{"product_id":"purcella-purcell-effect","title":"Purcella – The Purcell Effect \/ Cavity-Enhanced Emission Physics Sticker","description":"\u003cp\u003ePurcella, a fae of light, holds a glowing atom between two mirrors that change how fast it can shine.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eAn excited atom's spontaneous emission rate is not fixed: it depends on the electromagnetic modes around it. Put the atom in a small, high-quality resonant cavity tuned to its transition and it can emit much faster than in free space. E. M. Purcell pointed this out for nuclear magnetic moments at radio frequencies in a short abstract (“Spontaneous Emission Probabilities at Radio Frequencies”, Phys. Rev. 69, 681, 1946). The enhancement is the Purcell factor.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eF = 3Q(λ\/n)³ \/ (4π²V)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eF: Purcell factor, emission rate in the cavity over the free-space rate\u003c\/li\u003e\n\u003cli\u003eQ: quality factor of the cavity\u003c\/li\u003e\n\u003cli\u003eλ: free-space wavelength of the transition (m)\u003c\/li\u003e\n\u003cli\u003en: refractive index of the cavity medium\u003c\/li\u003e\n\u003cli\u003eV: mode volume of the cavity (m³)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eA high Q and a tiny mode volume mean a big enhancement. The effect is used in single-photon sources, small lasers and quantum-dot devices.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e This is the maximum, for an emitter exactly on resonance, at the field maximum and aligned with the field. Off resonance or detuned, the cavity can suppress emission instead.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003ePurcella holds a glowing atom between two round glass mirrors with light running between them. Printed text: \u003cstrong\u003ePURCELLA\u003c\/strong\u003e with the line \u003cstrong\u003eF = 3Q(λ\/n)³\/(4π²V)\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50963973603431,"sku":"14886908471949238815","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50963973636199,"sku":"13474278726422905401","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50963973668967,"sku":"53114513589582861003","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50963973701735,"sku":"26503525824137237847","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/2105424232538846152_1200.jpg?v=1793657507","url":"https:\/\/pixelatedphysics.com\/sv\/products\/purcella-purcell-effect","provider":"Pixelated Physics","version":"1.0","type":"link"}