> c.
Sieu ran: trang thai mdi cua vat chat
Dang Dinh Long', Hiam Thanh Dai
Kiioa Vat ly ky tiiuSt v^ Cong ngti$ nana, TnJdng Dai hoc Cdng ngti$, Dai hoc Quoc gia Ha Ndi Ngay nhan bk\ 26.4.2015, ngay chuydn phan br^n 28.4.2015, ngky nhgn ph3n bi§n 1.6.2015, ngay chl'p nh3n dang 28.6.2015
Sieu ran la mdt khai niem de chi mot traing thai di thudng cua v | t chat durgrc dira ra tir hon nu^ th^ ky triTffc nhtmg khdng co bang chung thiic nghiem cho thay co sir ton tai cua trang thai nay. Mai d^n nam 2004, nhdm cua Kim v^ Chan tai Dai hoc Penn State (Hoa Ky) m6i cong bo tim th^y trang thai nay trong h$ Helium-4 nhimg cho den nay sir ton tai cua trang thai nay van con la (te tai tranh lu^n soi noi vdl nhilu y kien trai chieu. Bai bao nay dira ra cac khai niem ca ban cd lien quan den tr^ng thai sieu ran, cac dSc trung cua nd cung cac dilu kj|n quan trgng de co thg quan sat thirc nghiem giup cho viec nhan thirc ve trang thai di thirong nay dmjrc sang to hon. Ngoai ra, bai bao cung chi ra mot he vat ly kha tbi co t h i quan sat dirgrc pha sieu ran, d6 la mang quang hgc. Cu6i ciing, bai b^o dira ra cac thao luan ve cac trang thdi dj t h u t n g khde cua vat ch^t kem theo cac kiln nghj.
Tit- khoa: helium-4, hf tuffng quan mgnh, mgng quang hgc, pha di thu&ng, pha sieu chay, pha sieu rdn.
Chi so phan logi 1.3
SUPERSOLIDITY: A NEW STATE OF MATTER
Summary
Supersolidity is an exotic phase of matter which has been proposed for a half of century. Unfortunately, there is a lack of evidence of its existence. Until 2004, there was a claim of finding this state in an experiment with a solid He-4 system established by Kim and Chan at Penn State University, USA. However, there is still many controversial discussions around this claim, and tbe existence of supersolid phase is still a mystery in science. In this paper, the authors propose several fundamental concepts associated with the supersolidity as well as its characteristics. Moreover, the authors also show the important conditions to achieve this phase in experiments and shed tbe light to this mysteric phase of matter. Finally, the authors discuss the potential experiments which can be a host for the supersolid phase and the other exotic phases Keywords: exotic phases, helium-4, optical lattice, strongly correlated system, superfluidity, supersolidity.
Classification number 1.3
'Tie gii diinii: Tel: 0967598223; Email: [email protected]
Trang thai sieu ran la gi?
Vi?c tim kiem cac cac pha mai cua vat chdt la mot nhu cau tit y8u ciia cpng ddng nghien cuu v^t ly noi chung va vat Iy chit rkn noi rieng. Nhimg nghien cuu ca ban nay mpt mat co tac dung thuc day phat trien khoa hpc va cong nghe, mat khac no CO tac dung dua nhan tiiuc cua chiing ta vk thg gioi vat chat len mgt tam cao mai.
Truac khi tim hiSu vh trang thai sieu rSn, chiing ta cSn hieu cac trang thai quen thuoc hem. Nhu chiing ta da biet, trang thai thuang gap cua v^t chat la ran, long, khi hoac plasma nhung cung co rat nhieu trang tiiai khac thucmg han ciia vat chdt, nhu tr^ng thai sieu din hay trgng thai sieu long ciia mot d6ng vi Helium (He-4 - mot loai hgt boson) tai nhiet do thip, vi du: duoi 2,17 K. Tinh chdt sieu chay ciia He-4 lan ddu tien dugc hik d6n vko ' nam 1937 nha phat hien ciia nha vat !y ngucri Nga Pyotr Kapitza [I] da ma ra mot hudng nghien ciiu moi trong vat ly chat ran nhdm tim kiem cac phat.
di thuang ciia vat chdt cho dgn tan ngay nay Sir, hdp ddn trong viec nghien cuu cac tinh-chdt siSu' "
chay den tir y nghia ciia no trong viec minh chiing „ cho vai tro ciia tuang tac trong ca hgc luong tiV,^
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Can chu y rang, vai tro ciia cac tucmg tac nay khong the hien ro net a cac he ca hoc co dien, vi du nhu cac he vat ly co kich thuac lan (he vT mo) hoac he khi a nhiet do cao...
Trong nhimg nam gan day, nghien ciiru con chi ra su hinh thanh pha sieu chay khong nhirng dugc tim thdy cf cac h? hat boson ma con co kha nang tun tiidy tren cac he hat fermion nhu he hat He-3 (mot d6ng vi cua Helium nhung la hat fermion) [2]. Ngoai ra, trong vat ly thong ke lugng tu chiing ta con bi6t den mgt hien tugng dgc trung cho cac hat boson nhu sau: khi nhiet do dugc ha xuong duoi nhiet do tdi han (nhu trong truong hgp cua He-4 la 2,17 K), cac hat boson co thS cung t6n tai trong mgt trang thai lugng tii vai miic nang lugng thap nhat ggi la hien tugng ngung tu Bose Einstein.
Dieu nay hoan toan khac vai cac hat fermion bi quy dinh boi nguyen ly loai tru PauH. Duong nhu c6 mgt moi lien he giua hien tugng ngung tu Bose Einstein va tinh sieu chay nhung dang tiec la cho d8n nay vin chua CO ai chi ra su lien h§ do thuc su nhu thS nao. Ngoai ra, chiing ta con biet rang: khi nghien ciiu chuyen pha hoac dac trung pha thi tham so trgt t\r la mgt tham so vat ly quan trgng b^c nhat va khong the thiSu dugc. Ci khia cgnh ly thuyet, pha sieu chay cung nhu ngung tu Bose Einstein dugc dac trung boi su ton tai ciia tham so trat tu ngoai duong cheo tam xa (Off Diagonal Long Range Order - ODLRO) dS phan biet voi tham s6 trat tir theo ducmg cheo (Long Range Order - LRO) dac trung cho cac nguyen tu bi dmh xii trong cac niit mang.
Y nghia cua khai ni?m ducmg cheo va ngoai duong cheo xuat phat tOr cac dgc trung cua tuong tac trong ma trgn ciia Hamiltonian dac trung cho h?. Cu the la: s6 hang mo ta ma tran th6 nang co dac tnmg la ma trgn ducmg cheo, cac so hang ngoai ducmg cheo deu bang khong. Ngugc lai, so hgng mo ta ma tran dgng nang CO dac trung la ma trgn duang cheo bang khong, con cac so hang ngoai ducmg cheo thi khac 0. Nhu chiing ta thay, hai tham so trat tu nay phii dinh nhau va truoc day ngucri ta khong cho rdng hai tham s6 trat ti; nay CO the d6ng thai t6n tai. Noi each khac, khong th^ co mgt pha c6 ddng thoi ca hai tham s6 trgt tu tren. Tuy . nhien. tropg qua trinh phat triln nghien cuu ly tiiuyet va thyc nghiem doi voi cac he boson lai cho ra kit
^jflua dang kinh ngac. Do la co till ddng thdi ton tgi hai Warn ^ t rat-tu neu tren trong cung mgt pha, va thuat
t
ngCr pha sieu ran ra ddi de chi su dong tdn tai cua hai tham sd trat tu nay. Dieu thii vi la trgng thai sieu ran lan dau tien dugc ggi ten bdi Penrose va Onsager tir nam 1956 nhimg khdng phai de mmh chiing cho sir tdn tai cua no ma ia de bac bd nd. Hg lap luan va kit luan rdng, khdng till tdn tgi frat tu ODLRO frong cac chdt rdn kit tinh. Tuy nhidn, Andreev v^ Liftshitz (1969) va Chester (1970) da de xudt buc tranh khac bdng each sir dung md hmh cua cac sai hdng mang nhdm giai thich cho kha nang tdn tgi ciia pha sieu rdn nay [2, 3]. Lap luan cua hg dua trSn quan diem cho rang, cac sai hdng mgng d nhiet dp thap trd nen linh ddng va cd thd la iing cu vien sd mgt cho trgng thai nln vdi muc nang lugng thap nhat cua cac he lugng tii nhu He-4. (3 nhiet do thap, do kha nang linh dgng n6n cac sai hdng nay cd the chuyin ddng khdng cd ma sat va di vao h ^ g tiiai ngung tu. Tuy nhien, sau nhilu nd lire tim kiem thuc nghiem deu that bgi thi den nam 2004, mdt cu0c bung nd trong nghien ciiu pha sieu rdn xay ra ngay sau khi E. Kim va W. Chan cdng bd da thanh cdng trong viec quan sat thuc nghidm thay pha sieu rdn [4]. Dang tiec la cho den nay, hien tugng nay vin cdn gay ra rdt nhilu tranh cai [5]. Mdt trong nhung nguyen nhan gay tranh cai dd la He-4 trong thi nghiem cd chiia nhieu tgp va cac tham sd vat ly khdng dieu khien dugc. Ndi each khac la he He-4 khdng sach va khdng kilm soat dugc.
May man la mgt nhom cac nha khoa hgc da dua ra kha nang phat hien dugc cac pha di thudng nhu pha sieu chay, pha ran trong mgng quang hgc trong qua trinh nghien ciiu cac tmh chat ciia he nay. Cac phat hien nay da md ra mdt ldi thoat cho viec tim kiem pha sieu ran tren mang quang hgc. Thuc te la mgng quang hgc dugc hinh thanh do cac chiim laser cung tan sd chieu ddi dau vao nhau de hinh thanh nen cac sdng dimg vdi cac hd the nam tgi cac vi tri day sdng. Cac nguyen tii d nhiet do thdp cd thi bi giam cdm trong cac hd the nay. Ciing bdi ly do la cac hd the trong mang quang hgc cd cau triic gidng cac mang tinh the nen ngudi ta su dung khai niem mang quang hgc de chi cau tnic mang cua h?
thdng quang hgc nay va quan niem nd nhu mdt mgng nhan tgo. LTU dilm ciia mang quang hgc la do tinh khiet so vdi He-4 va kha nang kilm soat tung tham sd cua he bdng each thay ddi cudng do cac chiim laser. Can chii y rdng, mgng quang hgc khdng gidng nhu mgng tinh till hoan toan vi khoang cdch giiia cac hd the dac
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tnmg cho mit mgng (cd mia budc sdng laser, vi du 300 nm vdi laser dd) gap hang nghin lan khoang each cac nguyen tu trong tinh the. Cgng dong nghien cihi ve cac pha di thudng va dgc biet la nhung nhdm dang tim kiem pha sieu ran ky vgng se quan sat thay pha nay xuat hien trong mgng quang hgc do mgng quang hgc sach va d l kiem soat hon. He cpja la cac ket qua se dang tin cay va gay tranh cai it hon. Vi vay, viec nghien ciiu cac dac trung va kha nang hinh thanh cac pha trong mang quang hgc trd thanh mgt de tai mang tinh thai sir ndng hdi trong nhiing nam gan day. Cau hdi dat ra la cac yeu td nao anh hudng den qua trinh hinh thanh pha lugng tu va sir chuyen pha giiia chiing dugc kiem soat nhu the nao?
Trang thai sieu Tin cua Helium
Mudn hieu ve dgc trung cua cac pha, chiing ta can hieu su hinh thanh ciia cac pha va yeu td vgt ly nao dieu khien co che hinh thanh cac pha dd. Ngoai ra, s]f bien ddi tir pha nay sang pha khac hay cdn ggi la sir chuyen pha la sir thay ddi trang thai tir muc do ddi xiing nay sang miic dg ddi xiing khac. Khdng phai sir chuyen pha nao ciing gidng nhau, vi du chuyen pha tii trgng thai sieu ldng sang trgng thai ran la chuyen pha logi hai, trong khi chuyen pha tu trgng thai sieu ran sang trang thai ran lgi la chuyen pha logi mgt.
Tham so trgt tu- trong pha rdn
Trong tinh the vat ran, cac mit mang - vi tri ciia cac nguyen tii - dugc sap xep mgt each trgt tu tudn hoan trong khdng gian ba chieu. De dgc trung cho vi tri cua mit mang trong tinh the, ngudi ta sir dung gia tri trung binh cua ham mat dO dinh xii p(r) cua cac hat trong khdng gian Q nhu sau:
trung cho mang tinh the:
pik) = j-\dUp(r)e-^ (2)
\d^rp(r) (1)
Ddi vdi cac pha khdng cd su pha vd bat bien tinh tien Hen tuc (pha long hoac khi) thi p(r) = p va do lech mat do djnh xir: Sp = p(r) - p = 0 . Tinh trat tu dugc bieu diln thdng qua dieu kien tuan hoan:
Sp{r) ^ Sp(r + 7") vdi vecta T la vecta mang tinh the.
Tiep den, chung ta xet khai trien chudi Fourier Sp(r) trong khdng gian ba chieu theo tap hgp vecta k dgc
Thuc t l la gia tri bmh phuang ciia P ( ^ ) cho ta he so cdu tnic tinh s(k). He sd nay md ta cac dinh cua cudng do tan xg cua anh sang trong tinh the. Nd cd lien he vdi G la vecto mgng dao theo cdng thuc: G.T - 2;rn (n la sd nguyen). 6 day, he sd cau tnic tinh la mdt tham sd trat tu d l md ta trat tu rdn cua tinh the. Ndi each khac, he so cau tnic tinh la dgc tnmg cho trat tu dudng cheo D L R O , hay su pha vd doi xung dich chuyen. Can chu y rdng, mgt he qua ngugc lai ciia mdi lien he nay khdng phai liic nao ciing diing.
Tham so tr&t tu trong pha sieu chay Mac du, Kapitza phat hien v l tinh sieu chay nam 1937 nhung phai mdt nam sau, md hinh ciia hien tugng sieu chay tren He-4 mdi dugc xay dung bdi Tisza (1938) [6] dua tren ham mat do djnh xii mgt hgt:
p{r) = Ps{r) + PN{,r) (3)
Trong dd, thanh phdn Psi^) = Ps va PA'C'') = PN tuong ling la mat do dinh xii trung binh dac tnmg cho pha sieu chay va pha ldng thdng thudng. Nhin vao cdng thiic (3) dl (iang thay rang, khi he He-4 di vao trang thai sieu chay thi chi cd mgt phan tham gia vao trgng thai nay. Thanh phdn dgc tnmg cho pha sieu chay cd tinh chat chay lien tuc khdng ma sat, trong khi thanh phan ldng thdng thudng thi cd sir tieu hao va mat mat nang lugng. Qua trinh hinh thanh pha sieu chay xay ra d nhiet do chuyen pha T^, khi dd thanh phan Ps ^ 0 va tang ddn khi tiep t^c ha nhiet do xudng dudi nhiet do chuyen pha 7" -> 0 - Ve mat nguyen tdc, Ps = Pvkty shpsi P tiln gan den 1 khi 7 -> 0 . Trong cac he ba chieu, hien tugng sieu chay di kem vdi hien tugng ngung tu Bose Einstein xay ra d nhiet do thap [7].
Chiing ta biet rang, khi he boson bi ngung tu trong mdt trang thai lugng tu thi phan bd ciia moment ddng lugng se cd dinh sac nhgn, ham nghia rang tdt ca cac nguyen tu tap trung tai mdt trgng thai nang.lugn^
|HMHOC \/.. u CdNGNGHfilie' ^an'<
Nguoi ta su dung ham phan b6 momen dong lugng lugng tli de mo ta qua trinh nay:
n(k) = {w\k)v(k))lN
(4) Trong do, ( / ( i ) va y/\k) la toan tu sinh huy Bose cua h^t CO dong lu<pvig fik, ky hieu ngoac < > bi8u diln gia trj ky vpng cua gia trj vjt ly co tinh d6n cac gioi h^n nhiet dgng luc hgc. Trong he co su ngimg tu Bose Einstein thi n(k) se c6 dang:n(k) = nj(k) + ii„c(k) < ' '
Sd hang dau tien bieu dien thanh phan tham gia vao trang thai ngung ty, n^ la dO ngung ti^. Trong khi dd thanh phan thii hai bieu diln nhung ddng gdp vao ddng lugng cua nhiing phan tii cd mdmen khac 0, hay cac thinh phan thdng thudng.
Mgt trong nhiing dgi lugng co ban de bilt dugc thinh phan sieu chay cd xudt hi?n trong he hay khdng, dd la sii dung khai niem ham ma trSn m^t do don hat nhu sau:
n{r,r') = (tp'^(r)fi/(r')^ (6)
Trong dd, V^ir) va i/'(r') la toan tii sinh hiiy Bose ciia hat tai cac vi tri r va r ' va nd la bien ddi Fourier ciia cac toan tit sinh buy Bose cua hat d trgng thai cd dgng lugng hk . Cdn ham ma tran mat do don hgt (6) Ik bien ddi Fourier cua ham phan bd mdmen dgng lugng (5). Thyc te la, trong cac he cd bat bien tinh tiln lien tyc (chdt ldng hogc khi) thi n(r,r') = n(r-r').
Khi bat bien tinh tien lien tyc bi phi vo, him mat dg tnmg binh theo khdng gian dugc tinh theo cdng thiic:
1 c 3
«('•) = — J ^ r'nir\r'+r) (7) D I ding thay phucmg hinh (7) cd tinh chdt
"('') : ^ " o khi r -> CO . Tli day, mgt h? qua quan trgng
dugc nit ra la: d gidi hgn nhiet dgng luc hgc, khi chiing ta hiiy di mdt hat d vi tri r thi anh hudng ciia nd ddi vdi mdt hgt ddng nhat khac d vi tri bat ky trong he la khac 0. Hi?u ling niy chi cd the xuat hi?n trgng co hgc lugng tir ma khdng cd trong co hgc cd dien. Dieu nay cho thay, viec phat hien ra hien tugng sieu chay khang dinh vai trd quan trgng cua cac hieu iing lugng tu d nhiet do tiiap. Ngoii ra, he qua nay cung la dac tnmg ciia trat tu ngoii dudng chdo ODLRO xudt hien trong cac h ^ g thai ngung tu Bose Einstein.
Tham so trgt tu trong pha sieu rdn
Nhu chung tdi da trinh bay v l trat tu rdn va trat tu sieu chay d tren thi hai trgt ty nay cd dgc tnmg hoan toin khac nhau. Trgt ty rdn dugc hd trg v i hinh thinh khi the nang tucmg tac trd nen rat manh so vdi ddng nang ciia hgt. Ngugc lai, trgt ty sieu ldng dugc hinh thanh nhd vio sy linh dgng va kha nang di chuyen khdng ma sat, ndi each khac, trgng thai niy dugc hinh thanh khi ddng nang lan at the nang. Chinh vi vay, hai trat ty niy phu dinh nhau. Tuy nhien, mgt cau hdi dugc dat ra la cd khi nig hai trat ty nay hd trg nhau v i ciing tdn tai khdng? Y tudng v l mgt pha chiia ddng thdi c i hai diit ty trai ngugc nhau da din din khai niem ve pha sieu ran, d dd cd su tdn tgi ddng thdi cua ca trit ty dudng cheo DLRO va tr§t ty ngoai dudng cheo ODLRO. Ndi mgt cich khac, trgt ty rin v i tr|t ty ldng cimg tdn tgi ddng thdi trong mgt pha ddng nhdt, d l phan biet vdi trang thai tach hai pha rieng biet trong cung mgt he. Trong trang thii tach pha cua mgt he se tdn tai hai bd phgn, mgt phin d pha sieu long, mgt phan d pha sieu ran va he khdng phii ddng nhat v l pha.
(5 khia cgnh nao do, nd gidng nhu trang thai da lanh trong nudc. Sy thii vi la d cho, pha sieu rdn cd c i hai die trung ve trat ty va l i mdt pha ddng nhdt chu khdng cd sy tich pha. Hien tai, nhieu ket qui nghien ciiu chi ra sy tdn tgi cua pha sieu rdn nhung ciing nhieu nhdm nghien ciiu bac bd sy tdn tgi cua pha niy. Nguyen nhan chu yen la do cac h^ He-4 cd tgp v i khdng kiem soat dugc tham sd. Nhu chiing tdi da trinh biy d phan dat van dl, cdng ddng khoa hgc mudn tun kiem va kiem nghiem sy ton tai cua cac pha di thudng nhu pha sieu ran trong mang quang hgc de giam bdt su tranh cai ddi vdi kit qua do. Ly do don gian l i vi mang quang hgc
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trung cho mit mgng (cd mia budc sdng laser, vi du 300 nm vdi laser dd) gap hang nghin lan khoing each cic nguyen ni trong tinh the. Cdng ddng nghien cuu ve cac pha di thudng v i die biet li nhung nhdm dang tim kiem pha sieu ran ky vgng se quan sat thay pha niy xuat hien trong mang quang hgc do mang quang hgc sgch va de kiem soat han. He qui l i cac ket qua se dang tin cay v i gay tranh cai it hon. Vi viy, viec nghien cihi cac dac tnmg va kha nang hinh thinh cac pha trong mgng quang hgc trd thanh mdt de tii mang tinh thdi sy ndng hdi trong nhirng nam gin day. Cau hdi dgt ra la cac yen td nio inh hudng den qua trinh hinh thinh pha lugng tii v i sy chuyen pha giira chiing dugc kiem soit nhu the nio?
Trang thai sleu r i n cua Helium
Mudn hieu ve dac trung ciia cac pha, chiing ta can hieu sy hinh thanh ciia cac pha v i yeu td vat ly nao dilu khiln co chl hinh thinh cac pha dd. Ngoai ra, sy bien ddi tir pha nay sang pha khac hay cdn ggi l i sy chuyen pha li sy thay ddi trang thai tir miic do ddi ximg nay sang miic do ddi xung khac. Khdng phai su chuyen pha nio cung gidng nhau, vi du chuyen pha tir trgng thii sieu ldng sang trang thai ran la chuyen pha logi hai, trong khi chuyen pha tu trang thai sieu ran sang trgng thii ran lai l i chuyen pha loai mdt.
Tham so trgt tfr trong pha rdn
Trong tinh thi vat rdn, cic mit mgng - vi tri ciia cac nguyen tir - dugc sip xep mdt each trit ty man hoin trong khdng gian ba chieu. De die tnmg cho vi tri cua mit mang trong tinh the, ngudi ta sii dung gia tri trung binh ciia him mat do dinh xii p(r) cua cic hat trong khdng gian Cl nhu sau:
1 -jrfVpW (1)
tnmg cho mang tmh the:
p{k) = Ud'rSp(r)e-''' (2) Thyc t l l i gia tri binh phuang ciia pi^) cho ta h^
sd cau tnic ffnh S(k). He sd niy md ta cic dinh cua cudng dd tan xg cua anh sang trong tinh the. Nd cd lien he vdi G Ii vecta mang dao theo cdng thftc: GT = Irrn (n l i so nguyen). Ci day, he sd cdu tnic tinh !a mdt tham sd trat tu d l md t i trat ty rdn cua tinh the. Ndi each khac, he sd cdu tinic tinh la die tnmg cho trat t\x dudng cheo DLRO, hay su pha vd doi xiing dich chuyen. Cin chii y rang, mdt he qua ngugc lai ciia mdi li6n he niy khdng phai liic nio cung diing.
Tham so trgt t^ trong pha sieu chdy
Mac du, Kapitza phat hien ve tinh sieu chay nam 1937 nhung phai mgt nam sau, md hinh cua hi?n tugng sieu chiy tren He-4 mdi dugc xay dyng bdi Tisza (1938) [6] dua tren ham mat do dinh xii mgt hat:
P{r) = ps{r) + p^{r) (3)
Ddi vdi cic pha khdng cd sy pha vd bat bien tinh tien lien tyc (pha ldng hoac khi) thi p{r) = p v i dd lech mat dg djnh xii: dp = p(r) - p = 0 . Tinh trgt ty dugc bieu diln thdng qua dieu kien tuan hoan:
Sp{r) = Sp(r + T) vdi vecto T l i vecta mang tinh the.
Tiep den, chiing ta xet khai trien chudi Fourier Spir) trong khdng gian ba chieu theo tap hgp vecto k die
Trong do, thinh phdn Ps ir) = Ps va PN i^) - PN tuong ling l i mat do dinh xii trung binh dac trung cho pha sieu chay va pha long thdng thudng. Nhin vio cdng tinic (3) de ding thay rdng, khi h^ He-4 di vio trgng thai sieu chay thi chi cd mdt phdn tham gia vio trgng thai nay. Thanh phan dgc tnmg cho pha sidu chiy cd tinh chat chiy lien tyc khdng ma sat, trong khi thanh phan ldng thdng thudng thi cd sy tieu hao v i mdt mat nang lugng. Qua trinh hinh thinh pha sieu chay xiy ra d nhiet do chuyen pha T , khi dd thanh phan Ps ^ 0 va tang dan khi tiep tuc hg nhiet do xudng dudi nhiet dg chuyen pha T ^ 0 - Ve mat nguyen tic, Ps ~ Pvaty | shpsi P tiln gdn din 1 khi T -> 0 - Trong cac h? ba j chieu, hien tugng sieu chiy di kem vdi hien tugng ngung ty Bose Einstein xay ra d nhiet dg thdp [7],
Chung ta biet rang, khi he boson bi ngung ty trong mgt trang thai lugng tir thi phan bd ciia moment dgng lugng se cd dinh sac nhgn, him nghTa rang tdt ca cac nguyen tii tip trung tgi mdt trgng thai nang.lugngr
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I S w N ^ ^ t • 3I'0) 10.2015
Ngudi ta su dung him phan bd momen dgng lugng lugng hi de md t i qua trinh nay:
h{k)^{w\k)iy{k))IN (4)
(5) Trong do, y/i.^) va y/\k) l i toin tii sinh buy Bose ciia hat cd dgng lugng hk, ky hi§u ngogc < > bieu dien gii tri ky vgng cua gii tri vat ly cd tinh din cac gidi han nhi$t dgng lyc hgc. Trong he cd su ngung tu Bose Einstein thi h{k) se cd dgng:
h{k) = n„5{k) + n^ci^)
Sd hgng diu tidn bieu dien thinh phin tham gia vio trang thai ngung ty, n^ la do ngung ty. Trong khi dd thanh phan thii hai bieu dien nhirng ddng gdp vio ddng lugng cua nhiing phdn tii cd mdmen khac 0, hay cic thanh phan thdng thudng.
Mgt trong nhihig dai lugng co bin de biet dugc thinh phdn sieu chiy cd xuat hien trong he hay khdng, dd la sii dyng khii niem ham ma trgn mat do don hgt nhu sau:
n{r,r') = (^y/\r)w{r^) (6)
Trong dd, y^ir) v i (5''(r') la toan tir sinh hiiy Bose cua hat tgi cic vi tri r va r ' va nd l i bidn ddi Fourier ciia cac toin tu sinh hiiy Bose ciia hat d trang thai cd dgng lugng hk. Cdn him ma tran mat dg dan hat (6) la bien ddi Fourier cua him phan bd mdmen ddng lugng (5). Thyc te li, trong cac he cd bat bien tinh tien lien tyc (chdt ldng hogc khi) till n{r,r') = n{r-r').
Khi bdt biln tjnh tiln li6n tuc bi phi vd, him mat do
^
hung binh theo khdng gian dugc tinh theo cdng thiic:
n(r) = — | r f V ' « ( r ' , r ' + r ) (7) Dd ding thdy phuang dinh (7) cd tmh chit
'"(') 7> "o khi r -> CO . Tu day, mdt he qua quan trgng
dugc nit ra la; d gidi han nhiet ddng lyc hgc, khi chiing ta huy di mdt hgt d vi d-i r thi anh hudng ciia nd ddi vdi mdt hat ddng nhdt khac d vi tri bat ky d-ong he l i khac 0. Hieu ling nay chi cd the xuat hien trgng ca hgc lugng tir m i khdng cd trong co hgc cd dien. Dieu niy cho thdy, viec phat hien ra hien tugng sieu chiy khang dinh vai trd quan d-gng cua cac hieu iing lugng di d nhiet dg tiidp. Ngoii ra, he qui nay cung l i dac trung cua d-gt d^
ngoii dudng cheo ODLRO xudt hien drong cic trgng thai ngung tu Bose Einstein.
Tham sd trgt tu trong pha sieu rdn
Nhu chung tdi da trinh bay v l trat di ran va trat di sieu chiy d tren thi hai trat ty niy cd dgc tnmg hoan toin khac nhau. Trit ty rdn dugc hd d-g v i hinh thinh khi the nang tuong tie trd nen rat manh so vdi ddng nang cua hgt. Ngugc lai, trgt ty sieu long dugc iiinh thinh nhd vao sy linh ddng v i khi ning di chuyen khdng ma sat, ndi each khic, trang thai nay dugc hinh thinh khi dgng nang lin it thi nang. Chinh vi vay, hai trat ty niy phu djnh nhau. Tuy nhien, mdt cau hdi dugc dat ra l i cd khi nio hai trgt di niy hd trg nhau va cung tdn tai khdng? Y tudng v l m^t pha chiia ddng thdi c i hai trit tu trai ngugc nhau da din den khai niem v l pha sieu rdn, d do cd su tdn tai ddng thdi cua c i frit dJ dudng cheo DLRO va trgt ty ngoai dudng cheo ODLRO. Ndi mgt cich khac, trat ty ran v i trat ty long Cling tdn tai ddng thdi trong mgt pha ddng nhit, de phan biet vdi trang thai tach hai pha rieng biet trong cimg mdt he. Trong trang thii tach pha ciia mgt he se tdn tai hai bg phgn, mdt phan d pha sieu long, mgt phan d pha sieu ran va he khdng phai ddng nhat ve pha.
O khia cgnh nao do, nd gidng nhu trang thii da lanh trong nudc. Sy thii vi la d chd, pha sieu ran cd ci hai dgc tnmg ve trat tu v i l i mgt pha ddng nhit chii khdng cd su tach pha. Hien tgi, nhieu kit qua nghien ciiu chi ra sy tdn tgi cua pha sieu rdn nhung cung nhieu nhdm nghien cuu bac bd su tdn tai cua pha niy. Nguyen nhin chii ylu l i do cac hd He-4 cd tgp va khdng kiem soat dugc tiiam sd. Nhu chiing tdi da dinh bay d phin dat vin dl, cdng ddng khoa hgc mudn tim kiem va kiem nghidm su tdn tai ciia cic pha dj thudng nhu pha sieu rdn d-ong mang quang hgc d l giim bdt su tranh cai ddi vdi kit qua do. Ly do don gian la vi mang quang hgc
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rit rinh khiet va cic tham sd nhu tuong tac v i hinh dang deu cd the dieu chinh dugc.
Mo hinh ly thuyet cua pha sieu rdn
Cho den nay, gidi nghien cuu thdng nhat cao ve su chua hoin chinh ciia cac bang chiing thuc nghiem de minh chiing cho mdt pha di thudng quan sit dugc trong h? He-4. Mac du cd rit nhieu biic tranh ly thuydt dugc dua ra nhung khdng cd ly thuyet nio cd the giii thich cung mdt luc tdt ca nhung cau hdi hoac nhimg mau thuin trong cac ket qua thyc nghiem [5]. Trong mgt nd lyc nghien cihi khic gan day, cac tic gii da dua ra mgt buc tranh vat ly van dung tinh toan tir nguyen ly ddu tien ip dung vio cic md hinh thuc te ciia tinh the He-4 nhdm giii thich cac quan sit thuc nghiem [8, 9].
Mdt cich tiep can khac nham giai thich cic ca che ben trong cic pha di thudng cimg vdi chuyen pha
^ lugng di giiia chung (vi dy, tii pha sieu ran sang sieu ldng) v i vai trd ciia cac yen td dinh xii cd ngudn gdc tir fe tuong tie, bdt dft ty hoac su cam tit ciia cac hgt trong I cac mgng giin doan. Trong trudng hgp niy, sy phi I vd ddi xiing tinh tiln tu phat dugc gin vdi ddi xiing I tinh tien giin doan cua Hamihonian. Uu diem cua
f
cic nghien ciiu nay la ngudi ta cd the sir dung cic md hinh don giin rdi ap dyng cic phuong phip tinh toan sd chinh xic de giai quydt rat nhieu van de ly thuyet lien quan din cac pha d i de cap d tren. Cac nghien cihi nay khdng nhung giii thich dugc cic ket qua thyc nghiem m i cdn dua ra nhiing dinh hudng cho cic thi nghiem. That vay, ngudi ta da sir dyng Hamiltonian mang de giai thich cho pha lien quan den iing xii cua He-4 trong nhihig nd lyc khio sat ly thuyet dau tien.Ldp cic Hamiltonian nay ggi l i ldp cic md hinh Bose Hubbard cd dang nhu sau:
H = -jY,{btbj-^ii£)^]-UY^hi{h,-\)-fiY,n, (8)
<ij> ^ < i
Trong dd; b^ v i b* li toan di sinh huy hat boson d vi tri thli i trong mang v i tuin theo quy tic:
[b^, ZJ* ] = S-, toan txx ri^= bib- la toin di sd hgt, J la ma trgn nhiy md ta ddng nang cua he, U l i the ning tuong tic giua cic boson tren ciing mdt vi tri trong
mang, p la thi hda cd vai trd dieu khien sd hat trong he v i chinh la h i m the hda trong phan bd thdng ke ldn.
Hamiltonian (8) l i md hinh tdi gian de md ta pha sieu chay ciia he boson. V l mat vat ly. khi dgng nang thing thi hay tuang tic giua cic boson rat yeu, J > U, he se d trgng thai sieu chiy, cdn ngugc Iai, khi tuong tic trd nen mgnh hon so vdi ddng nang J < U thi he se chuyin sang trgng thai dien mdi Mott. Cac ket qua nay da dugc kilm nghiem ca ve ly thuyet lan thyc nghiem [10]. Mac dil Hamiltonian (8) md ta rat tot pha sieu chiy cua he boson nhu He-4 chang han, nhung nd van chua du d l md t i pha sieu ran. Cd nhieu each de md ta pha sieu ran dya tren ldp cic md hinh Bose Hubbard (8) bdng cich them cac tuang tac tam xa, vi du cic tuong tic lan can gdn nhdt v i xa hon niia That thii vi l i khi them cac tuang tac tdm xa thi anh hudng ciia yeu td hinh hgc lai ddng vai trd quyet dinh. Cu the la. khi them drong tic lan can gin nhat vao Hamihoman (8), ngudi ta thay cd sy tdn tai cua pha sieu ran trong mang tam giic nhung khdng xuat hien trong mang vudng [11-15].
Quay trd Igi bai toan cua chiing ta, khi cac hat composite boson kieu He-4 tham gia vao qua trinh vgt ly. Do He cd ldp cic orbital mang dien tich am bao phii quanh hat nhan nen thuc te li rat khd de cac He-4 nam cimg mdt vi tri do nguyen ly loai trir Pauli. Ndi each khac, ddi vdi tnrdng hgp nay thi the nang tuang tac tren ciing mdt vi tri mit mang C = x , hay tai mgt vi tri nut chi tdn tai khdng nhieu hon mdt phan tii, dieu kien niy thudng dugc ggi la dieu kien boson loi cimg, mat do phan tli P thda man 0 < p < 1 . Viec xet cac lin can xa hon l i cin thiet de thu dugc cac md ta chinh xac han cua cac pha di thudng. Vi dy: neu khdng cd lan can thir hai trong mang vudng, se khdng the md ta dugc pha sieu ran. Vdi dieu kien niy. Hamiltonian (8) se trd thinh:
^ = -'/Z(**^,^M + 'iZ".-'V: I 'V';-ZM'', (9)
<ij> <ij> « i j » I
Trong do, V, la the nang tucmg tac giua cac phan tu lan can gan nhat, V^ la the nang tucmg tac giiia-cac cap lan can gan thij hai. Mo hinh nay dugc mo ta t'er.
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3(10)10.2015'A-
hgc va tucmg tic trong hinh 2. Myc dich ciia nghien ciiu niy dl cho ta sy nhin bilt so bg ve cic pha d cac mat do khac nhau.• V,
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Hinh I: mo hinh mang vd cac tucmg tdc trong mo hinh boson loi ran Su dung md hinh niy, chiing tdi khio sit giin dd pha de tim ra cac dieu ki?n xuat hien trang thai sieu ran. Phuong phip chiing tdi sii dyng de nghien ciiu li phuong phip Monte Carlo lugng tii co ap dung thuat toan Worm [16, 17]. Vdi phuang phap nay, chiing tdi cd the nghien ciiu dugc giin dd pha d cic nhi?t do bit ky vdi do chinh xic tiiy y. Hai tham sd trit tu ODLRO va DLRO dugc chimg tdi sii dung nhu mdt thudc do cho sy xuat hien ciia pha sieu ran. Tham sd trgt ty ODLRO dugc the hi?n vdi sy xuit hi^n cua mat dg sieu ldng Pg, cdn tham sd trit ty ODLRO dugc md ta bdi h? sd ciu tnic ttnh ky hieu la S(k), cd gia trj khac khdng. Vdi cic mang cd hinh dang khac nhau thi tinh the hinh thanh d cac mat d^ khic nhau se dugc die tnmg bdi cic vecto mgng dio khic nhau. He qua l i gia trj vecto k cung khac nhau tuong iing. Vi du: vdi mgng vudng thi tinh the d bin cd se dugc die tnmg bdi vecto hai chilu k = (kj^,ky) = {7r,7r), d-ong khi dd tinh thi cd hinh dang dai bing lgi cd vecto die tnmg k = (k^,ky) = {0,^) = {^,0). Dang luu y, chung ta cdn phan bi?t pha sieu ran vdi trgng thii tach pha, d dd hai tham so trat ty ciing khic khdng. De phan bidt dugc, chiing ta nhin vao sy phu thudc ciia mat dg sidu Idng vao mat do hat trong he. Neu do thj bieu diln cd nhay bac thi do la trang thai tach pha. Sir dung phuang phap Monte Carlo lugng hr, chung tdi de ding quan sit dugc cac tham sd trat tu p^, S(k) va phan GieTaU^ pha sieu ran va sy tach pha. De mmh hoa c!io nhirng tien , doin ly thuyet, chiing tdi nghien cim mi)t tnrdng hgp mang tinh the la mang vudng va quan sat cac dgc tnmg vat Iv ciia he. Trudc tien, chiing tdi nghi3n ciiu sy phu ttWid? cua mil do hat vao ty sd tuong ddi giua the hda
Hinh 2. sifphv thupc ciia mdt dp hgt vdo the hoa hoc fi trong mgng vuong cua mo hinh boson loi rdn Nhin vio hinh 2, chiing ta dl ding phan biet dugc cic trang thii khic nhau cua h? tai cic mat dg hat boson trong trudng hgp mgng vudng. Do md hinh ldi ran (9) cd tinh ddi xung giua hgt v i Id trdng nen chung tdi chi ve mat do hat tir 0 din 0,5. Mat do hat di 0,5 den 1,0 li hoin toin tuang dj. Chiing ta quan sat thay mat dg hat cd xudt hi$n bgc thang tai mat do hat p = 0,25, chiing td tai dd cd trgng thii tinh the hinh sao. Lan can cua bac thang v l phia mat dO thdp, ta thay su lien d^c cua mat do hat the hi^n pha ddng nhat nhung lan can ve phia mgt do cao cd nhiy bac. Day chinh la dau hieu ciia sy tach pha. De tim hieu sau han ve dgc tnmg pha ciia cic trgng thii niy, chung tdi quan sat mat dg sieu chay pg v i he sd ciu tnic tmh S(k) nhu trong hinh 3.
PSOA-
Hinh 3: sir phu thuQC cua mgt dQ sieu chdy (hinh tren) vd cdu true tfnh (hinh difdi) S [(0. n); (n, 0)f vd S(n,n) vdo mgt dp hat vm cde kich thu&c khac nhau L = 12. 24 vd tuang tdc F, =8,0. V^ = 3,5
Hinh 3 cho chiing ta thdy, trgng thai sieu rin tdn tai trong mdt mien mgt do rit rgng 0,175 < p < 0,25. Cin luu y rdng, day la mdt kit qui dang chii y vi tnrdc nam
CJIlSEVietNani^'^-""'-^"''
rdt tinh khilt v i c ^ tham so nhu tuong tac v i hinh dang deu cd the dieu chinh dugc.
Mo hinh ly thuyit cda pha sieu rdn
Cho den nay, gidi nghien ciiu thdng nhdt cao ve sy chua hoin chinh ciia cac bang chimg thyc nghiem de minh chiing cho mdt pha di thudng quan sit dugc trong he He-4. Mac du cd rit nhieu biic tranh ly thuyet dugc dua ra nhung khdng cd ly thuyet nao cd the giii thich ciing mdt liic tdt c i nhung cau hdi hogc nhung mau thuan trong cic kit qui thyc nghiem [5]. Trong mgt no lyc nghien ciiu khic gan day, cic tic gja da dua ra mgt biic tranh vit Iy van dung tinh toin tir nguyen ly dau tien ap dyng vio cic md hinh thuc te cua tinh the He-4 nhdm giii thich cic quan sat thyc nghiem [8, 9].
Mgt cich tiep can khac nhim giai thich cac co che ben trong cic pha di thudng ciing vdi chuyen pha lugng di giira chiing (vi dy, tir pha sieu ran sang sieu long) v i vai trd ciia cic yen td dinh xir cd ngudn gdc tir tuong tac, bat trgt ty hogc sy cam tii ciia cac hgt trong cac mgng giin dogn. Trong trudng hgp niy, su phi vd ddi xiing tinh tien tu phat dugc gan vdi ddi xiing tinh tiln gian doan ciia Hamiltonian. Uii diem ciia cic nghien cuu nay la ngudi ta cd the su dung cac md hinh don gian rdi i p dung cic phuong phip tinh toan sd chinh xac de giai quyet rdt nhieu van de ly tiiuylt lien quan den cac pha d i d l cap d tren. Cac nghien ciru niy khdng nhung giii thich dugc cac ket qua thyc nghi?m ma cdn dua ra nhiing dinh hudng cho cic thi nghi?m. That vay, ngudi ta da sir dung Hamiltonian mang de giii thich cho pha hen quan den ung xii cua He-4 trong nhiing nd lyc khao sit ly thuyet diu tien.
Ldp cic Hamiltonian niy ggi la ldp cic md hinh Bose Hubbard cd dang nhu sau:
H =-j'^ibtbj+hr)+^uY,ni{n,-i)-Ml,n, (8)
<ij> ^ i i Trong dd: b^ v i b^ l i toan di sinh hiiy hat boson d vi tri thli i trong mgng va tuan theo quy tic:
[b^,b*] = S^ , toan di n. = b~b^ !a toin tir sd hat, J l i ma tran nhay md t i ddng nang ciia he, U la the nang tuong tic giua cic boson tren ciing mdt vi tri trong
mgng, p l i the hda cdvMtrd dieu khien so hat trong he va chinh la him t h e ^ H trong phan bd thdng ke ldn.
Hamiltonian (8) l i r ^ J n h tdi gian de md ta pha sieu chay cua he boson. ( B mat %at ly. khi dgng nang thing t h i hay tuang tic giira cac boson rat >'eu, J > L.
he se d drgng thii sieu chay. cdn ngugc tai. khi drong tic trd nen manh honso vdi dgng nang J 5 L thi he se chuyin sang t r a n g ^ ^ H e n mdi Mon. Cac ket qui niy da dugc kilm nghiem J \ e ly thu\'et lin thuc nghiem [10]. Mac du ^ ^ ^ H p " <^l ™^ ^ ^^^ ^°^ P^^ ^'^"
chiy ciia he boson nhu|pe-4 chang ban. nhimg nd van chua dli d l md ta pha si8u ran. Co nhieu each de md ta pha sieu rdn dya tren 1%) cac md hinh Bose Hubbard (8) bdng cich them cic tuong tic tam xa. vi du cac tuong tic lin can gan m a t \ a xa hem niia. That thii vj l i khi them cac t u a n g | | | tam xa thi anh huong ciia \eu td hinh hgc lai ddng vai trd quyet dinh. Cu the li. khi them tuong tie lan caij^an nhat vio Hamiltonian (8).
ngudi ta thdy cd sy tdn tai cua pha sieu ran trong mang tam giac nhung khdng xuat hien trong mang xTidng [11-15].
Quay trd lai bii toan cua chiing ta. khi cac hat composite boson kieu1S[e-4 tham gia \ ao qua trinh vat ly. Do He cd ldp cic o | t a l mang dien tich am bao phu quanh hgt nhan nen thyc te la rit khd de cac H e ^ nim cimg mgt vi tri do J B p n ly loai trir Pauli. Ndi cich khic, ddi vdi tnrdng gBP nay thi the nang mong tic tren cung mdt vi tri niitjiang f." = x . hay tai mgt vi tri mit chi tdn tai k h d n g ^ K u hon mdt phan tir. dieu kien niy thudng dugc ggi l i dieu kien boson Idi ciing. mat do phin hi P thda m a n ^ < p<\ . Viec xet cic lan can xa hem la c a n l ^ ^ w w H dugc cac md ti chinh xac hem cua cic pha di thudng. Vi du: neu khong cd lin can thii hai trong mang vudng.
sieu ran. Vdi dieu|
thinh;
H=-J'^ibibj+h£)
"h^
e khong the md ta dugc pha nay. Hamiltonian (8) se trd
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Trong dd, V, l i the nang tuong tac giira cac phan * tii lan can gan nhat, V^ la the nang tuong lac giiia cac cap lan can gin thii hai. Md hinh nay dugc mo ta fen h m h l .
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hgc v i tuong tic trong hinh 2. Muc dich cua nghien ciiu nay de cho ta su nhan biet so bg ve cac pha d cic mat do khic nhau.
Hinh 1: mo hinh mgng vd cde tuang tdc trong mo hinh boson Ioi rdn Su dung md hinh nay, chiing tdi khio sit giin do pha de tim ra cic dieu kien xuat hien trang thii sieu ran. Phucmg phip chiing tdi sir dung de nghien ciiu l i phuang phip Monte Carlo lugng tir cd ap dung thuat toin Worm [16, 17]. Vdi phuong phap nay, chiing tdi cd the nghidn ciiu dugc giin dd pha d cac nhiet do bat ky vdi dg chinh xic tuy y. Hai tham sd trit ty ODLRO v i DLRO dugc chiing tdi sit dung nhu mgt thudc do cho sy xudt hi^n ciia pha sieu rin. Tham sd trat ty ODLRO dugc the hien vdi su xuat hien ciia mat &^
sieu ldng p^, cdn tham sd trat ty ODLRO dugc md t i bdi he sd cau tnic tinh ky hi?u la S(k), cd gii tri khac khdng. Vdi cac mgng cd hinh dang khac nhau thi tinh the hinh thanh d cic mat do khac nhau se dugc dgc trung bdi cic vecto mang dao khac nhau. He qui Ii gii tri vecto k ciing khac nhau tuong iing. Vi du: vdi mang vudng thi tinh the d ban cd se dugc die trung bdi vecto hai chilu k = {kx,ky) = [7t,7t), hong khi do tinh the cd hinh dang dai bang lgi cd vecto die tnmg
k = {k^,ky) = [Q,n) = {7i:,Qi). Ding luu y, chiing ta cdn phan biet pha sieu rin vdi trang thai tach pha, d do hai tiiam sd trgt ty cung khac khdng. De phin biet dugc, chiing ta nhin vio su phu thudc cua mit do sieu vao m^t dg hat trong he. N I U dd thi bieu dien cd nhay bac thi dd I;i trang thai tach pha. Sii dung phuang phap Monte Carlo lugng tir, chimg toi d l ding quan sat ' dugc cic tham sd trat tu p^, S(k) \ a phin biet dugc pha i ^ieu ran va su tach pha. De minh hga cho nhimg tien lijj'*^doin ly thuyet, chiing ldi nghien cim mdt trudng hgp li mang tinh the la mang vudng va quan sit cac dac tnmg r'' , vat ly cua he. Trudc tien, chiing toi nghien ciiu sy phu
^ff ''^Wid? cua mat dp hat vio ty sd tuony doi giiia the hda
Hinh 2: sttphif thupc ci'ia mgt dg hgt vdo the hoa hgcp trong mgng vuong cua mo hinh boson loi rdn Nhin vao hinh 2, chiing ta dl ding phan biet dugc cac trgng thai khic nhau cua he tai cac mat dg hat boson trong trudng hgp mgng vudng. Do md hinh loi rdn (9) cd tinh ddi xiing giiia hat v i Id trdng nen chiing tdi chi ve mat dg hgt tir 0 den 0,5. Mat do hgt tir 0,5 den 1,0 la hoan toan drong tu. Chung ta quan sat thiy mat 6.^ hgt cd xuat hien bic thang tai mat do hgt p = 0,25, chiing td tgi dd cd trgng thii tinh the hinh sao. Lan can ciia bac thang v l phia mat dg thdp, ta thay sy lien tyc ciia mgt do hgt thi hi^n pha ddng nhat nhung lan can ve phia mgt dg cao cd nhiy bac. Day chinh la dau hieu ciia su tich pha. De tim hilu sau hon ve dac trung pha ciia cic trgng thii niy, chiing tdi quan sat mat do sieu chiy Pg v i he sd cdu tnic tinh S(k) nhu trong hinh 3.
PSOA
Hinh 3: sifphif thugc cua mgt dg sieu chdy (hinh tren) vd cdu true ttnh (hinh duoi) S [(0. n). (n, 0)/ vd S(n.K) vdo mat dg hat vm cde kich thu&c khac nhau L = 12, 24 vd tuang Idc K, = 8,0. V^ = 3.5
Hinh 3 cho chiing ta thdy, trgng thii sieu ran tdn tgi trong mdt mien mat dg rit rdng 0,175 < p < 0,25. Can luu y rang, day la mdt ket qua dang chii y vi trudc nam
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3(10) 10.20152008 chua cd nhdm tie gia nio phit hien ra su tdn tgi cua trgng thii chit ran trong lin can ciia pha tinh the d mien mat do thap.
Chiing tdi quan sat tgi cac dieu kien khic nhau ciia tuong tic trong md hinh (9) va ve dugc gian do pha tgi cic mat do hgt p = 0,25 va 0,5 nhu hinh 4. Diem thii vj l i khi nghien ciiu pha tgi cic mat do hgt lan can vdi mat dg hat neu tren, chung tdi thu dugc mdt dieu kien tdng quit cho viec xudt hien pha sieu ran nhu sau: neu tgi mgt do hgt p = 0,25 he l i trang thii tinh the hinh sao va tgi p = 0,5 h? trong trgng thii tmh the d ban cd thi he nim trong trgng thai sieu ran tren toin mien mat dd tren v i dudi cua p = 0,25. Day la mdt ket qui mang tinh tdng quit.
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^^^^-^''^ ^ Tinh the ) 4 « 8 Hinh 4: gidn do pba cua trgng thdi nen (ground slale) vai cde pha CO the xudt hien tgi cde mgt dg hat khde nhau. Ky hieu (o) phdn cdch tmh the cdu true hinh sao vd trang thai sieu chdy a mat dg hat p"^ 1/4.
Ky hi4u (9) phdn each linh the cdu tnic 6 ban ca vd trang thdi sieu chdy tgi mdt do hat p=I/2. Ky hieu (m) plidn cdch imh the cdu true ddi
vd trgng thdi sieu chdy tgi mat dg hatp=I/4 Md hinh mgng sii dung tren day khdng chi la mgt cdng cy ly thuyet don thuin m i nd cdn dugc hien thyc hda trong cic he quang hgc. Y nghia quan trgng nhat cua cic nghien cuu niy l i ngudi ta cd the tien hanh so sinh tryc tiep giua ly thuyet va thuc nghiem ddi vdi mang quang vdi do chinh xic rit cao. Tuy?t vdi hon niia la nhiing ket qua nghien cuu sii dung md hinh niy se giim thieu nhung tranh lugn khi dimg nd de giii tiiich pha sieu ran trong tiii nghiem vdi He-4.
Trang thai sieu r i n trong mang quang hgc Nhu chiing tdi de cap d tren, mgng quang la mdt
"ung cir vien" tdt cho viec quan sat trang thii sieu ran.
Thyc te, mgng quang li mdt mang nhan tao, cd cau true trgt ty gidng nhu mang tinh the, dugc hinh thinh
khi chieu cic chiim tia laser ddi ddu nhau tao thanh cic hd the bay cic nguyen tii sieu Ignh, vi du cic boson d trgng thii ngung tu Bose Einstein. Cac nguyen tii niy dugc lam Ignh sin d trang thii ngung tu Bose vi ling xii trong mgng quang nhu cic mang tinh the thyc.
Trong tinh thd thyc cd nhieu tuong tic phuc tap va chiia nhilu tgp nen rat khd de kiem soat cac tham sd vat ly ciia nd, vi dy do ldn cua cic tuang tie. Thgt may mdn, trong mang quang ngudi ta cd the thay ddi de ding tdt ca cac tiiam sd dgc dung ciia mgng nhu chieu dai CO sd mang, chieu siu cua hd the v i tuong tic giua cac nguyen tir. Chinh vi ly do nay, mgng quang hgc cung cap md hinh ly tudng dd khio sit inh hudng cua cac tham sd trong cac vat lieu va cho chiing ta mgt biic tranh ro ring han ve vai trd ciia cic tham sd. Trong mgng quang, cic hd the dugc hinh thinh tgi cac diy the ciia chiim laser giao thoa. Khac vdi mgng tinh the, cic hd the tuan hoin hinh thinh do tuong tic giira cic ion cd dinh tai cac mit mgng sinh ra trudng tinh the. Hat ty do trong mang tinh the l i electron, cdn hat tu do trong mgng quang l i cic nguydn di sieu Ignh. De hieu sau hon ve mang quang, chiing ta can hieu sau hon vl qua trinh hinh thinh cac hd the nhu sau:
Biy dien thi trong mang quang dugc hinh thanh dua tren tuong tic giiia mdmen ludng cue dien vdi dien tnrdng cua anh sang laser. Khi nguyen di dugc chieu sing bdi laser, dien trudng E cua sdng anh sang va mdmen luong cue dao ddng vdi tdn sd co dugc bieu dien nhu sau:
E{r,t) ='eE(r)exp(-iCi)t) p{r,t) ='ep(r)exp(-iO)t) p(r) = a(fi))E(r)
Vdi E(r) va p(r) la bien do ciia dao dgng, e la vecta don vi phin cyc, a(co) l i do phan cue phiic phy thudc vao tdn sd. Dien thi tuong tic giiia mdmen ludng cue v i dien trudng ciia sdng inh sing hinh thinh nen thi tuong tac vdi chieu sau hd thd;
Vjifi'-)-
lEff R e ( a ) / ( r )
Voi Ej va c lan lugt la cac.,Mt}g sS dien moi va vta t6c anh sang, cuong do A ' ' ) ^ | f e i E ^ . do do nguyen
aillGI J J ^ y g ' . .. 3(10)10.2015 28
\
di se bi bay tai cic vi tri bien do cua dien trudng cd cyc dai hogc cyc tiiu. Ngoii ra, vi dien trudng dao ddng tuan hoin nen thd ning ciing dao ddng tudn hoin theo.
Su dung md hinh Lorentz d l bilu diln a((B), ta thu dugc mdi lien he giua dien thd hieu dyng nhu sau:
^dipir):
'24
/ ( r )Trong dd: A = 00 - cOj, l i do lech tdn sd giira tdn sd laser m va tdn sd dac frimg trong md hinh Lorentz md t i dao dgng cd dien ciia dien di (d^, cdn hdng sd r lien quan den sy chuyen ddi die trung cua nguyen tir. Vdi ciu hinh khac nhau cua cic nguon anh sing laser, chiing ta cd thi tao ra cic dgng hinh hgc khic nhau nhu dang mang tam giic, vudng..., hogc mgng 1 chieu, 2 chidu, 3 chieu. Quan trgng hon niia li tdt c i cac sd hang trong md hinh Hamiltonian (8) va (9) diu cd the didu khien dugc thdng qua viec thay ddi cudng do chiim laser. Mdt trong nhiing thinh tyu gay tilng vang khi nghien cim mgng quang hgc l i vi?c sii dung md hinh Bose Hubbard (8) nhu mdt md hinh hoin hio d l md t i mang quang [18, 19]. Nhd phat hi^n thii vi niy ma md hinh (8) v i (9) khdng cdn la md hinh dd choi niia m i nd thuc su li mgt md hinh die thii cua mang quang hgc.
Thdng thudng, bat ky loai nguyen di nao cung cd the bi biy trong mang quang hgc, nhung cic nguyen tu kidm dugc sir dyng li chii ylu do dgc tinh cua chiing dugc md t i dan gian trong mang quang. Ket qua thuc nghiem diu tien cho thay tinh diing din trong tien doan ly thuyet ve sy xuat hien ciia cac pha sieu chiy v i dien mdi Mott khi tang cudng do chum laser (tuong iing vdi viec gia tang drong tie). Ket qua nay md ra hing loat i_cac nghien ciiu khic nham kiem nghiem lgi cac dinh l u ^ H ly trong mgng quang. That ding tiec la cho den n a ^ ™ i chua cd bang chiing thuc nghiem nao cho thdy
^ J t a i cua trgng tiiai sieu ran hong mang quang hgc
^ nhihig tien doin ly thuylt l i rdt chic chin va ro dng cugc tim kiem trgng tiiii sieu rin vin dugc
^tiep die rdt sdi ndi.
Nhung trang thai dUhuvng khac Ngoai pha di t ^
5 tren, gdn day c^j
ran nhu chiing tdi de cap
;hien ciiu vat ly cdn quan
tam den mdt pha thii vi khac thd hien vai trd ldn ciia cic hieu img lugng tir d nhiet dg thap, dd la cac pha spin ldng lugng tir [20]. Trang thai niy thuc su van cdn khd hieu ddi vdi c i thuc nghidm lin cic md hinh ly thuyet trong vi^c tim ra die tnmg pha cua nd. Ly do mgt phan l i sy cin bang mong manh cua tuong tic vi md da khdng the tao ra su phi vd ddi xiing thdng thudng d nhiet do thip. Mdt phan la pha thiiy tinh sieu ldng thieu tham sd trat ty die trung cho nd, khdng gidng nhu pha sieu rdn cd thi die tnmg bang tham sd trit dJ DLRO va ODLRO. Do vgy, ngudi ta khdng cd each nio de nghien ciiu chuyen pha giiia cac trang thai. Hien tai, d l xic djnh trgng thii niy, ngudi ta diing phuang phap loai trir, die la loai bd tat ca cac tham sd trit tu thdng thudng gan lien vdi cac pha da biet khic.
Tuy nhien, trong thdi gian gin day, cic nghien ciiu ly thuyet da phan loai dugc mdt ldp cac pha spin Idng dua tren su suy bidn topo cua him sdng. Vi du, mgt vii tac gia de xudt md hinh Hamiltonian vdi trgng thai nen li pha spin ldng vdi trgt tu topo Z^. Mdt trong cic md hinh dau tien dugc nghien ciiu l i md hinh dimer mang tam giic [21]. Mdt hudng khic trong nghien ciiu bgc topo l i cac he toric code [22] vi nd la ldp cac md hinh don gian nhat cd the giai chinh xac dugc, vi dy nhu md hinh Levin-Wen [23]. Cdn chii y la, d l mgt md hinh thyc sy giai thich cung nhu cd the so sinh dugc vdi thyc nghiem thi md hinh do phai chiia cac sd hgng tuong tic hai niit giiia hai ddi tugng (vi dy: giua hai spin Ian can nhau) va trang thai spin ldng dgc tnmg cho hat di topo. Mdt trong nhirng nd lyc thanh cdng v i dugc khi nhieu ngudi sii dung dd l i md hinh Kagome/
Bose Hubbard xay dyng bdi Balent, Girvin va Fisher [24]. Mac du md hinh nay chira tuong tic 4 niit nhung trgng thai chat ldng spin Z^ cd mat tren mdt miln kha rgng ciia giin do pha [25]. Cho ddn nay, cic nd Iuc tim kidm dgc tnmg cua cic pha di thudng van dugc tiep tuc va cho thay rdt nhilu tin hidu kha quan.
Y nghia cua viec nghien cuu cac trang thai moi cua vat c h i t
Viec nghien ciiu cic h-gng thai mdi cua vat chat khdng chi cd y nghia v l khoa hgc: tao ra mgt co sd ly thuylt cho nghidn ciiu thuc nghi?m mi no cdn cd thi cd tidm nang ling dung ldn. Mgt trong nhimg cau hdi ldn hong vit ly cho din nay vin chua cd ciu tri
IfeTHSStVaL^'-'—
ldi thda ding dd li hien tugng sieu din d nhiet do cao.
Nhung nd Iyc nghien ciiu khdng met mdi de tim ra bin chat vgt ly va dac trung cua pha sieu dan nhiet do cao di tgo ra nhieu hudng di mdi trong nghien ciiu cac pha di thudng cua vat chit. Thuc te li, sy hieu biet ve cic trang thii di thudng nhu trang thii sieu long va trang thai sieu rin... Ia mdt trgng nhung nd lyc de hieu ve trang thii sieu din nhiet dg cao vdi nhidu bi in dang chd kham phi. Ngoii ra, mdt trong nhiing ung dung ro net nhat ciia trang thai spin ldng lugng tu li viec tim ra h? vat li?u cd trgng thai bao ve qubit (protected qubit) cin thiet de chiia thdng tin lugng tu - nen tang co ban ciia miy tinh lugng di. Miy tinh lugng tir da va dang dugc cgng ddng cdng nghe ky vgng la the he tiep theo cua mgt cdng nghe hoan toan mdi, cd chiic nang uu vi?t hon va hieu qua Iam viec tdt hon cdng nghe may tinh thdng thudng.
Tai lieu tham khao
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