L. Besombes et al., PRL93, 207403, 2004

Single exciton spectroscopy in a semimagnetic nanocrystal

J. Fernández-RossierInstitute of Materials Science, University of Alicante, SPAIN

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

Absorption Emission

CdTe nanocrystal

CdTe nanocrystal+ 1Mn

Goal: Calculate PL and quantum information

Spin relaxation

PLPL

6NMn

S=5/22S+1=6

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

FORMALISM

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

Valence band Spin orbit: Ising

coupling

)(

)(

Izz

I

IhI

xSM

xSM

SHAPE MATTERS:

Quenching of transverse Hole-Mn exchange

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),...,(),...,( XpgSSSSGpX NSNG

Photon measurement=SPINMEASUREMENT

24*6=144 XSM to GSMOnly 12 are allowed

PL, experiment

)()(

N=3. Narrowing and shift

0T

2T

4T

6T

8T

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

Conclusions

• Model Hamiltonian gives good account of PL experiments:– Single Mn – Broadening and narrowing of lines– Voigt wider than Faraday

• Optical detection of quantum state of N=1,..4 spin S=5/2

in semiconductor nanocrystal.

Related papers:1) JFR, in preparation2) JFR, L. Brey, Phys. Rev. Lett. 93 117201 (2004)3) G. Chiappe, JFR, et al, Condmat/0407639