Quantum Entanglement in Superconducting Beamsplitters

kitefleaUrban and Civil

Nov 15, 2013 (3 years and 11 months ago)

70 views

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