Efficiency of Mesoscopic Detectors

Abstract

W e consi dera m esoscopi c m easuri ng devi ce w hose conductance i ssensi ti ve to the state ofa tw o-l evel system . T he detector i sdescri bed w i th the hel p ofi ts scatteri ng m atri x. Itsel em entscan be used to cal cul ate the rel axati on and decoherence ti m e ofthe system ,and determ i ne the characteri sti c ti m e for a rel i abl e m easurem ent. W e deri ve condi ti ons needed for an e ci ent rati o of decoherence and m easurem ent ti m e. To i l l ustrate the theory w e di scuss the di stri buti on functi on ofthe e ci ency of an ensem bl e ofopen chaoti c cavi ti es.PA C S num bers: 03. 65. Ta,03. 67. Lx M esoscopi c physi cs i s evol vi ng toward a stage w here the understandi ng ofthe m easurem ent process becom es ofi ncreasi ng i m portance.O fi nterestare detectorsw hi ch al l ow a fastdeterm i nati on ofthe state ofthe system but at the sam e ti m e l eave the coherence of the m easured system as una ected as possi bl e. T hese are con i cti ng requi rem ents:Fori nstancea tunnelcontacti san e ci ent butsl ow detector.T herefore,the questi on ari sesw hether i ti spossi bl eto devel op detectorsw hi ch areboth fastand e ci ent. To answer thi s questi on we i nvesti gate m esoscopi c m ul ti channelconductors and anal yze thei r speed and e ci ency. T he e ci ency ofa detector i s determ i ned by the rati o ofthe m easurem ent ti m e and the decoherence ti m e ofthe m easured system .T hee ectofa detectoron a phasecoherentm esoscopi c system hasbeen el egantl y dem onstrated i n recentexperi m ents [ 1{3] . T heoreti caldi scussi ons addressed di erent aspectsofweak m easurem enti n m esoscopi csystem s:the rel ati on to scatteri ng theory [ 1,4,5]and screeni ng [ 5] ,the m easurem ent ti m e and i nteracti ons [ 6]and the rel ati on between detector noi se and decoherence rate [ 7,8] . T he ti m e evol uti on ofsystem and detector has been studi ed usi ng a m aster equati on approach [ 9,10] . R e ned cal cul ati ons consi der the condi ti onalevol uti on ofthe system dependi ng on the outcom e of the m easurem ent [ 11,12] . Tunnelcontactsand si ngl eel ectron transi storshavebeen i denti ed ascandi datesfore ci entm easurem entdevi ces [ 13] . B oth the m easurem ent ti m e and the decoherence rate depend on the scatteri ng m atri x ofthe conductor(detector). C onsequentl y both of these quanti ti es depend on the sam pl e speci c geom etry and i m puri ty di stri buti on of the detector. It i s therefore necessary to i nvesti gate the di stri buti on of the quanti ti es of i nterest (m easurem entti m e,decoherence rate and e ci ency)ofensem bl es ofm acroscopi cal l y i denti caldetectors. H ere we focus on bal l i sti cdetectorsforw hi ch ensem bl em em bersdi eronl y i n thei r geom etry.T he m odelwe consi der i s show n i n Fi g. 1. It consi sts ofa doubl e dot(D D )thatpl aysthe rol eofthe system .It i s an e ecti ve two-l evelsystem : T he topm ostel ectron i n theD D can ei theroccupy theupperorthel owerdot.T he detector i s a m esoscopi c two-term i nalconductor (M C ): I...

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