SMR/ JOINT ICTP-INFM SCHOOL/WORKSHOP ON "ENTANGLEMENT AT THE NANOSCALE" (28 October - 8 November 2002)

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1 ii-i ii \,s:s: ^"n the abdus salam international centre for theoretical physics SMR/ JOINT ICTP-INFM SCHOOL/WORKSHOP ON "ENTANGLEMENT AT THE NANOSCALE" (28 October - 8 November 2002) "Adiabatic charge transport in arrays of Josephson junctions and the Cooper pair pump " presented by: J. Pekola Helsinki University of Technology Finland strada costiera. I I triesie italy - tel I I fax sc!_info@ictp. trieste.it -

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3 Adiabatic charge transport in arrays of Josephson junctions and the Cooper pair pump Jukka Pekola, Helsinki University of Technology, Finland with Jussi Toppari and Matias Aunola, University of Jyvaskyla, Finland Dmitri Averin (SUNY), Rosario Fazio (Pisa), Frank Hekking (UJF Grenoble)

4 Contents 1. Controlled charge transport in various systems 2. Focus on Josephson arrays and pumps 3. Adiabatic transport 4. Measurement of current 5. Experimental issues

5 Pumping of single electrons in a 3-junction pump c H. Pothier, P. Lafarge, C. Urbina, D. Esteve, M. Devoret, EPL 17,249 (1992).

6 Metrological charge pump of electron counting using a T-junction W, Kei;ter J»n«8 John IV1- iviriinfe Andrew R Stelnb-achr'.ISLAND -si ff f.: 10" O A ^ JrJr.r.rl.... <*-->^->^ S " HI Tune»:s) Appl. Phys. Lett. 69,1804 (1996). $jij : A -

7 Surface acoustic wave (SAW) driven I = ef J. Shilton et al., J. Phys. C 8, L531 (1996). V. Talyanskii et al., PRB 56,15180 (1997). J. Cunningham et al., PRB 62,1654 (2000). A. Robinson et al., PRB 65, (2002). J. Pekola et al, PRB 50,11255 (1994).

8 3 junction CPP V Irn L. Geerligs et al., Z. Phys. B: Condensed Matter 85,349 (1991).

9 Adiabatic manipulation of Cooper pairs in arrays of JJs fs r4p fa ta ra fs i* SJR-:./Wvf WW jmuwv.i.awj«^aiw 5 f i c c ( W... ^ Adiabatic quantum computing, D. Averin (1998). Topologically stable Josephson qubits, Ioffe, Feigelman (2002). Cooper pair manipulations in geometric qubits, Catania group (2000-).

10 Coherent and incoherent Cooper pair pumping 1. Ideal coherent and incoherent (adiabatic) pumping 2. Phase fluctuations in dissipative environment 3. Inductance limited phase fluctuations

11 Coherent vs incoherent Cooper pair pumping R-pump, R»R Q Coherent pump S. Lotkhov, S. Bogoslovsky, A. Zorin, J. Niemeyer, APL 78, 946 (2001).

12 Why Cooper pair pump? 1. New experimental method to measure dissipation and decoherence 2. Multi-gate control of multi-junction qubits 3. Metrological applications 10

13 Charging energy 11

14 Experimental determination of the gate dependences J. Toppari et al, unpublished 12

15 Adiabatic transport of Cooper pairs If the Hamiltonian of the system varies slowly enough, we may study its behaviour using the adiabatic approximation of quantum mechanics. ;*,.. -'ntwtnjnwtwr. varies due to gate operations QF rri jinn F F \n rn u (m = Q for transport in the ground state) J. Pekola, J. Toppari, M. Aunola, M. Savolainen, D. Averin, PRB 60, 9931 (1999). 13

16 Adiabatic transport in a Cooper pair box Wrdql (The same result can be seen directly from the composition of the ground state!) 14

17 Coherent adiabatic CPP, basic results p _ p I p /(2ef) = 1 - (triangular path) 15

18 Cooper pair trap As a CPP, but instead of the third JJ there is a (classical) capacitor 16

19 Adiabatic transport vs. Landau-Zener band-crossing Adiabatic approximation is valid, if Band-crossing (LZ) becomes important, if this condition is violated. For periodic gate operation this happens at fxj G: 17

20 Phase fluctuations due to environment Simple idea: Determine the fluctuations of cp (in real time). J. Pekola and J. Toppari, PRB 64, (2001). If<(Acp) 2 > «coherent If<(Acp) 2 >» incoherent (JT/2) 2, pumping is (JT/2) 2, pumping is In the latter case: 18

21 Pumping regimes determined by Landau-Zener bandcrossing and decoherence 19

22 Phase fluctuations due to environment FDT: n a) x 1 coth \2kR T, [cos 20

23 * Phase fluctuations: results in resistive environment r=o T>0 In \ + y. 1 <(A(p) 2 > = (K/2) 2 at / = 21

24 Measurement schemes to avoid phase fluctuations? mmmmmmm Measuring current SQUID ammeter? 22

25 1 SQUID amplifier or escape junction Current measurement by: (a) SQUID amplifier (b) Biased Josephson junction ! ' ', 1 I [ [ 1 [ [ ^ [ [! ^ f [ \ vto ( A/e Uech (mv) F. Balestro, O. Buisson et al., Grenoble 23

26 Circuit models of SQUID amplifier and escape measurement 24

27 Inductance limited dephasing (underdamped case) Fazio, Hekking, Pekola, unpublished (2002) 25

28 Inductance limited dephasing (overdamped case) 26

29 Parameters of the planned measurement Pumping frequency <100 MHz, current <30 pa (aluminium) Niobium would allow > 1 GHz and > 0.3 na (?) Measurement bandwidth > 1MHz 27

30 Experiments on Nb structures N. Kim, J. Toppari, L. Taskinen, S. Paraoanu, K. Hansen, J. P. m ' two ;arrg!e. evaporation- UbiAlOJAl Dotataefsi.APL(2002) 28

31 Metallisation set-up a vacuum p\ - dun h Cm; 29

32 Nb-wires Kfcrn el a!.. JVSTS 20, 3&S #002"! 3" i\ 8-5 S.O 7.S 7,

33 Nb-SSETs mmm iiiiiiiiiiii^ 1! lliilii i ^M! fc l i \ \ 1 ; 1 I! HI Hi HI ni «ilill i;s!!is;lili;is;!ii;i:li; 1 i H n 1 Ml ::;;;;;; m \ \ \:;; mi m *2oo ;.;;: -IS -10»S V(mV) 31