Quantum Entanglement in Superconducting Beamsplitters

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15 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

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Quantum
Entanglement

in
Superconducting

Beamsplitters

Henning Soller

Capri, 16.4.2012

Definition
of

Entanglement

The
state

of

the

system

cannot

be

written

as

a
product

state
.

R. F. Werner, Phys.
Rev
. A
40,
4277, 1989

J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev.
108
,1175 (1957)

spin

states

ground

state

of

BCS
superconductor

L. Hofstetter, S.
Csonka
, J.
Nygard
,
and

C. Schönenberger
,

Nature
461
, 960, 2009

L. Herrmann, F. Portier, P. Roche, A. Levy
Yeyati
, T. Kontos,
and

C. Strunk Phys.
Rev
.
Lett
.
104
, 026801, 2010

L. Hofstetter, S.
Csonka
, A. Baumgartner, G.
Fülöp
, S.
d’Hollosy
, J.
Nygård
,
and

C. Schönenberger

Phys.
Rev
.
Lett
.

107,
136801
,
2011

J. Wei
and

V. Chandrasekhar Nature
Physics

6, 494

498 (2010)



C. Schönenberger, Physik in

unserer Zeit
2
, 58
-
59, 2010

How

to

detect
?

Result
:

Result
:

Now

let

us

consider

just tunnel
contacts
:

A. Di Lorenzo and Yu. V.
Nazarov
, Phys. Rev.
Lett
.
94
,
210601, 2005

for

chosen

axes

m

and

m‘

Nice in
principle
, but…


What

happens

for

setups

closer

to

actual

experiments
?


What

about

interaction

effects
?


Polarisation > 84 %
is

needed


Time
-
resolved

detection

scheme

Other
entanglement

detection

schemes
:


D. Loss and E. V.
Sukhorukov
, Phys. Rev.
Lett
.
84
, 1035,
2000

G.
Burkard
, D. Loss, and E. V.
Sukhorukov
, Phys. Rev.
B
61
, R16303, 2000

N. M.
Chtchelkatchev
, G.
Blatter
, G. B.
Lesovik
, and T. Martin, Phys. Rev. B
66,

161320, 2002

A. Bednorz and W.
Belzig
, Phys. Rev. B
83
, 125304, 2011

Setups
closer

to

experiment

Chaotic

cavity

instead

of

tunnel
contacts
:


J. P. Morten, D. Huertas
-
Hernando, W. Belzig, and
A.
Brataas
,
Europhys
.
Lett
.
81
, 40002, 2008

Result

for

the

Bell
parameter

stays

the

same!

Quantum
dots

instead

of

tunnel
contacts
:


H. Soller
and

A
.
Komnik
, Eur. Phys. J. D
63
, 3, 2011

Result

for

the

Bell
parameter

stays

the

same!

Interaction
effects

1.
Geometric

suppression

factors

or

usage

of

a
topological

insulator

lead

to

length

dependence

of

the

nonlocal

conductances

Result

for

the

Bell
parameter

stays

the

same!

2.
Onsite

interaction

(
phonons
, Coulomb
interaction
,… )

Result

for

the

Bell
parameter

stays

the

same!

Polarisation > 84 %
needed

Entanglement
: The
state

of

the

system

cannot

be

written

as

product

state
.

Bell
inequality
:
ε

> 2
means

that

local

reality

is

violated
!

Entanglement

and

Bell
violation

does

not
mean

the

same
and

generically


it

is

easier

to

verify

the

presence

of

entanglement

than

the

violation

of

local

reality
.

S. M. Roy, Phys.
Rev
.
Lett
.
94
, 010402, 2005

J.
Uffink

and M.
Seevinck
, Physics Letters A
372
, 1205
, 2008

If

Alice‘s

and

Bob‘s

measurement directions for spin are orthogonal we can prove that the

maximal value for
ε

for

a
separable

state

is

only

√2

We

only

need

polarisation

P > 70%
for

an
entanglement

witness

Only

need

ε

> √2
to

verify

the

presence

of

entanglement

Experimental Setup

G1

G2

F2

F1

G4

G3

F3

F4

S

InAs

QD 1

QD 2

QD 3

QD 4

measure

nonlocal

conductances

directly

eliminates

the

need

for

time
-
resolved

measurement

L. Hofstetter, S.
Csonka
, A. Baumgartner, G.
Fülöp
, S.
d'Hollosy
, J.
Nygård

and

C. Schönenberger, Phys.
Rev
.
Lett
.
107
, 136801, 2011

Kondo
effect

in
superconductor
-
ferromagnet

hybrids

enhances

the

spin

polarisation

to

≈70%

H. Soller, L. Hofstetter, S.
Csonka
, A. Levy
Yeyati
, C.
Schönenberger
and

A
.
Komnik
, in
preparation

Synthetic

antiferromagnets

allow

for

small

switchable

magnets

C. Wang, Y. Cui, J. A.
Katine
, R. A.
Buhrman

and


D. C. Ralph,
Nat. Phys.
7
, 496

501, 2011

Conclusion


Scheme

for

Bell
measurements


Theoretical

Improvements


Experimental
Realisation