Single Spin DetectionJ. Fernández-Rossier

IUMA, Universidad de Alicante, Spain

Manipulation and Measurementof the Quantum State of a single spin in a solid state environment

 

Needle in a Hay Stack

Talk available in: www.ua.es/jfrossier/personal

1023 atoms, 1025 spinsSignal for only 1

CdTe nanocrystal

+ 1Mn

L. Besombes et al., PRL 93, 207403, (2004)

PLS=5/22S+1=6

Single Spin Detection

OutlineI. MotivationII. Basic StuffIII. Quantum SimulationsIV. Conclusions

The institute of Complex Adaptative Matter encourages (forces) scientist to explain their work to other scientist in pedestrian terms. I have learned more science through workshops organized by this institute and the personal contacts they generated than I have from all other professional activities combined.

R. Laughlin, A Different Universe, (2005)

Single Spin Detection

RELATED WORK•J. Fernández-Rossier, C. Piermarocchi, P.C. Chen, L. J. Sham, and A. H. MacDonald, Theory of Laser induced ferromagnetism

Phys. Rev. Lett. 93, 127201 (2004) •J. Fernández-Rossier, L. BreyFerromagnetism mediated by few electrons in semimagnetic quantum dots

Phys. Rev. Lett. 93, 1172001 (2004)•G. Chiappe, J. Fernández-Rossier, E. Anda, E. LouisSingle-photon exchange interaction in a semiconductor microcavity

Cond-mat/0407639

Talk available in: www.ua.es/jfrossier/personal

I. MotivationII. Basic ConceptsIII. Quantum SimulationsIV. Results and Conclusions

=

Motivation I.Understanding QM from

small...

deadalive

.....to big

“Shut up and calculate”. -- R. Feynman

Not only a philosophycal

question

104-106 Atoms

1 Atom

1023 Atoms: BULK

"I think it is safe to say that no one understands quantum mechanics." -- R. Feynman

Motivation II. The limits of miniaturization

Going Nano

‘Single electron’ transistor

Miniaturization: The limits

‘Single atom’ magnet

Going Nano

Going around THE LIMITS

•Different Materials: •Molecular Electronics•Oxides

•Different Ideas: •Spintronics•DNA•Quantum Computing

•New Questions:•Smallest wire?•Smallest magnet?•Smallest diode?•Smallest transistor?

•New challenges:•Single spin control•Single molecule transport•Nanocrystal formation

Electronics: we ain´t seen nothing yet

I. MotivationII. Basic ConceptsIII. Quantum SimulationsIV. Conclusions

Basic Concepts

•Quantum computing for absolute beginners:

•Quantum bit vs classical bit•Spin S=1/2 as a qbit•Quantum software and hardware

•Diluted Magnetic Semiconductors•Quantum Dots

What is a qbit?

Will you marry me?

noayesa ny

n

y

nny

yny

PC

CP

aaa

aaa *

*

*2

2

Quantum information

n

y

P

P

0

0

Classical information

00

011yes

10

000no

What is a qbit (II)?

2sin

2cos

iny enoayesa

A qbit is like a spin ½

What is a quantum computation?

I. Prepare initial state

II. Perform a well defined sequence ofquantum operations (Quantum gates)

III. Read final state (single spin detection)

21212121 dcba

iHtetU )( “Engineering” Hamiltonian.Universal Gates

Can something useful be done?

Number of steps: n 2n

Classical factorizationalgorithm

Quantum factorizationAlgorithm (Shor ’90)

Number of bits: N=2n

Number of steps: n2

Example n=10Qsteps: 100Csteps: 10.000

QUANTUM SOFTWARE:A few algorithms and ideas

Quantum Hardware: Proposals

Sytem Qbit Nmax Who, where

NMR Nuclei spin 7 Chuang (IBM)

Ion traps Motional state 3 Colorado (JILA)

SC Flux state 2 (Girvin,Devoret) Yale, Saclay

P Donors E spin 1 Kane (Australia)

Electrons in QD E spin 1 Di Vincenzo (IBM), Delft

Exciton in QD Eh spin 2 Sham (UCSD), D. Steel

Not in yet

Diluted Magnetic Semiconductors

Charge doping of Semiconductors

Pure ZnTe N- ZnTe(Zn,Ga)Te

p- ZnTeZn (Te,N)

CHARGE DOPING

Metal

Spin doping: diluted Magnetic Semiconductors

(DMS)(Zn,Mn)Te

SPIN DOPING

Zn: Ar: 3d10 4s2

Mn: Ar: 3d5 4s2

Conduction BandMainly s orbitals of ZnValence BandMainly p orbitals of TeMn d levels

S=5/2

S=3/2

Why S=5/2 ?

S=1/2

S=5/2. LOWEST Coulomb Repulsion (Hunds Rule)

Magnetic MomentSPIN S=5/2

Real Space Cartoon

Ground State

Excited States

Mn SPIN ROTATIONAL INVARIANCES=5/2. 2S+1=6 DEGENARATE STATES

5/2 3/2 1/2

How to manipulate the spins ?

Electrons, holes, Mn and their interactions

I

IIeee rrMSJH

LSrrMSJH hI

SOIIhhh

eS

Spin of the CB electron and VB hole

SPIN FLIPSPIN attraction SPIN repulsion

hS

SPIN ORBIT MATTERS A LOT

CARRIER WAVE FUNCTION ENGINEERING

Single quantum spectroscopy?CdSe nanocrystal: TEM

5nm

Absorption

Emission

CONFINEMENT

I. MotivationII. Basic ConceptsIII. Quantum SimulationsIV. Conclusions

S=5/2 qbits in semiconductor nanocrystals?

Absorption EmissionSpin

evolution

L. Besombes et al., PRL 93, 207403, (2004)

PLS=5/22S+1=6

11

00

01

10

dummy

dummy

1 SPIN 5/2 = 2 QBITS

Method :1) Calculation of one-body wave

functions (for a given dot)2) Evaluation of many body

exciton-Mn spin Hamiltonian3) Exact diagonalization of GSM4) Exact diagonalization of XSM5) Linear reponse theory

Ground State Manifold (GSM)

Exciton States Manifold (XSM)

4x6N

6N

-1 +1-1 +2

1

4

)()(

NMnGSM Qbits

1 6 2

2 36 5

3 216 7

4 1296 10

HAMILTONIAN

I

IBII

IIII MBgMMJH

',

'',0

Ground State Manifold (GSM)

NN SSSS ...),...,( 11 GEGH G0

4 6N

e

h

IIhIh

VB

IeI

IeCB

xSMJH

xSMJHH

)(

)(1

XEXHH X 10

Exciton States Manifold (XSM)

6N

SPIN ORBIT INTERACTION )(

)(

Iz

Iz

IhI

xSM

xSM

Heisenberg

Ising

-1 +1-1 +2

1

4

)()(

Absorption

iyxHH 1

iyxHH 2

Spin orbit and OPTICAL SELECTION RULES

eiyxiyxs

HHiyxs

e

e

2

EreH matterlight

How can light affect spin?

Valence band Spin orbit: Ising

coupling

)(

)(

Izz

I

IhI

xSM

xSM

SHAPE MATTERS:

Quenching the Hole-Mn spin flip

GSM and XSM spectrum

E(meV)

1 MnNG=6NX=24

2 MnNG=36NX=244

3MnNG=216NX=864

E(meV)

Magnetic Field (0,0,5)

XEXHH X 10 XEXHH X 10

XX

X

TkE

XXX Z

eEPPL

BX /

)()(

Photoluminescence (PL) Theory

G

GXX EEGpX 22

Spontaneous Emission from X to G

Energy conservation

OpticalSelection rules

SPIN BLOCKADE

PL SPECTRUM

Occupation of excited state

Thermal like occupation

Energy (meV)

PL, theory PL, experiment

PL: results

)()(

OPTICAL SPIN BLOCKADE

Franck Condon=Spin Blockade

Standardoptical selection rule

GS

M

XSM

G

GXX EEGpX 22

22

11

2)_,...,()_,...,( XpgNSSNSSGpX SG

Photon QUANTUM MEASUREMENT

PL, experiment

)()(

N=3. Narrowing and shift

0T

2T

4T

6T

8T

10TP. S. Dorozhkin,Phys. Rev. B 68, 195313 (2003)

Bell States in DMS?

eheh

HIGLY ENTANGLED

Intriguing question: can the detection of a linearly polarized photon yield a Bell state?

Lowest energy stateOf XSM

GSM

CONCLUSIONS (and future work)

• Single spin detection possible due to

• Chemical Engineering (nanocrystals)• Advanced material processing and

electronics (multilayers, photodetectors)• Laser technology, low temperatures• DEEP UNDERSTANDING of the

ELECTRONIC STRUCTURE (Solid state physics and chemistry)

• S=5/2 qbits. • Detection ok (at least N=2)• Time resolved control ok• 2 qbit operations ok