
rubby chakr

bhautiki mein, rubby chakr (yaa rubby flop) ack dolak chaalan kshetra kii upasthiti mein dou-stariya quantum pranali kaa chakreeya vyavhaar haye. quantum computing, sanghanit padaarth, paramanu aur aanvik bhautiki, aur paramanu aur kann bhautiki key kshetron seey sambandhit bhautik prakriyaon kii ack badee vividhata kaa dou-stariya quantum yaantrik pranaliyon key sandarbh mein aasaani seey adhyayan kiya jaa sakata haye, aur ack optical driving kshetra mein jode jaane parr rubby flopping pradarshit kiya jaa sakata haye. prabhaav quantum prakashiki, chumbakiya anunaad aur quantum computing mein mahatvapurna haye, aur iska naam isidor isaq rubby key naam parr rakhaa gayaa haye.
dou-stariya pranali vaha haye jisamen dou sambhaavit oorjaa star hotey hain. yeye donon star cumm oorjaa key saath ack jamini avastha aur uchch oorjaa key saath ack uttejit avastha hain. yadi oorjaa kaa star apakshayi naheen haye (i.ee. samaan oorjaa naheen honey parr), pranali oorjaa kii ack matra koo avashoshit curr sakati haye aur jamini avastha seey "uttejit" avastha mein sankraman curr sakati haye. jaba ack paramanu (yaa kuchh anya dou-stariya pranali) photon kii ack susangat kiran dwara prakaashit hotaa haye, tou yeh chakreeya roop seey photon koo avashoshit karega aur uttejit utsarjan dwara unhein phir seey utsarjit karega. aise ack chakr koo rubby chakr kahaa jaataa haye, aur isaki avadhi kaa vyutkram photon beam kii rubby aavritti haye. prabhaav koo jaine-cumming model aur block vector aupchaariktaa kaa upayog karke model kiya jaa sakata haye.
ganitiya vivaran.
rubby samasya key liye prishth parr prabhaav kaa ack vistrit ganitiya vivaran paaya jaa sakata haye. udaaharan key liye, ack dou-avastha paramanu (ack paramanu jisamen ack electron yaa tou uttejit yaa jamini sthiti mein hoe sakata haye) key liye ack vidyut chumbakiya kshetra mein aavritti key saath uttejana oorjaa key liye tune kiya jaataa haye, uttejit avastha mein paramanu koo khojane kii sambhavana bloach samikaranon seey paaee jaati haye
jahan sootra _ 2 rubby aavritti haye.
adhik aam taur parr, ack aisee pranali parr vichaar kiya jaa sakata haye jahan vicharadhin dou star oorjaa eigenstate naheen hain. isaliye, yadi pranali koo inmein seey kissy ack star mein aarambh kiya jaataa haye, tou samay vikas pratyek star kii jansankhya koo kuchh visheshta aavritti key saath dolan karega, jisaki koniya aavritti koo rubby aavritti key roop mein bhee jaanaa jaataa haye. dou-avastha quantum pranali kii sthiti koo dou-ayami jatil hilbert sthaan key vactor key roop mein darshaaya jaa sakata haye, jiska arth haye kii pratyek avastha vector sootra _ 3 koo jatil nirdeshank dwara darshaaya jaataa haih
jahan sootra _ 5 aur sootra _ 6 nirdeshank hain.
yadi vactor samanya hain, tou sootra 5 aur sootra 6 sootra 9 seey sambandhit hain. aadhar vactor koo sootra 10 aur sootra 11 key roop mein darshaaya jaayega.
iss pranali seey judee sabhi avalokan yogya bhautik maatraaen 2 × 2 hermician matricks hain, jiska arth haye kii pranali kaa hamiltonian bhee ack samaan matricks haye.
prakriya.
nimnalikhit charanon key madhyam seey ack dolan prayog kaa nirmaan kiya jaa sakata haih
yadi sootra _ 12, h kaa ack eigenstate haye, tou sootra _ 16 hoga aur koee dolan naheen hoga. yadi dou avasthaaen sootra 17 aur sootra 12 apakshayi hain, tou sootra 12 sahit pratyek avastha aich kii ack igen state haye. isake parinamswarup koee dolan naheen hoga.
doosari or, yadi aich mein koee apakshayi eigenstate naheen haye, aur praarambhik sthiti ack eigenstate naheen haye, tou dolan honge. dou-raajya pranali key hamiltonian kaa sabse samanya roop diyaa gayaa haye.
yahaan, sootra _ 21 aur sootra _ 22 vaastavik sankhyaaen hain. iss matricks koo vighatit kiya jaa sakata haye,
matricks sootra _ 24 2 sootra _ 25 2 pehchaan matricks haye aur matricks sootra _ 26 pauli matricks hain. yeh apghatan pranali key vishleshan koo saral banaata haye, vishesh roop seey samay-swatantra mamle mein jahaan sootra _ 27 aur sootra _ 22 key maan sthiraank hain. ack chumbakiya kshetra sootra mein ack spin-1/2 kann key mamle parr vichaar karein _ 29. iss pranali key liye antahkriya hamiltonian haye
jahan sootra 32 kann key chumbakiya kshan kaa parimaan haye, sootra 33 gair-chumbakiya anupaat haye aur sootra 34 pauli matricks kaa vector haye. yahaan hamiltonian key eigenstate sootra _ 35 key eigenstate hain, joe sootra _ 17 aur sootra _ 12 haye, sootra _ 38 key sambandhit igenvalue key saath. sambhavana haye kii raajya sootra _ 39 mein ack pranali manmaane avastha sootra _ 40 mein paaee jaa sakati haye, sootra _ 41 dwara dee gaee haye.
system koo samay sootra 43 parr avastha sootra 42 mein taiyar kiya jaae. dhyaan dein kii sootra 42 sootra 45 kaa ack eigenstate haih
yahaan hamiltonian samay swatantra haye. iss prakaar sthir schroedinger sameekaran koo hull karke, samay key baad kii avastha sootra 47 dwara pranali sootra 48 kii kull oorjaa key saath dee jaati haye. isaliye samay t key baad kii sthiti iss prakaar dee jaati haih
abb maan leejiye kii spin koo samay t parr x-disha mein maapa jaataa haye. spin-upp khojane kii sambhavana iss prakaar dee jaati haih sootra 50 jahan sootra 2 sootra 52 dwara dee gaee ack visheshta koniya aavritti haye, jahan yeh sootra 53 maanaa gayaa haye. isaliye iss mamle mein x-disha mein spin-upp khojane kii sambhavana samay sootra 54 mein dolansheel haye jaba pranali kaa spin shuru mein sootra 42 disha mein hotaa haye. isi tarah, yadi humm sootra _ 56-disha mein spin koo maapate hain, tou pranali key sootra _ 57 key roop mein spin koo maapane kii sambhavana sootra _ 58 haye. apakshayi mamle mein jahaan sootra _ 59 haye, visheshta aavritti 0 haye aur koee dolan naheen haye.
dhyaan dein kii yadi koee pranali kissy diye gaye hamiltonian key igen state mein haye, tou pranali usa sthiti mein bunny rahati haye.
yeh samay parr nirbhar hamilton key logon key liye bhee sach haye. udaaharan key liye sootra _ 60 lete hue; yadi pranali kii praarambhik spin sthiti sootra _ 61 haye, tou y-disha mein spin key maap key parinamswarup sootra _ 62 mein samay sootra _ 54 sootra _ 64 haye.
polly matricks key madhyam seey gair-vikshobh prakriya kaa upayog karke vyutpatti.
formula _ 65 key ack hamiltonian parr vichaar karein, iss matricks key igenvalue formula _ 66 dwara diye gaye hain.
abb yeh sambhavana haye kii raajya sootra _ 67 mein ack pranali raajya sootra _ 68 mein paaee jaayegi, jise formula _ 69 dwara diyaa gayaa haye, ise saral banaaya jaa sakata haye 
</ganit>. quantum computing mein iss operation kaa mahatvapurna mahatva haye. sameekaran anivarya roop seey ack lazer key kshetra mein dou star key paramanu key mamle mein samaan hotey hain jaba aam taur parr achchi tarah seey santusht ghoornan tarang sanniktan kiya jaataa haye. phir sootra _ 70 dou paramanu staron key beach oorjaa antar haye, sootra _ 2 lazer tarang kii aavritti haye aur raabi aavritti sootra _ 72 paramanu sootra _ 73 key sankraman vidyut dwidhruv kshan key utpaad key samanupati haye aur lazer tarang key vidyut kshetra sootra _ 74 joe sootra _ 75 haye. saransh mein, raabi dolan mool prakriya haye jiska upayog cubits koo herfer karane key liye kiya jaataa haye. yeye dolan upayukt roop seey samaayojit samay antaral key dauran aavadhik vidyut yaa chumbakiya kshetron key liye cubit koo ujagar karke praapt kiye jaate hain.