WANI ROTOR MAI NAUYIN MILLIGRAM ƊAYA, DA AKA HANA SHI MOTSI TA HANYAR KALLONSA

A cikin shekaru ashirin da suka wuce, masana kimiyyar lissafi sun koyi sarrafa abubuwa na zahiri masu motsi (mechanical objects) kusa da iyakokinsu na kwantam (quantum limits) — daga ƙananan na’urori masu girgiza (resonators) masu girman nanomita da nauyin femtogram, har zuwa madubai masu nauyin kilogram da dama na na’urorin gano raƙuman nauyi. Amma kusan dukkansu masu kai-da-komo ne (oscillators): wani abu, kamar sipirin, yana jan su baya zuwa tsakiya. Mafi sauƙin tsarin quantum mechanics, ƙwaya mai ’yanci (free particle), wadda babu abin da ke jan ta baya, ta ƙi irin wannan sarrafawa. A ƙananan mitoci (frequencies) inda motsi mai ’yanci ke faruwa, gogayya (friction) da hayaniya daga kewaye suna nutsar da komai.

Duk da haka taro masu ’yanci (free masses) su ne ainihin abin da manyan tambayoyi da dama ke buƙata: gwada ko ƙarfin jan hankali (gravity) na kwantam ne, binciken sauye-sauyen da aka gabatar wa quantum mechanics, neman sababbin ƙarfi masu gajeren zango (short-range forces).

Madubi a kan zaren gilashi

Umang Mishra, Teodor Strömberg, Onur Hosten da abokan aiki a Institute of Science and Technology Austria sun gina abin gwajin: wata sandar madubi mai nauyin milligram 1 ta fused silica (gilashin silica da aka narkar), tsawonta milimita 2, rataye da wani zaren fused silica mai tsawon santimita 15 da kaurin micrometre 1, a cikin wuri marar iska (vacuum) ƙasa da millibar 10⁻¹⁰. A zahiri, sandar pendulum na murɗewa (torsion pendulum) ce da ke kai-da-komo sau ɗaya a kowace daƙiƙa 15. Amma a ma’aunin lokaci da ke da muhimmanci a nan, millisecond goma-goma, da ƙyar take jin wannan jan: tana aiki kamar abu mai ’yanci.

Keɓewarta (isolation) ta kai matuƙa. Ƙungiyar ta auna murɗe-murɗe na bazuwa (random torques) da ke hargitsa ta kuma ba ta sami wata hayaniya fiye da abin da adadin rage motsi (damping rate) na nanohertz 7 kawai zai samar ba. Idan aka yi amfani da ita a matsayin ma’aunin hanzari (accelerometer), ƙarshen sandar zai fi mafi kyawun gwaje-gwajen baya a wannan nauyi hankali (sensitivity) kusan sau ɗari.

Don kallon ta, wani “double optical lever” (maɗaukin haske biyu) yana sa hasken laser biyu su bugi madubin su dawo ta hanyoyi masu saɓani, ta yadda girgizar laser ɗin kansa za ta soke kanta kuma juyawar sandar kaɗai ta rage. Haske na uku zai iya tura sandar da matsin haske. Dukan tsarin yana tsaye a kan wani dandali na keɓewa daga girgizar ƙasa (seismic isolation platform), kuma wani ƙaramin interferometer mai nasa madubin da ke rataye yana bin duk wani sauran motsin wannan dandali.

Aunawa a madadin tarko

Babban ra’ayin shi ne cewa aunawa ba tare da tsayawa ba (continuous measurement) za ta iya maye gurbin tarkon. Idan aka bar shi shi kaɗai, matsayi da saurin abu mai ’yanci suna ƙara bazuwa cikin rashin tabbas. Idan ana auna shi ba tsayawa, hanyar tafiyarsa (trajectory) tana bayyana yayin da yake tafiya, kuma iliminmu game da yanayinsa yana kwanciya zuwa wani dusashewa (blur) tsayayye, mai iyaka. A nan wannan dusashewar tana tsayawa cikin kusan millisecond 26.

Ana iya mayar da wannan sauran rashin tabbas zuwa zafi (temperature), ta hanyar ma’anar littattafan karatu da ke haɗa zafi da sauye-sauyen entropy. Wannan “entropic temperature” (zafin entropy) yana faɗin yadda aka san motsin rotor ɗin da kaifi, kuma yana ba da damar kwatanta abubuwa masu ’yanci da masu kai-da-komo.

Ƙungiyar ta kama sandar da haske, ta sake ta, kuma ta rubuta kusurwarta a cikin tsawon lokaci 100 na daƙiƙa 1.25. An kwatanta hanyoyi biyu na sake gina yanayinta: ƙiyasi na “causal” (bisa abin da ya gabata) da ke amfani da ma’aunan da suka gabata kawai, da na “smoothed” (wanda aka santsanta) da ke amfani kuma da ma’aunan da aka yi bayan haka. Bambancin da ke tsakaninsu ya ba da sabuwar hanya ta duba yadda aka san yanayin da gaske.

Nanokelvin 140

• Daga bayanan da suka gabata kaɗai, yanayin rotor ɗin yana daidai da microkelvin 1.2.
• Da santsantawa (smoothing), yana sauka zuwa nanokelvin 140 — kashi 140 cikin biliyan na digiri sama da sifili cikakke (absolute zero).

Wannan yana da sanyi fiye da gwaje-gwajen baya da aka yi a kan tebur da abubuwa na zahiri masu motsi da kusan darajoji biyu na girma (two orders of magnitude). Marubutan sun lura cewa yana kawo irin waɗannan tsare-tsare cikin yankin matsanancin sanyi (ultracold regime), wanda har yanzu aka fi danganta shi da gizagizan atoms da aka sanyaya ta hanyar ƙafewa (evaporation). Sanyaya ta hanyar mayar da martani (feedback cooling) ta gargajiya ba za ta iya kaiwa gare shi ba.

Akwai iyaka ta ƙasa. Ga wannan matakin keɓewa, samfurin yana hasashen cewa zafin ba zai iya sauka ƙasa da kusan nanokelvin 15 ba: bisa ƙa’idar rashin tabbas ta Heisenberg (uncertainty principle), auna matsayi da ƙara daidaito yana ƙara dusashe saurin juyawa.

Amfanin taro mai ’yanci mai natsuwa

Amfani biyu suna zuwa nan take. Wasu ka’idoji suna gyara quantum mechanics ta yadda dusashewar kwantam za ta rushe da kanta (collapse spontaneously), abin da zai ƙara ɗan girgiza mara ƙarfi, na bazuwa ga kowane abu. Natsuwar rotor ɗin da aka auna ta kawar da sabon kewayon waɗannan samfura a ƙananan mitoci, mai cike gurbin iyakokin da aikin sararin samaniya na LISA Pathfinder ya sanya.

Amfani na biyu shi ne ƙarfin jan hankali (gravity). Ko ƙarfin jan hankali zai iya haɗa taro biyu cikin entanglement babbar tambaya ce da har yanzu ba a amsa ba. Bisa ma’aunin inganci (figure of merit) na ƙungiyar, irin waɗannan rotor biyu za su riga su doke kowane tsarin da aka nuna a baya da kusan darajoji biyu na girma a kan rabo tsakanin samar da entanglement da rasa shi, duk da cewa suna nesa da manufar. Ƙara wani ƙaramin optical cavity (ramin haske) don karanta juyawar, marubutan sun rubuta, zai kawo tsabtar (purity) da ake buƙata cikin isa.