,"sku":"19959159884944404020","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936521654375,"sku":"92062878998517850574","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936521687143,"sku":"16047085425154341093","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936521719911,"sku":"53221667803130555534","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936521752679,"sku":"77996216353740220709","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936521785447,"sku":"12996728659376152034","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936521818215,"sku":"10896656128958784195","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936521850983,"sku":"52757066808292385281","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/doppler-cooling-limit_front_02_white.png?v=1793595417","url":"https:\/\/pixelatedphysics.com\/ko\/products\/molassa-the-doppler-cooling-limit-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}