Single electron experiments in quantum conductors : the on-demand single electron source the charge relaxation resistance

Transcription

1 Singl lctron xprimnts in quantum conductors : th on-dmand singl lctron sourc th charg rlaxation rsistanc «DEG tam» Laboratoir Pirr Aigrain, Ecol Normal Supériur Sampls : Y. Jin, A. avanna, B. Etinn (LPN-NRS Marcoussis) Symposium on Quantum Phnomna and Dvics at Low Tmpraturs ULTI Symposium, March 9th., 008

2 DEG tam PdD :François Parmntir PhD : Adrin Mahé Julin Gablli (LPS-Orsay) Gwndal Fèv (LPA-ENS) Takis Kontos Jan-Marc Brroir Brnard Plaçais hristian Glattli ULTI Symposium, March 9th., 008

3 Motivation : doing quantum optics with lctrons bam-splittr : Sourc : Dtctor : Thrmal sourc ohrnt sourc photon gun singl cohrnt mod : Optic fibr / coaxial cabl -lctron Hanbury-Brown and Twiss xprimnt Dtctor ULTI Symposium, March 9th., 008

4 -particl Hanbury-Brown and Twiss xprimnt Sourc bam-splittr : Sourc : Dtctor : singl cohrnt mod : Nd : Tim and nrgy control Dtctor ULTI Symposium, March 9th., 008

5 Elctronic analog of quantum optics : QHE in DEGs bam-splittr : Quantum Point ontact Sourc hv F kt ~ qqs0µm à 00mK Sourc : Biasd sourc contact Or Singl lctron sourc singl cohrnt mod : Edg stats (QHE) Dtctor : Drain contact Or Singl lctron dtctor Hanbury-Brown and Twiss intnsity corrlations Dtctor ULTI Symposium, March 9th., 008

6 Two-dimnsionnal lctron gas Modulation-dopd htrostructurs At T~30 mk λ F ~ 30 nm L ~ 0-0 µm L φ ~ 0 µm ohrnt ballistic lctronic transport ULTI Symposium, March 9th., 008

7 B r r V drift B E 0 5 Quantum Hall rgim m/s E r GaAs AlGaAs B r Enrgy ε F Intrfac onfinmnt D Landau Lvls k, x x Singl mod conductor :D, spin polarizd dg stats ULTI Symposium, March 9th., 008

8 Two-lctron collidr schm V A ULTI Symposium, March 9th., 008 A V

9 Two-lctron collidr schm V A nrgy control of th mittd lctron tim control : 0. 0 ns ULTI Symposium, March 9th., 008 A V

10 τ V D biasd Frmi sa noislss lctron sourc : h V Singl lctron sourc? D I I ( D ) No tmporal control f ,0 0,8 0,6 0,4 0, 0,0 D ( T ) 3 0 Kumar t al. PRL (996) ( ) T T + T Fano rduction factor onductanc ² / h A. Kumar t al. Phys. Rv. Ltt. 76 (996) M. Rznikov t al. Phys. Rv. Ltt. 75 (995) mtallic singl lctron pumps : / δε >> D No control of th mittd stat ULTI Symposium, March 9th., 008

11 injcting lctrons with a msoscopic capacitor V A quantum dot with top-gat quantum point contact ULTI Symposium, March 9th., 008 A V

12 Outlin : th msoscopic capacitor Th linar A conductanc charg rlaxation rsistanc (Büttikr 93) Ralization of a tim controlld singl lctron sourc A currnt quantization ULTI Symposium, March 9th., 008

13 A conductanc of th msoscopic capacitor A I(t ) V G B r l < µm V xc (t ) V G ULTI Symposium, March 9th., 008

14 onductanc quantization of a quantum point contact B r w dg stats quipotntials ULTI Symposium, March 9th., conductanc ( / h ) D Vg ( mv ) Landaur formula : G 0 h n D n

15 Msoscopic capacitor quantum dot Φ π ε z B ˆ V G V G B.3 T ν 4 no spin dgnracy -D transport (dg channl) ULTI Symposium, March 9th., 008 D t K

16 onductanc in th cohrnt rgim QP B r N ( ε ) q F N ( ε F ), dot dnsity of stats harg rlaxation rsistanc IS NOT th Landaur rsistanc! τ n harg h n h rlaxation rsistanc : R q Landaur formula : R L τ n n n D n ULTI Symposium, March 9th., 008 M. Büttikr t al PRL 70 44, PLA80, (993)

17 Finit (low) tmpratur ffct (k B T<<D ) hv k B F T Quantum dot B r Φ π ε Dt V G V G q h N ( ε F ), τ R q q hn ( ε F ) R q indpndnt of ε F, cohrnt rgim R q h ( M.Büttikr t al '93 ) ULTI Symposium, March 9th., 008 D

18 hv k B F T Finit (high) tmpratur ffct (k B T>>D ) Quantum dot B r Φ π ε V G V G k B T >>, q, τ R q q D τ 0 + D R τ 0 + D D R 3 τ h τ D 0 squntial rgim R q h D D h ( S.Nigg t al '08 ) incohrnt rgim R q R L h D ULTI Symposium, March 9th., 008 Dt

19 GX+iY local ULTI Symposium, March 9th., 008 St-up 3 mm 3 cm dc rf

20 omplx conductanc R 0.4 Im( G ) + ( ω R ω ) f.5ghz B.8T Im(G) -R(G) R( G ) ( ) R ω + ( R ω ) R( Im( G G ) ) R ω V G (V) D (transmission) ULTI Symposium, March 9th., 008

21 omplx conductanc R Quantum capacitanc oscillations 0.4 Im( G ) + ( ω R ω ) f.5ghz B.8T Im(G) -R(G) apacitanc platau R( G ) ( ) R ω + ( R ω ) Rlaxation rsistanc R( Im( G G ) ) R ω V G (V) D (transmission) ULTI Symposium, March 9th., 008

22 Half quantization of th charg rlaxation rsistanc Sampl E3 ω/π. GHz -0,85-0,84-0,83 A R q h / µ ff B Sampl E ω/π.085 GHz -0,74-0,7 V G (V) R q h / µ.4 ff Gablli t al Scinc (006) D Im(Z) (h/ ) R(Z) (h/ ) ULTI Symposium, March 9th., 008

23 omparison with D modl µ K K K fit using: D ( V G ) V mv V 0.9 mv ULTI Symposium, March 9th., 008 0,3 0, 0, 0,0-0, -0, 0,0 0,05 0,00-0,05 0,04 0,0 0,00-0, f.5 GHz f 55 MHz data modling f 80 MHz onductanc G ( /h) D ( V ) G V G V V ,9-0,90-0,89 V G (V) Im(G) -R(G) D

24 onclusions on A conductanc. A conductanc brings nw information on cohrnt transport rlatd to th dwll tim of lctrons (Büttikr). harg rlaxation rsistanc IS NOT th Landaur rsistanc 3. harg rlaxation tim τ hn(ε F ) (cohrnt rgim) ULTI Symposium, March 9th., 008

25 th msoscopic capacitor Th linar A conductanc charg rlaxation rsistanc Landaur rsistanc Ralization of a tim controlld singl lctron sourc A currnt quantization ULTI Symposium, March 9th., 008

26 th singl lctron sourc I(t ) V G l < µm V xc (t ) V G ULTI Symposium, March 9th., 008

27 Principl of singl lctron injction + µ / Dot µ B r V(t) QP D Gas V(t) V xc µ + µ ULTI Symposium, March 9th., 008 t

28 Principl of singl lctron injction / QP D Gas µ µ + Dot B r V(t) V(t) V xc µ t ULTI Symposium, March 9th., 008

29 Principl of singl lctron injction mission + QP D Gas µ Dot / µ B r V(t) V(t) V xc µ τ h/ D ( ) τ 00 ps for.5 K and D 0. t ULTI Symposium, March 9th., 008

30 Principl of singl lctron injction / µ µ + Dot V(t) QP D Gas B r V(t) V xc µ τ h/ D ( ) τ 00 ps for.5 K and D 0. t ULTI Symposium, March 9th., 008

31 Principl of singl lctron injction absorption + QP D Gas µ / Dot µ B r V(t) V(t) V xc µ t ULTI Symposium, March 9th., 008

32 Principl of singl lctron injction / µ µ + V(t) Dot QP D Gas B r I(t) dt V(t) V xc µ ( ) I t τ h/ D ( ) t ULTI Symposium, March 9th., 008

33 Dirct tim domain masurmnt (fast acquisition card, f<00 MHz, τ> ns) Bandwidth: GHz V xc µ f 3. 5 MHz Τ 3 ns Sampling tim: 500 ps τ ns Acquisition tim: ~ s Tmps tim (ns) ULTI Symposium, March 9th., 008

34 Exprimnt : tim domain volution of currnt D 0. 0 I (u.a) V xc µ Tmps tim (ns) ULTI Symposium, March 9th., 008

35 Exprimnt : tim domain volution of currnt D 0. 0 I (u.a) xponntial fit V xc µ Tmps tim (ns) τ 09. ns ULTI Symposium, March 9th., 008

36 Exprimnt : tim domain volution of currnt D I (u.a) xponntial fit V xc µ Tmps tim (ns) τ 36. ns ULTI Symposium, March 9th., 008

37 Tim domain volution of currnt D I (u.a) xponntial fit V xc µ Tmps tim (ns) τ 0 ns ULTI Symposium, March 9th., 008 q I( t ) τ t / τ τ h D

38 Frquncy domain masurmnt (homodyn dtction, f>00 MHz, τ< ns) I qf i ωτ << I ω qf, ϕ tan i ωτ ω ϕ 3 f 80 MHz D0. V xc Iω ( f ) 0 0 V xc / ULTI Symposium, March 9th., 008 ωτ t

39 First harmonic of th currnt 3 f 80 MHz D0. V xc Iω ( f ) 0 0 V xc / ULTI Symposium, March 9th., 008 t

40 First harmonic of th currnt 3 f 80 MHz D0. V xc Iω ( f ) q 0 0 V xc / ULTI Symposium, March 9th., 008 t

41 Dot-potntial dpndnc quilibrium potntial : 3 f 80 MHz D 0. Iω ( f ) q 0 0 V xc / ULTI Symposium, March 9th., 008

42 Dot-potntial dpndnc quilibrium potntial : 3 f 80 MHz D 0. Iω ( f ) q 0 0 V xc / ULTI Symposium, March 9th., 008

43 QP transmission dpndnc quilibrium potntial : 3 f 80 MHz D 0.9 Iω ( f ) 0 0 V xc / quantization lost by quantum fluctuations ULTI Symposium, March 9th., 008

44 omparison with D-modl Non linar scattring thory G.Fèv t al Scinc (007) S also : M. Moskalts t al. Phys. Rv. Ltt (008) 3 D 0. D 0.9 Iω ( f ) 0 0 V xc / 0 V xc / No fr paramtr (dducd from linar rgim) ULTI Symposium, March 9th., 008

45 A-currnt quantization diamonds I ω ( f ) Exprimnt : D Modling : Vxc /.5 ULTI Symposium, March 9th., V G (V) G.Fèv t al Scinc (007)

46 Singl lctron mission tim 0 τ (ns) 0, f 55 MHz f 80 MHz Tim domain τ h / D π/ π/4 0 f80 MHz / 3 / φ (rad) τ h D -0,90-0,905-0,900 V G ( V ) Emission tim τ(d) is indpndnt of dot potntial and xcitation amplitud ULTI Symposium, March 9th., 008

47 conclusions ralization of an on-dmand singl lctron sourc mission tim τ h/d is tunnling rat of a singl lvl τ can b controlld in a wid rang from 0. to 0 ns xcllnt agrmnt with a simpl modl charactriz th nois of th mission procss? msoscopic capacitor is a basic and powrful dvic! ULTI Symposium, March 9th., 008