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ABSTRACT Quasiparticle Trapping in Andreev Bound States Maciej Zgirski*, L. Bretheau, Q. Le Masne, H. Pothier, C. Urbina, D. Esteve Quantronics Group,

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Presentation on theme: "ABSTRACT Quasiparticle Trapping in Andreev Bound States Maciej Zgirski*, L. Bretheau, Q. Le Masne, H. Pothier, C. Urbina, D. Esteve Quantronics Group,"— Presentation transcript:

1 ABSTRACT Quasiparticle Trapping in Andreev Bound States Maciej Zgirski*, L. Bretheau, Q. Le Masne, H. Pothier, C. Urbina, D. Esteve Quantronics Group, SPEC, CEA Saclay, France *presently: Institute of Physics, PAN, Warsaw Electron transport through superconducting weak links can be understood in terms of Andreev bound states. They originate from conduction channels with each conduction channel giving rise to two Andreev bound states. In order to get access to single Andreev bound states we have used a system with a few conduction channels at most – quantum point contact. We have studied supercurrent across such a phase-biased atomic size contacts. For broad phase interval around  we have found suppresion of supercurrent – effect attributed to quasiparticle trapping in one of the discrete subgap Andreev bound states formed at the contact. Since single Andreev bound state can sustain supercurrent up to 50nA, such a trapping has a sound influence on the response of the atomic contact. Next to single Cooper-pair devices in which parity of the total number of electrons matters, it is another demonstration of a situation, when a single quasiparticle leaves a macroscopic trace. However, unlike a single Cooper device, atomic contact contains no island at all. The trapped quasiparticles are long-lived, with lifetimes up to hundreds of  s. Trapping occurs essentially when the Andreev energy is smaller than half the superconducting gap . The origin of this sharp energy threshold is presently not understood. PRL,106, (2011)

2 Quasiparticle Trapping in Andreev Bound States Maciej Zgirski*, L. Bretheau, Q. Le Masne, H. Pothier, C. Urbina, D. Esteve Quantronics Group, SPEC, CEA Saclay, France *presently: Institute of Physics, PAN, Warsaw L. Bretheau Q. Le Masne D. Esteve C. Urbina H. Pothier

3 MOTIVATION Josephson effect in superconducting weak links – unified approach Spectroscopy of Andreev Levels Andreev Qubit S SI  S S E(  )  -E A +E A ++ -- 0

4 ANDREEV REFLECTION COUPLING OF e  AND h  S N N-S interface

5 PHASE-BIASED SHORT, BALLISTIC SINGLE CHANNEL L  Fabry-Perot resonator LL RR 1

6 ANDREEV BOUND STATES in a short ballistic channel (  ) Andreev spectrum E(  )  22 ++ -- 0 E→E→ E←E← 2 resonances E ++ -- 0  = 1 LL RR

7 ANDREEV BOUND STATES in a short reflective channel (  ) Furusaki, Tsukada C.W.J. Beenakker (1991) E(  )  -E A +E A ++ -- 0 Andreev spectrum  < 1 Central prediction of the mesoscopic theory of the Josephson effect E ++ -- 0

8 SUPERCONDUCTING WEAK LINKS S SI Tunnel junction: N  infinity  ->0  S S Atomic contact: N ~ 1  < 1 N – number of transmission channels  - transmission Current phase- relation  =  L -  R Weak link = ensamble of independent transmitting channels, each characterized by transmission  (Landauer picture) I ac (  ) = ?

9 FROM ANDREEV BOUND STATES TO SUPERCURRENT E(  )  -E A +E A ++ -- 0 Current-phase relation Ground state :

10 Current – phase relation… …is a probe of a configuration of Andreev bound states E(  )  ++ -- 0

11 TOWARDS ANDREEV QUBITS Chtchelkatchev and Nazarov, PRL (2003) Use quasiparticle (spin ½) states E(  )  -E A +E A ++ -- 0 Zazunov, Shumeiko,Bratus’, Lantz and Wendin, PRL (2003) Use even states

12 ATOMIC CONTACT = SIMPLEST WEAK LINK fabrication & characterization I S S V 1 atom contact = few conduction channels (Al: 3) Stable system Can be completely characterized

13 insulating layer counter- support Flexible substrate metallic film pushing rods MICROFABRICATED BREAK-JUNCTIONS

14 PIN code of the atomic contact Scheer et al. PRL 1997

15 Current bias in not enough…

16 Atomic Squid…

17 …allows to determine channels transmissions… IbIb I V measurement transmissions {  i } OPEN

18 …and impose phase on atomic contact “Strength” of the weak link ~ critical current measurement I JJ >> I AC IbIb  SHORT

19 IbIb V   switching retrapping Switching of the Atomic Squid

20 I b Pulse height V time tptp TrTr N T r =20µs t p =1µs N=5000 usually Switching probability I b (nA) P « s curve » SWITCHING MEASUREMENTS I b (nA) V (µV) Supercurrent branch n

21 Flux Modulation pattern for ATOMIC SQUID = I(  ) of the atomic contact I 0 -switching current of junction alone When SQUID switches, phase across JJ is approx. the same independently of applied magnetic flux => interference pattern is current-phase relation of atomic contact The ground Andreev state is well-known… Theses in Quantronics: M. Chauvin, B. Huard, Q. Le Masne Della Rocca et al., PRL 2007

22 P (I b,  ) A vertical cut is an s-curve P = 0 P = 1 P 1 0 s = I b /I 0 I 0 - critical current of JJ alone Switching probability map with normal leads

23 SAMPLE

24 Sample design antenn a bias line designed to be 50  at T < 1K e-beam lithography

25 T=40mK, Period= 20µs  ={0.95, 0.445, 0.097} Switching probability map with superconducting electrodes j1j1 j2j2 time tptp TrTr N Height of plateau is period dependent => some relaxation going on in the system

26 P 1 (I b ) P 2 (I b ) pP 1 (I b )+(1-p)P 2 (I b ) Switching curve with prepulse After switching, system is where we expect it to be with probability p {0.45, 0.10} {0.95, 0.45, 0.10} Erase memory of the previous history before each measurement: delay ~ 0.1µs 1s1s « prepulse »

27 Blocking the most transmitting channel {0.95, 0.45, 0.10} {0.45, 0.10}

28 QUASIPARTICLES IN A SUPERCONDUCTING POINT CONTACT E  -- 0 Ground state 1-qp states EAEA -E A 2 qps E(  )  ++ -- 0

29 Excitation picture All electrons paired The smallest excitation breaking parity = one unpaired quasiparticle Excited Cooper pair

30 Two scenarios QP E n QP E n QP Weight = p Weight = 1 - p Channel switched off Channel switched on Switching probability is the weighted average of these 2 scenarios. Initial state

31 Modulation curves on different contacts {1,0.7,0.24,0.24,0.06} AC3 {1,0.072,0.072} AC1 {0.998,0.56,0.124} AC2 The most transmitting channel is sometimes switched off

32 1QP STATE RELAXATION MEASUREMENTS Current line waiting time 0 IbIb T R (  ) P inf (  ) Flux line ii ww  Phase across contact ii

33 A few 100  s relaxation time T=29mK Symmetry around  Monotonous behaviour {1,0.07,0.07} -0.6    phase across atomic contact

34 T=29mK Relaxation as a function of phase across Atomic Contact for different transmissions

35 Energy threshold for relaxation E(  )  E-E- 22  ++ -- 0 Relaxation instantaneous only for Andreev Bound states with energies bigger than 0.5  ~25GHz ~1K

36 Energy threshold for relaxation E n QP E  /2  WHY?

37 Possible explanation E n QP E  /2  h ~  /2 h

38 Conclusions Atomic contacts with tunable transmissions Atomic Squid to measure current-phase relation of atomic contact with switching measurements - for ground Andreev bound states excellent agreement with theory No evidence of excited Andreev state in 2 different experiments (switching measurements, coupling to resonator ) Quasiparticle poisoning => disappearence of the most transmitting channel; long relaxation for Andreev Cooper pair binding energies smaller than 0.5  sharp cut off for binding energies bigger than 0.5  Dispersive measurements of resonant frequency of resonator + atomic squid Trials to observe avoided level crossing (atomic contact embedded in resonator) Current Status: Josephson Junction spectroscopy of Atomic Squid – observed avoided level crossing PLASMA FREQUENCY – ANDREEV GAP

39 {1,0.07,0.07} Temperature dependence

40 Does excited Andreev state exist? (OPTIONAL)

41 Sample design antenn a bias line designed to be 50  at T < 1K e-beam lithography

42 Capacitor + inductive lines inductive lines, 900nm wide, nm thick Al 680µm 10µm gap 140µ m antenna (5µm wide short of CPW) Capacitor C = 60 pF L total = 1.8nH Andreevmon (or Andreevnium)

43 Electromagnetic environment is important

44 Trials to observe excited Andreev state Peak position is frequency- dependent I  Expected

45 Andreev Qubit in cavity Weak coupling

46 strong coupling regime V AC in V AC out Cavity Quantum Electrodynamics

47 Let 2 level system interact with resonator avoided level crossing Coherent exchange of energy between resonator and artificial atom Andreev Gap Bare Resonator eigenfrequency Interaction “on” Interaction “off” Red – expected position of resonance

48 {0.95, 0.94, 0.60, 0.34, 0.30, 0.29, 0.27, 0.26, 0.24, 0.2} 2 CHANNELS POISONING

49 {0.957, 0.948, 0.601, 0.344, 0.295, 0.291, 0.27, 0.262, 0.242, 0.2} Pollution of 2 channels All channels 2 channels blocked 1 channel blocked 49/19

50 Atomic SQUID in cavity

51 Flux pulse cleans excited Andreev state Flux line V flux big enough Current line period delay RF line

52 MULTIPLE CHARGE TRANSFER PROCESSES Blonder, Tinkham, Klapwijk (‘82) 2  / 12  / 22  / 3 V I  S S 52/19

53 S S Atomic contact few channels, {  i } tunable Al film ΔxΔx pushing rod counter- support Elastic substrate ΔzΔz {  i } measurable 53/19

54 QUASIPARTICLES IN A BULK SUPERCONDUCTOR E  -- 0 Ground state 1-qp states 2 qps

55 QUASIPARTICLES AND SUPERCURRENT IN A SUPERCONDUCTING POINT CONTACT E(  )  ++ -- 0 Lowest-lying 1-qp excitationsGround state1-qp stateExcited singlet

56 CORRELATED SWITCHING EVENTS V(t)  Need a ‘’reset’’ between pulses

57 V(t) MEASURING THE SWITCHING PROBABILITY 1µs sI0sI0 meas t hold V b (t)/R b

58 V(t) MEASURING THE SWITCHING PROBABILITY tt 1µs 1.3 sI 0 sI0sI0 prepulse (reset) meas t hold V b (t)/R b  Uncorrelated switching events

59 QP Reaching 1QP odd state Ground state 1QP state (x2) 2QP state for Al E n QP

60 RELAXATION VERSUS ANDREEV ENERGY


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