Quantum Electron Optics Electron Entanglement

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Quantum Electron Optics Electron Entanglement Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Quantum Electron Optics and Electron Entanglement Na Young Kim (Stanford, AP) Manuel Aranzana (ENS) William D. Oliver (Stanford, EE) Leo Di Carlo (Harvard) Fumiko Yamaguchi (Stanford, AP/EE) Gwendal Feve (ENS) Yoshihisa Yamamoto (Stanford, AP/EE) Jungsang Kim (Lucent) Robert Liu (UCSF) Jing Kong (Stanford, Chem) Xavier Maitre (CNRS) Hongjie Dai (Stanford, Chem)

Electron Entanglement via a Quantum Dot Single electron tunneling suppressed by energy conservation EL = ER1 = ER2 Two-electron virtual tunneling is allowed EL1 + EL2 = ER1 + ER2 Only singlet-state remains at output: indistinguishability and Fermi statistics including Pauli Exclusion Principle Non-linearity: Coulomb charging energy U Optical analogy: Chi-(3) four-wave mixing process L R2 R1 VL VR1 VR2 ER1 Ed U ER2 X EL1 EL2 W. D. Oliver et al., PRL 88, 037901 (2002)

Noise Suppression in Carbon Nanotubes Experimental Fano factor (noise suppresion) LED/PD CNT 200 nm SWCNT R = 17.4 kW 400 800 1200 1600 I PD (nA) , 50 150 200 250 S (arb. units) SCNT = 0.17 (2eI) Elastic scattering: 1-T (transparent contacts) ST = 2eI(1-T) = 0.63 (2eI) Remainder of suppression: LL parameter g S = 2e*IB = 2 (ge) I(1-T) = g (1-T) 2eI g, elastic scattering yield noise suppression CNT: g = 0.2 ~ 0.3 theory, g = 0.28 expt SCNT = g(1-T) 2eI= 0.17 (2eI)

Integrated CNT / SC Structures for Electron Entanglement CNT as a quantum dot (0D) structure ~20 nm Easy to make strong tunnel barriers Strong confinement w/out surface depletion effect Very small CNT quantum dot entangler CNT as a quantum wire (1D) structure “Ideal” 1D channel, minimize intermode coupling Reduced scattering phase space (cf., 2D leads) “interconnect” with long mean free path (?) Caveat: LL quasi-particle not free electron (cf., Fermi Liquid) collective excitation (CDW, SDW) TBD: how does this effect entanglement ?? CNT as 0D and 1D structure “Kinks”, CNT overlap, AFM tip, etc. create tunnel barrier

Future Directions Theory of regulated entangled pair generation “unitary limit” of conductance with resonant biasing ….. “natural regulation” turnstile-like operation ….. “engineered regulation” Luttinger Liquid theory Experimental demonstration of electron entangler Integrated semiconductor / CNT structure Bunching / Anti-bunching experiment Noise Properties of the 0.7 Structure HBT-type Experiment: shows noise suppression one channel in unitary limit one channel partially conducting Collision experiment: spin polarized vs. unpolarized 0.8 -0.1 -0.2 0.6 3 1 2 4 -0.3 Conductance (G/GQ) Normalized xcov 0.4 -0.4 -0.5 0.2 -0.6 -0.7 -2.9 -2.8 -2.7 -2.6 -2.5 Gate Voltage (V)