Recher et al, PRB 63, 16531 01

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(No Transcript)
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Recher et al, PRB 63, 16531 (01)
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Spin-entangler

• s-wave SC BCS theory

• (DD) Coulomb blockade coherent tunnel effect
• at resonance ? ?1 ?2 ?S (2 Breit-Wigner)
• tunnel into the same lead supp. by U / ? , U
  Coulomb repulsion

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Regime of interest
Recher et Loss, cond-mat/0205484)

• avoid correlations coherent tunnel
  effect ?l ? ?S same dot transport
  Itotal max. TSD lt TDL vanishing
  occupation proba. of dot levels (DD)
  stationnary occupation small if ?? gt kB T
• (D) spin-flip excluded ground state
  even nb. of e- no e- (leaving,?) ? e-
  (outgoing,-?) if ??gt??gt kB T no hole-e-
  excitations out of F. sea if ?l2??l ?TDL?² lt ??

(1)
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Transport via 1dot and 2 Normal leads

• Transmition probability T(?) ?
  accumulated phase

• strong barrier Lorentzian approximation near
  resonance

• Widening of the level ?

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Transport via 1 dot results

• Linear response small voltage
  Landauer

• Current Coulomb blockade near CGVG/e integer

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Spin-entangler hamiltonian
(2)
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Stationnary current
(3)

• Transition rate

• T-matrix

• initial state igt0gtS0gtD?lgtl and ?i2?S0

• no Kondo effect

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Stationnary current Results
?rr1-r2
? coherence length of a Cooper pair
a) double occupancy with energy 1/U b) excitation
energy in SC ? cost 1/?

• fgt2-1/2(a1p?a2p?a1p?a2p?)igt non-local
  EPR pair
• Tunneling into different lead

? Breit-Wigner resonance when ?1-?2

• Tunneling into same lead

(4)
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Prospects

• suppression factor (E/?)² for I1/I2
• desired regime if (1) E/? gt kF?r and ?r lt ?

• lower-dimensional SC Recher et al, PRB 65,
  165327 (02)
• 2D I1?1/kF?r
• 1D no decay of Andreev amplitude, only
  oscillations.

• exp(-2?r/?) ? power-law for metallic system
  instead of dot.
• Bena et al, PRL 89, 037901 (02)
• Recher et al, cond-mat/0112298 (01)

• exponentional suppression on the scale ? ? meas.
  of ?

• ZERO dephasing so role of gate voltage
  fluctuations ?
• role of dot size ?

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Other entanglers

• s-wave SC 2 LL Recher et al, PRB 65, 165327
  (02)

• voltage lt ? stationnary I

• Interaction in LL-leads ? tunneling only into a
  LL suppressed
• tunnel. of 2e- into ? LL suppressed by ?r
  cf. dim. of the SC (power-law)

• e- no quasiparticle of LL but spin information
  transported via spin density fluctuations