Phase diagram and frustration of decoherence in Y-shaped Josephson junction networks. D.Giuliano(Cosenza), P. Sodano(Perugia)

Transcription

1 Phas dagram ad frustrato of dcohrc Y-shapd Josphso jucto tworks D.GulaoCosza, P. SodaoPruga Frz, Frz, Octobr Octobr

2 Ma da Y-Shapd twork of Josphso jucto chas YJJN wth a magtc frustrato Ft-couplg fxd pot FFP th phas dagram; YJJN workg ar th FFP Frustrato of dcohrc th mrgg two-lvl quatum systm QS; Applcato: grg of a rducd-dcohrc QS. Tchology: rormalzato groupboudary coformal fld thory.

3 Pla of th talk:.th YJJN as a jucto of chargd, o-dmsoal, bosoc systms;.th paramtrs ad th phas dagram of th YJJN: wakly coupld ad strogly coupld fxd pots;.emrgc of a FFP th phas dagram; 4. Currt s pattr th YJJN ar th fxd pots: th YJJN as a quatum swtch ; 5.Spctral dsty ad frustrato of dcohrc th YJJN workg ar th FFP; 6. Coclusos, possbl applcatos, prspctvs.

4 . Th YJJN ad ts fld-thortcal dscrpto E J λ ϕ ϕ λ Φ E J λ E J ϕ

5 Ctral rgo Hamltoa [ / * J g C hc E W E H ϕ φ φ φ E C >>E J Effctv -sp Hamltoa * h N W g [ 0 0 N S z φ 0 [ 0 S φ { } / [ [ [ J z c h S S E S h H ϕ

6 ow-rgy gstats h>e J ε0 h [ ε h EJ ϕ cos [ ε h E J ϕ cos [ ε E J h ϕ cos Oly ths stats wll b kpt th ffctv thory

7 Charg tulg at th r boudars HT λ cos[ φ 0 φ Wak tulg lmt:λ<<h,e J Schrffr-Wolff trasformato Boudary tracto trm H B φ φ EW [ γ h. c. E W λe 4h J [cos ϕ 9s ϕ ϕ γ arcta[ ta

8 Effctv fld thory of a JJ-cha. I. Glazma ad A. I. ark, PR 79, , D. Gulao ad P. Sodao, NPB 7, [ 0 6 cos k j k j k j C J Z j k j k j J j k j C E E E E N E H φ φ φ Mappg oto sp chajorda-wgr frmosbosozato uttgr lqud ffctv Hamltoa Φ Φ 0 4 k k k dx t u x u g H N/

9 paramtrs ad boudary codtos Wak boudary couplg E W /E J << Numa boudary codtos at th r boudary Φ k 0/x0; Couplg to th bulk suprcoductors Drchlt boudary codtos at th outr boudary Φ k k φ k ; g v v F F g g g g 4 4 u F v g g 4 g z J g4 4 a [coskf E 6E a C

10 X x Φ x χ x [ Φ x Φ x χ x [ Φ x Φ x Φ x 6 Normal flds χ ϕ ϕ φ φφ χ Boudary Hamltoa HBou E W xp[ r r χ0 γ,0;, ;, hc..

11 Dyamcal boudary codtos at th r boudary r ug χ r r r x EW s[ χ 0 γ 0 r χ x Wakly coupld FP 0 Strogly coupld FP Mmum of H Bou

12 . Phas dagram of th YJJN: wakly ad strogly coupld fxd pots Wakly coupld fxd pot ut x g t x cos[, ξ χ Mod xpaso for th plasmo flds ϕ ϕ ξ φ φ φ ξ

13 : : ' [ : :: : ' / ' τ χ τ χ τ χ τ τ r r r r r r k j g k j O.P.E. btw boudary vrtcs: Dmsolss boudary couplg GE W a/ /g

14 Scod-ordr rormalzato group quatos γ γ γ G G g d G d 0 [ / l [ cos [ / l 0 G G g d dg γ s / l 0 G d d γ γ

15 Phas dagram γ / / g< * g<:stabl fxd pot at Gγ0; fxd ls at γ0,/,/. γ / 0 / <g<9/4 *<g<9/4:strogly coupld fxd pot for γ /; ft couplg fxd pot for γ/. γ 0 / *9/4<g: strogly coupld stabl FP / 9/4<g 0 G

16 Strogly coupld fxd pot G-> Drchlt boudary codtos at th r boudary, as wll. χ 0, χ 0 spa a tragular lattc, dpdg o th valu of γ sublattc A sublattc B sublattc C For γ/ th mma l o a hoycomb lattc mrgg of two tragular sublattcs

17 Mod xpaso of th plasmo flds at th SFP ut x x P vt g t x θ ψ cos[, Dual flds ut x x P g t x ξ χ s[,

18 For γ k / th mma spa oly o of th thr sublattcs : ths cas, th ladg boudary prturbato s gv by a combato of log V- statos. H S Y V 0 h. c. V j τ : xp ± ρ j ψ τ : ρ 0,; ρ, ; ρ, Th V-stato oprators hav coformal dmso h S g4g/: for ¾<g< ad for γ k/ both th wakly coupld ad th strogly coupld fxd pot s stabl rpulsv FFP.

19 . Emrgc of a stabl ft couplg fxd pot For γk / two tragular sublattcs bcom dgrat rgy: thy mrg to form a hoycomb lattc. I ths cas, th ladg boudary prturbato s gv by a combato of short W-stato. HF ς τ W0 hc.. W j τ : xp ± j ψ τ : τ,τ - ar ffctv sosp oprators, coctg sts o quvalt sublattcs

20 Prturbatv rormalzato group quato for th rug couplg strgth d d ζ l / 0 4g 9 ζ ζ Th W-stato oprators hav coformal dmso h F g4g/9: for <g<9/4 thr th wakly coupld, or th strogly coupld fxd pot s stabl: th IR bhavor of th systm s drv by a attractv FFP

21 attc A attc B attc C Wstato Vstato

22 4. Currt pattr ar th W ad S fxd pots l * l 6 l * l 6 l * Z g I Z Z g I Z Z g I ϕ ϕ 6 ϕ ϕ ϕ Currt: logarthmc drvatvs of th partto fucto Z

23 Wakly coupld fxd pot Prturbatv calculato: th rsult s th typcal susodal bhavor, as a fucto of th appld phas dffrcs [ [ [ s s * s s * s s * γ γ γ γ γ γ g G I g G I g G I

24 Strogly coupld fxd pot Zro-mod cotrbuto to th rgy gvalus E E[, E osc E[, vg εl ε A B C 0, ε, ε O a ft-sz systm ths braks th dgracy btw th mma of th boudary pottal lablld by th s

25 Th ma cotrbuto to th total currt coms from th zro-mod trm th total rgy: ths mpls abrupt jumps prturbatvly roudd by V-statos at th dgracy btw two gvalus * 6 * 6 * vg I vg I vg I

26 Tug two gstats of th zro-mod oprator ar by a dgracy ffctv two-lvl quatum dvc For stac: sttg < < 6 6 δ δ << Th followg two stats df a ffctv QD 0,0> ; 0,> >, > A A

27 Opratg th systm as a quatum swtch I I I > δ Strog couplg δ δ 0 > a b δ masurs th dtug off th dgracy: actg o ths paramtr o maks th systm swtch btw th two stats

28 5. Th systm workg ar th FFP: currt pattr ad frustrato of dcohrc Th currt pattr ar th FFP Though t s possbl to st up a slf-cosstt formalsm to formally drv th currt pattr ar th FFP, a closd-formula ca b gv oly for g9/4-ε, wth ε<<. I ths cas, o may st th paramtrs as g * δ δ 6 ζ * ε

29 * 6 * 4 * 6 * 4 * ζ δ ζ δ vg I v I v I Currt across th thr arms

30 I I Ft couplg δ δ δ 0 a b Aga, ths s a smoothd sawtooth-lk bhavor but, ow, t s assocatd to a stabl FP > >

31 W rlat th dcohrc to th taglmt of th systm wth th plasmo bath spctral dsty of stats of th ffctv QD, Χ Ω/Ω E. Novas t al., Phys. Rv. B 7, a χ [ Ω b [ χ RPA Ω χ 0 [ Ω χ 0 [ Ω ζ ζ [ χ RPA Ω

32 ε ε ς χ 8 9 * [ 8 9 [ Ω Γ Ω Ω r RPA / [ * * E ς r r

33 Usg th RPA approxmato sktchd abov ylds χ Ω/Ω FFP DFP NFP Ω

34 Nar th SFP: o taglmt btw th QD ad th bath, but o quatum tulg btw th stats thr o rgy rormalzato; Nar th WFP: full taglmt btw th QD ad th bath full dcohrc; Nar th FFP: cosstt ad robust tul splttg of th two stats, wth a accttabl lvl of frustratd dcohrc

35 6. Coclusos. A Y-shapd JJ-twork may xhbt a FFP ts phas dagram;. At th FFP a ffctv -lvl quatum dvcs mrgs, wth hacd quatum cohrc;. Rlvat ssus for a practcal ralzato: stablzg γ, applyg th xtral phass, cotrollg othr sourcs of os