Cooper-pair splitter: towards an efficient source of spin-entangled EPR pairs

Transcription

1 Cooper-pair splitter: towards an efficient source of spin-entangled EPR pairs L. Hofstetter 1, A. Kleine 1, S. Csonka 1,2, A. Geresdi 2, M. Aagesen 3, J. Nygard 3, A. Baumgartner 1, J. Trbovic 1, and C. Schönenberger 1 Department of Physics, University of Basel, Klingelbergstr. 82, CH 4056, Basel, Switzerland 2 Department of Physics, Budapest University of Technology and Economics, Budafoki u. 6, 1111 Budapest, Hungary 3 Nano Science Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK 2100 Copenhagen, Denmark. HYSWITCH Hanbury-Brown and Twiss (HBT) Australia Radio stars: R. Hanbury Brown and R. Q. Twiss, "A New Type of Interferometer for Use in Radio Astronomy", Philosophical Magazine (7) 45 p663 (1954) Optical:R. Hanbury Brown and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius", Nature 178 p1046 (1956)

2 bunching / antibunching C = > 0 photons < 0 electrons bunching anti-bunching bunching / antibunching C = > 0 photons < 0 electrons bunching anti-bunching M. Henny et al. Science 284, 296 (1999) it depends on the statistics

3 HBT and particle statistics C = Δn T Δn R Δn 2 n fluctuations particle nature sub- Poissonian C < 0 Δn 2 < n Poissonian C = 0 Δn 2 = n super- Poissonian C > 0 Δn 2 > n Photons can antibunch nitrogen-vacancy in diamond (no bleaching)

4 bunching / antibunching C = > 0 photons < 0 electrons bunching anti-bunching it depends on the statistics if photons may antibunch... can one make electrons to bunch? Andreev entangler Due to the Pauli principle: no double occupancy for Fermions (no bunching possible like it is for photons) Simultaneous emission of two electrons, for example from a superconductor: S S I Ψ 1 e e Ψ 2 [ Ψ 1) Ψ (2) + Ψ (1) Ψ (2)] (, ) Ψ =, 1( Cooper pair: spin singlet electron pair (naturally entangled pair) source of mobile entangled EPR electron pairs

5 Entanglement and EPR pairs point of origin Entanglers (EPR source) 2 entangled photons by parametric down conversion Kwiat et al., PRL 75, p4337 (95)

6 Entanglers (EPR source) electronic control, hence: possible on demand Nature 465, p594 (2010) EPR source in spin-based qubits D. Loss and D. P. DiVincenzo, "Quantum computation with quantum dots", Phys. Rev. A 57, p120 (1998) Loss-DiVincenzo quantum computer

7 Spin-based solid-state realization III-V semiconductors carbon nanotubes AFM from QT Delft H=p+e M. Gräber et al. Uni Basel graphene like chemical bonds Liu, Hug, Vandensypen EPR source in spin-based qubits e.g. double dot

8 Andreev entangler S S Ψ 1 e I e Ψ 2 [ Ψ 1) Ψ (2) + Ψ (1) Ψ (2)] (, ) Ψ =, 1( Cooper pair: spin singlet electron pair (naturally entangled pair) source of mobile entangled electrons (flying qubits) Andreev entangler (2001) Eropean Phys. J. (2001)

9 Andreev entangler P. Recher, E.V. Sukhorukov, and D. Loss, Phys. Rev. B 63, (2001) N. M. Chtchelkatchev et al. Phys. Rev. B 66, (2002) P. Recher and D. Loss, Phys. Rev. B 65, (2002) C. Bena, S.Vishveshwara et al. PRL 89, (2002) O. Sauret, D. Feinberg, T. Martin PRB 70, (2004) Efficient and controlled pair splitting? exploit Coulomb interaction Charging energy prohibits direct pair tunneling Andreev source for HBT experiment S S I Ψ 1 e e Ψ 2 Radio stars: R. Hanbury Brown and R. Q. Twiss, "A New Type of Interferometer for Use in Radio Astronomy", Philosophical Magazine (7) 45 p663 (1954)

10 Andreev entangler? C C = h I 1 I 2 i B. R.Choi et al., Phys. Rev. B (2005) Andreev entangler? Lukas Hofstetter and Stefan Oberholzer, unpublished P.Samuelson and M.Büttiker, PRL and PRB (2002)

11 Nonlocal Andreev reflection Russo et al.; Phys. Rev. Lett. 95, (2005) three-terminal CAR = crossed Andreev reflection Beckmann et al.; PRL 93, (2004) inj-det distance: 310nm CAR Deutscher and Feinberg, APL 76 (2000) local Andreev reflection non-local Andreev = crossed Andreev reflections Nonlocal differential resistance: R nl =U nl,ac /I loc,ac

12 Competing nonlocal subgap processes Crossed Andreev reflection (CAR) R nl <0 ΔQ S =-2e G 12 ~e -d/ξ Elastic cotunneling (EC) R nl >0 ΔQ S =0 G 12 ~e -d/ξ Nonlocal charge imbalance (CI): ρ* Diffusion of quasiparticles R nl >0 -e < ΔQ < 0 N2 d N1 CAR in the literature: Theory: CAR and EC are of similar strength and tend to compensate each other: - CAR and EC exactly cancel in lowest order tunneling [Falci et al., Europhys. Lett. 54, 255 (2001)] - EC dominates CAR [e.g. Mélin et al.; PRB 70, (2004)] - CAR can dominate EC: interactions [Levi Yeyati et al., Nature Phys. 3, 455 (2007); Futterer et al., Phys. Rev. B (2009); Golubev and Zaikin, arxiv: v1 (2009)]

13 CAR experiments Elastic cotunneling (EC) V nl > 0 R nl > 0 Russo et al.; Phys. Rev. Lett. 95, (2005) Crossed Andreev reflection (CAR) V nl < 0 R nl < 0 Conclusions: low bias: EC dominant high bias: CAR dominant Possible explanation: Levi Yeyati et al., Nature Phys. 3, 455 (2007) Samples - supercond. (S): 50 nm Al - barrier: AlO x - normal (N): 40 nm Pd A. Kleine et al. (2008)

14 Sample A K 0.4K 2 R nl [Ω] U dc [mv] R inj [kω] 0.39 R det [kω] 0.51 A. Kleine et al., EPL, 87 (2009) Sample A R nl [Ω] K 0.4K 0.8K 0.9K 1.05K 1.6K at zero bias: U dc [mv] R inj [kω] 0.39 R det [kω] 0.51 crossed Andreev reflection + charge imbalance A. Kleine et al., EPL, 87 (2009) 27011

15 Sample B K 0.8K 1.6K R nl [Ω] U dc [mv] R inj [kω] 0.80 R det [kω] 5.51 at zero bias: crossed Andreev reflection + elastic cotunneling A. Kleine et al., EPL, 87 (2009) Sample C R nl [Ω] K 0.4K K 1.6K U dc [mv] at zero bias: elastic cotunneling R inj [kω] 2.60 R det [kω] A. Kleine et al., EPL, 87 (2009) 27011

16 Comparing the curve shapes T=230 mk 3 2 Sample A Sample B Sample C CAR 3 2 CAR+EC EC R nl [Ω] U dc [mv] R nl [Ω] U dc [mv] R nl [Ω] U dc [mv] A. Kleine et al., EPL, 87 (2009) observations: sample A: R nl <0 in gap, increase with T R nl [Ω] sample C: R nl >0 for U 0, rest of gap: R nl <0 All signals reduced with T EC T [K] U dc =0 What determines the shape? 3 2 Sample A Sample B Sample C CAR 3 2 CAR+EC EC R nl [Ω] U dc [mv] R nl [Ω] U dc [mv] R nl [Ω] U dc [mv] A B C l [nm] ξ [nm] R inj [kω] R det [kω] d [nm] A inj *R inj, A det *R det [Ωμm 2 ] 8.5, , , (RA det -RA inj )/(RA det +RA inj )

17 Dynamical CB favors EC over CAR Crossed Andreev reflection (CAR) R nl <0 ΔQ S =2e Elastic co-tunneling (EC) R nl >0 ΔQ S =0 P(E) theory Conclusion there is CAR to some degree CAR can even dominate sub-gap transport in some window of contact resistances EC dominates CAR in devices with higher contact resistances (at zero bias) BUT: control over tunneling resistance is very difficult can one do better?

18 Andreev entangler (2001) Cooper pair splitter S... D1 gate gate 1 gate gate 2 D2 Ψ = [ Ψ 1) Ψ (2) + Ψ (1) Ψ (2)] (,, ) 1( 2 2 1

19 Measurement principle and device sensing gate V SG V ac V TG tuning gate S I S I T S-electrode connected to two tunable qdots InAs nanowire d 80nm superconductor (Ti/Al), w 150nm top gates: Ti/Au with surface oxide 2 InAs NW qdots separately tuned by top gates (V SG and V TG ) I/V sensing qdot tuning qdot I/V G=I S S /V ac G=I/V T T ac G nonlocal (V TG ) = G S (V TG ) -(α+βv TG ) NONLOCAL MEASUREMENT: current measurement of sensing qdot while sweeping the gate of the tuning qdot Cooper pair splitting contributes to I S depends on sensing QD and tuning QD Explanation Regime: U >> Δ >> T; ε >> Δ, Γ << Δ; ξ w S Transport happens in pairs of electrons Cooper pair splitting CPS Direct pair tunneling DPT Direct pair tunneling DPT

20 Explanation Simple non-interacting tunneling picture (T i <<1) I S = I DPT + I CPS /2 T S T T I DPT ~ T S T S I CPS ~ T S T T G Nonlocal ~ T T Measurement principle and device V sd [mv] GS (G0) GS (G0) V SG SG [V] (mv) V SG (mv) G S [G 0 ] V TG (mv) quantum dot with U 2-4meV, ε 1meV clear subgap feature, gap visible, Δ 160μV very weak ( 1/1000) cross capacitance cross capacitance = ΔV SG /ΔV TG ; ΔG S (ΔV SG ) = ΔG S (ΔV TG )

21 Measurement principle and device V sd [mv] GS (G0) GS (G0) V SG SG [V] (mv) V SG (mv) G S [G 0 ] V TG (mv) clear subgap feature, gap visible, Δ 160μV very weak ( 1/1000) cross capacitance averaging (~10 2 ) necessary to make signal visible Results G Nonlocal [10-3 G 0 ] GT [G 0 ] V TG [V] 0.0 Coulomb blockade peaks through green tuning qdot positive nonlocal signal through red sensing qdot while sweeping tuning qdot

22 Classical expectation V ac V R 200 Ω R 200 Ω S I 1 R 1 R 2 I 2 G 1 :=I 1 /V G 2 :=I 2 /V I S sensing arm 1 MΩ 200 Ω tuning arm 200 Ω I T 1 MΩ δg 2 > 0 δg 1 < 0 δg R 1 δg2 R1 resistive cross-talk is negative (as expected for charge conversation) I/V G S =I S /V ac G T =I T /V ac I/V Results B = 120mT G Nonlocal [G 0 ] B = 0mT GT [G 0 ] Current in sensor dot (I S ): positive non local signal while sweeping the V TG at B = 0! B > B c signal changes sign and corresponds to the classical circuit response (no fitting parameters) V TG [V] 0.0

23 Results B = 120mT G Nonlocal [G 0 ] B = 0mT GT [G 0 ] Current in sensor dot (I S ): positive non local signal while sweeping the V TG at B = 0! B > B c signal changes sign and corresponds to the classical circuit response (no fitting parameters) V TG [V] 0.0 Results non local signal vanishes at ~ 200mK but superconducting gap still visible up to 600mK (T C = 1.2 K) T dependence on top, left and right side of sensing qdot s Coulomb blockade peak monotonous decay of the nonlocal signal with T L. Hofstetter, S. Csonka, J. Nygard, and C. Schönenberger, Cooper pair splitter realized in a two-quantum-dot Y-junction, Nature 460, 906 (2009).

24 Results V TG [V] V TG [V] G T [G 0 ] G Nonlocal [G 0 ] the sign of the non-local signal depends on the state of the sensing qdot: dot sensing out of resonance: G Nonlocal [G 0 ] GS [G 0 ] G Nonlocal follows G T Cooper pair splitting dot sensing in resonance: classical V TG [V] V SG [V] 0.0 filtering of DPT is not efficient reproduced with 3 samples B = 0 T

25 reproduced with 3 samples Discussion Efficiency of Pair Splitting δr ΔG Nonlocal /(G S +G T ) a few %... 10% why? L. Hofstetter, S. Csonka, J. Nygard, and C. Schönenberger, Cooper pair splitter realized in a two-quantum-dot Y-junction, Nature 460, 906 (2009). L.G. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, and C. Strunk, Carbon Nanotubes as Cooper Pair Beam Splitters, Phys. Rev. Lett. 104, p (2010) C. Strunk, Nature Nanotechnology 5, (2009).

26 Discussion Efficiency of Pair Splitting δr ΔG Nonlocal /(G S +G T ) a few %... 10% why? important paparmeters: ΔE, U, Δ, Γ as well as δr I CPS ~ p(δr): electrons tunnel at distance δr p(δr) ~ [sin(k F δr)/(k F δr)] 2 exp(-δr/ξ) (ball. limit) p(δr) ~ 1/(k F δr) 1/k F l exp(-δr/ξ) (diff. limit) λ F =3.5Å, l=5nm δr =150nm, ~ Recher et al. PRB, 63, (2001), D. Feinberg Eur. Phys. J. B 36, 419 (2003) Outlook: lower gamma

27 Outlook: finite bias Recher et al. PRB, 63, (2001) Outlook: entanglement detection spin entanglement detected via orbital (charge) degrees of freedom probing symmetry of orbital wave-function by current noise measurements C = h I 1 I 2 i bunch (+) for S anti-bunch (-) for T G.Burkhard, D.Loss,E.V.Sukhorukov, PRB 61, R16303 (2000) P. Recher, E. V. Sukhorukov, and D. Loss, PRB 63, (2001). P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, PRB 70, (2004)

28 Outlook: entanglement detection 1 μm N1 SG1 N QD S QD QD1 SC1 SC2 QD2 SG2 N2 N/F N/F going to carbon nanotubes... Aharonov-Bohm effect in CNT loops? Thanks to... Lukas Hofstetter Andreas Kleine Jelena Trbovic Andreas Baumgartner Jens Schindele Hagen Aurich Scabolcs Csonka Attila Geresdi Jesper Nygard Martin Aagesen