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Positive Electronic Cross-Correlations in a Highly Transparent Normal-Superconducting Beam Splitter Rgis Mlin, Institut NEL, Grenoble May 24, 2012

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Positive Electronic Cross-Correlations in a Highly Transparent Normal-Superconducting Beam Splitter

Régis Mélin, Institut NÉEL, Grenoble May 24, 2012

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Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Introduction

Condensed matter theory

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Introduction

Condensed matter theory Proposal and interpretation of experiments

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

SLIDE 4

Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

SLIDE 5

Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity Long term goal is to realize devices based on electronic entanglement

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

SLIDE 6

Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity Long term goal is to realize devices based on electronic entanglement All Hamiltonians are quadratic

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity Long term goal is to realize devices based on electronic entanglement All Hamiltonians are quadratic Ballistic (localizing effects of disorder treated qualitatively)

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity Long term goal is to realize devices based on electronic entanglement All Hamiltonians are quadratic Ballistic (localizing effects of disorder treated qualitatively) Technical difficulty: Calculation of nonequilibrium transport properties (current and noise), even for strong nonequilibrium

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity Long term goal is to realize devices based on electronic entanglement All Hamiltonians are quadratic Ballistic (localizing effects of disorder treated qualitatively) Technical difficulty: Calculation of nonequilibrium transport properties (current and noise), even for strong nonequilibrium All considered systems are solvable:

Two types of methods:

Scattering calculations (wave-function approach) Non equilibrium microscopic Green’s functions

Two types of solutions

Exact analytical expressions Numerical calculations = very small error-bars

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

SLIDE 10

Introduction

Condensed matter theory Proposal and interpretation of experiments Field of nanoscale superconductivity Long term goal is to realize devices based on electronic entanglement All Hamiltonians are quadratic Ballistic (localizing effects of disorder treated qualitatively) Technical difficulty: Calculation of nonequilibrium transport properties (current and noise), even for strong nonequilibrium All considered systems are solvable:

Two types of methods:

Scattering calculations (wave-function approach) Non equilibrium microscopic Green’s functions

Two types of solutions

Exact analytical expressions Numerical calculations = very small error-bars

Physical difficulty: Often, interpretation comes at the end, as for experiments → sometimes, surprises and nontrivial effects

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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SN Junction: Andreev Reflection (1/2)

e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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SN Junction: Andreev Reflection (2/2) e e h e S N I V x y

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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SN Junction: Nonlocal Andreev Reflection (1/3) e e S N I V h e y x

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Nonlocal Andreev Reflection (2/3) e e S N I V e h x y

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Nonlocal Andreev Reflection ≡ Cooper Pair Splitting (3/3)

Three-terminal set-up required in experiments Quest: Manipulation of spatially separated spin-entangled pairs of electron

First theoretical contributions: Byers-Flatté, Martin, Anatram-Datta, Deutscher-Feinberg, Falci-Hekking, Choi-Bruder-Loss, Mélin

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Highly Transparent Contacts (Chandrasekhar group, North-Western University, PRL ’06) High values of interface transparency

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Highly Transparent Contacts (Chandrasekhar group, North-Western University, PRL ’06) Yes or no is it a way to obtain a massive signal for separated pairs ?

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Highly Transparent Contacts (Chandrasekhar group, North-Western University, PRL ’06) Yes or no is it a way to obtain a massive signal for separated pairs ? Answer is no: Experimental signal not controlled by Cooper pair splitting

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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ANR PNANO Elec-EPR (2008-2011): The Noise

Lefloch / Courtois experiment, PRL 2011 Incoherent SNSNS SQUID-based amplifiers CEA-Grenoble / NEEL Current noise Sa,a and current noise cross-correlations Sa,b Sa,a(t′) = δˆ Ia(t + t′)δˆ Ia(t) and Sa,b(t′) = δˆ Ia(t + t′)δˆ Ib(t)

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Race to Positive Current-Current Cross-Correlations: Example of Exact Analytical Solution Collaboration with Martina Flöser Axel Freyn

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Small transparency Cooper pair splitting ⇒ Positive current-current cross-correlations

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Small transparency Cooper pair splitting ⇒ Positive current-current cross-correlations Common wisdom for all transparency Positive current-current cross-correlations ⇒ Cooper pair splitting

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Small transparency Cooper pair splitting ⇒ Positive current-current cross-correlations Common wisdom for all transparency Positive current-current cross-correlations ⇒ Cooper pair splitting What we have shown at high transparency Positive current-current cross-correlations Cooper pair splitting

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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The method (Blonder, Tinkham, Klapwijk PRB 1982)

δ V(x)=H (x) N S Spin−up electron Spin−down hole Spin−up electron

One-dimensional geometry Two-component wave-functions for electrons and holes Matching of ψ(x) and ∂ψ(x)/∂x at the interfaces Below the gap:

Evanescent wave-functions in S + response linear in voltage Current is conserved: quasi-particles converted as pairs

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Wave-function matching for a NSN structure

δ V(x)=H (x)

b a

V(x)=H (x) δ Na Nb S ξ R spin−down hole spin−up electron spin−up electron spin−down hole spin−up electron

Calculation of the s-matrix Asumption: applied voltages small compared to the gap ⇒ Evanescent wave-functions in S Mimicking a multichannel 3D junction with a 1D systems ⇒ averaging over λF oscillations in 1D model Analytic expression for the average Sa,b = δˆ Iaδˆ Ib at arbitrary transparency ⇒ Sa,b > 0 at high transparency without Cooper pair splitting Unusual sign due to exchange of two fermions

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ?

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ? Probing entanglement at high transparency ?

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ? Probing entanglement at high transparency ? Presumably NO in spite of positive cross-correlations (absence of Cooper pair splitting)

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ? Probing entanglement at high transparency ? Presumably NO in spite of positive cross-correlations (absence of Cooper pair splitting) Probing entanglement at moderate of interface transparency ?

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ? Probing entanglement at high transparency ? Presumably NO in spite of positive cross-correlations (absence of Cooper pair splitting) Probing entanglement at moderate of interface transparency ? Answer is NO (absence of positive cross-correlations)

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ? Probing entanglement at high transparency ? Presumably NO in spite of positive cross-correlations (absence of Cooper pair splitting) Probing entanglement at moderate of interface transparency ? Answer is NO (absence of positive cross-correlations) Probing entanglement for tunnel contacts ?

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (1/2): Present-time status of entanglement in NSN

What is the value of interface transparency for probing entanglement ? Probing entanglement at high transparency ? Presumably NO in spite of positive cross-correlations (absence of Cooper pair splitting) Probing entanglement at moderate of interface transparency ? Answer is NO (absence of positive cross-correlations) Probing entanglement for tunnel contacts ? Simple theoretical anwser is YES (Cooper pair splitting) ... But simple perturbation theory contradicted by experiments (Delft, Karlsruhe, Northwestern University)

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter

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Conclusion (2/2)

NSN structures should be abandoned in order to produce entangled pairs of electrons Three promising directions:

N-dot-S-dot-N (production of split pairs) S-N-S-N-S (production of nonlocal pairs of pairs) S-dot-S-dot-S (production of nonlocal pairs of pairs)

Régis Mélin Positive Cross-Correlations in a NSN Beam Splitter