Seus resultados confirmam as previsaµes das teorias centrais da física qua¢ntica. As descobertas também podem apontar o caminho para novos tipos de sensores que podem medir forças diminutas. O estudo foi publicado na revista Science .
![](data:image/jpeg;base64,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)
Leon Espert Miranda, Dr. Julian Schmitt e Erik Busley. Crédito: Volker Lannert/Universidade de Bonn
Pesquisadores da Universidade de Bonn criaram um gás departículas leves que podem ser extremamente comprimidas. Seus resultados confirmam as previsaµes das teorias centrais da física qua¢ntica. As descobertas também podem apontar o caminho para novos tipos de sensores que podem medir forças diminutas. O estudo foi publicado na revista Science .
Se vocêconectar a saada de uma bomba de ar com o dedo, ainda podera¡ empurrar o pistão para baixo. O motivo: os gases são bastante fa¡ceis de comprimir osao contra¡rio dos laquidos, por exemplo. Se a bomba contivesse águaem vez de ar, seria praticamente impossível mover o pistão, mesmo com o maior esfora§o.
Os gases geralmente consistem em a¡tomos ou moléculas que giram mais ou menos rapidamente pelo Espaço. a‰ bastante semelhante com a luz: seus menores blocos de construção são fa³tons , que em alguns aspectos se comportam como partículas E esses fa³tons também podem ser tratados como um gás, no entanto, um que se comporta de maneira um tanto incomum: vocêpode comprimi-lo sob certas condições quase sem esfora§o. Pelo menos éo que a teoria prevaª.
Fa³tons na caixa do espelho
Pesquisadores do Instituto de Fasica Aplicada (IAP) da Universidade de Bonn agora demonstraram esse efeito em experimentos pela primeira vez. "Para fazer isso, armazenamospartículas de luz em uma pequena caixa feita de espelhos", explica o Dr. Julian Schmitt do IAP, que éum dos principais pesquisadores do grupo do Prof. Dr. Martin Weitz. "Quanto mais fa³tons colocamos la¡, mais denso o gás de fa³tons se torna."
O microrressonador a³ptico realiza a 'caixa de fa³tons'. Crédito: Volker
Lannert/Universidade de Bonn
A regra geralmente éa seguinte: quanto mais denso um gás, mais difacil écomprimir. Este também éo caso da bomba de ar obstruada - no inacio, o pistão pode ser empurrado para baixo com muita facilidade, mas em algum momento dificilmente pode ser movido mais, mesmo quando se aplica muita força. Os experimentos de Bonn foram inicialmente semelhantes: quanto mais fa³tons eles colocavam na caixa do espelho, mais difacil se tornava comprimir o gás.
No entanto, o comportamento mudou abruptamente em um certo ponto: assim que o gás fa³ton excedeu uma densidade especafica, ele pode ser comprimido de repente com quase nenhuma resistência. "Esse efeito resulta das regras da meca¢nica qua¢ntica", explica Schmitt, que também émembro associado do Cluster de Excelaªncia "Matanãria e Luz para Computação Qua¢ntica" e lider do projeto no Transregio Collaborative Research Center 185. O motivo: A luz aspartículas exibem uma "indefinição" - em termos simples, sua localização éum pouco confusa. Amedida que se aproximam muito em altas densidades, os fa³tons comea§am a se sobrepor. Os fasicos também falam de uma "degeneração qua¢ntica" do gás. E torna-se muito mais fa¡cil comprimir um gás tão degenerado qua¢ntico.
Â
Fa³tons auto-organizados
Se a sobreposição for forte o suficiente, aspartículas de luz se fundem para formar uma espanãcie de superfa³ton , um condensado de Bose-Einstein. Em termos muito simplificados, esse processo pode ser comparado ao congelamento da a¡gua: no estado laquido, as moléculas de águaestãodesordenadas; então, no ponto de congelamento , os primeiros cristais de gelo se formam, que eventualmente se fundem em uma camada de gelo estendida e altamente ordenada. "Ilhas de ordem" também são formadas pouco antes da formação do condensado de Bose-Einstein, e se tornam cada vez maiores com a adição de fa³tons.
O condensado éformado apenas quando essas ilhas crescem tanto que a ordem se estende por toda a caixa de espelhos que contanãm os fa³tons. Isso pode ser comparado a um lago no qual blocos de gelo independentes finalmente se juntaram para formar umasuperfÍcie uniforme. Naturalmente, isso requer um número muito maior departículas de luz em uma caixa estendida em comparação com uma pequena. "Conseguimos demonstrar essa relação em nossos experimentos", ressalta Schmitt.
Para criar um gás com número departículas varia¡vel e temperatura bem definida, os pesquisadores usam um “banho de calorâ€: “Inserimos moléculas na caixa do espelho que podem absorver os fa³tonsâ€, explica Schmitt. "Subsequentemente, eles emitem novos fa³tons que, em média, possuem a temperatura das moléculas - no nosso caso, pouco menos de 300 Kelvin, que éaproximadamente a temperatura ambiente ."
Os pesquisadores também tiveram que superar outro obsta¡culo: gases de fa³tons geralmente não são uniformemente densos osha¡ muito maispartículas em alguns lugares do que em outros. Isso se deve ao formato da armadilha em que eles geralmente estãocontidos. "Na³s adotamos uma abordagem diferente em nossos experimentos", diz Erik Busley, primeiro autor da publicação. "Na³s capturamos os fa³tons em uma caixa de espelho de fundo plano que criamos usando um manãtodo de microestruturação. Isso nos permitiu criar um gás qua¢ntico homogaªneo de fa³tons pela primeira vez."
No futuro, a compressibilidade qua¢ntica aprimorada do gás permitira¡ a pesquisa de novos sensores que podem medir forças minaºsculas. Além das perspectivas tecnologiicas, os resultados também são de grande interesse para a pesquisa fundamental.