Download Single Spin Detection

Single Spin Detection
J. Fernández-Rossier
IUMA, Universidad de Alicante, Spain
Manipulation and
Measurement
of the Quantum State of
a single spin in a solid
state environment
1023 atoms, 1025 spins
Signal for only 1
Needle in a Hay Stack
Talk available in: www.ua.es/jfrossier/personal
Single Spin Detection
CdTe nanocrystal
+ 1Mn
PL
S=5/2
2S+1=6
L. Besombes et al., PRL 93, 207403, (2004)
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)
Outline
I. Motivation
II. Basic Stuff
III. Quantum Simulations
IV. Conclusions
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. Brey
Ferromagnetism mediated by few electrons in semimagnetic quantum dots
Phys. Rev. Lett. 93, 1172001 (2004)
•G. Chiappe, J. Fernández-Rossier, E. Anda, E. Louis
Single-photon exchange interaction in a semiconductor microcavity
Cond-mat/0407639
Talk available in: www.ua.es/jfrossier/personal
I.
Motivation
II. Basic Concepts
III. Quantum Simulations
IV. Results and Conclusions
Motivation I.
Understanding QM from small...
=
      
.....to big
  alive  dead
Not only a
philosophycal
question
1 Atom
“Shut up and
calculate”.
-- R. Feynman
"I think it is safe to say
that no one understands
quantum mechanics."
-- R. Feynman
104-106 Atoms
1023 Atoms: BULK
Motivation II. The limits of
miniaturization
‘Single electron’
transistor
Going Nano
Miniaturization: The limits
Going Nano
‘Single atom’ magnet
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.
Motivation
II. Basic Concepts
III. Quantum Simulations
IV. 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?
Classical information
  a y yes  an no
Will you
marry me?
 Py

0
0

Pn 
1 0

yes  1  
 0 0
0 0

no  0  
0 1
Quantum information
 a 2 a a *  P
y
n y 
 y


 a a * a 2   C
n
 y n

C *

Pn 
What is a qbit (II)?
 
 
i
  a y yes  an no    cos    e sin   
2
2
A qbit is like a spin ½
What is a quantum computation?
I. Prepare initial state
  a  1  2 b  1  2 c  1  2 d  1 
2
II. Perform a well defined sequence of
quantum operations (Quantum gates)
U (t )   e 
iHt
“Engineering” Hamiltonian.
Universal Gates
III. Read final state
(single spin detection)
Can something useful be done?
Classical factorization
algorithm
Quantum factorization
Algorithm (Shor ’90)
Number of bits: N=2n
Number of steps: n2
Example n=10
Qsteps: 100
Csteps: 10.000
Number of steps: n 2n
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
2
Sham (UCSD), D. Steel
Exciton in QD Eh spin
Not in
yet
Diluted Magnetic
Semiconductors
Charge doping of Semiconductors
Pure ZnTe
N- ZnTe
(Zn,Ga)Te
CHARGE DOPING
p- ZnTe
Zn (Te,N)
Metal
Spin doping: diluted Magnetic
Semiconductors (DMS)
(Zn,Mn)Te
Zn: Ar: 3d10 4s2
Mn: Ar: 3d5 4s2
Conduction Band
Mainly s orbitals of Zn
Valence Band
Mainly p orbitals of Te
Mn d levels
SPIN DOPING
Why S=5/2 ?
S=5/2
Ground State
S=3/2
Excited States
S=1/2
Real Space Cartoon
S=5/2. LOWEST
Coulomb Repulsion
(Hunds Rule)
Magnetic Moment
SPIN S=5/2
Mn SPIN
ROTATIONAL
INVARIANCE
S=5/2. 2S+1=6
DEGENARATE
STATES
5/2 3/2
1/2
How to manipulate the spins ?
Electrons, holes, Mn and their interactions

  
H e   J e Se   M I  r  rI 
I
SPIN attraction
SPIN FLIP

 
  
H h   J h S h   M I  r  rI    SO S h  L
I
 
Se Sh
Spin of the CB electron and VB hole
SPIN ORBIT MATTERS A LOT
CARRIER WAVE FUNCTION ENGINEERING
SPIN repulsion
Single quantum spectroscopy?
CdSe nanocrystal: TEM
CONFINEMENT
Absorption
Emission
5nm
I. Motivation
II. Basic Concepts
III. Quantum Simulations
IV. Conclusions
S=5/2 qbits in semiconductor nanocrystals?
PL
S=5/2
2S+1=6
1 0
11
0 0
0 1
L. Besombes et al., PRL 93, 207403, (2004)
Absorption
Spin
evolution
Emission
1 SPIN 5/2 = 2 QBITS
dummy
dummy
4x6N
4
-1
-1
+1
 ( )
+2
 ( )
1
Exciton States Manifold
(XSM)
6N
Ground State Manifold
(GSM)
Method :
1) Calculation of one-body wave
functions (for a given dot)
2) Evaluation of many body excitonMn spin Hamiltonian
3) Exact diagonalization of GSM
4) Exact diagonalization of XSM
5) Linear reponse theory
NMn
1
2
3
4
GSM Qbits
6
2
36
5
216 7
1296 10
HAMILTONIAN
Ground State Manifold (GSM)
 


H 0   J I , I ' M I  M I '  g B B   M I
I ,I '
I
(S1 ,..., S N )  S1  ...  S N
H 0 G  EG G
6N
Exciton States Manifold (XSM)
e
  
H1  H  J e  M I  Se ( xI )  Heisenberg
I
  
VB
 H  J h  M I  S h ( xI )
Ising
CB
4 6N
h
H 0  H1  X
I
 EX X
SPIN ORBIT
INTERACTION
  
M I  S h ( xI ) 

M z I S z ( xI )
Spin orbit and OPTICAL SELECTION RULES
 
H lightmatter  er  E
4
-1
-1
+1
 ( )
+2
 ( )
How can light affect spin?
1
HH 1   x  iy
HH 2   x  iy
Absorption
s e x  iy  HH 2 
 e  s x  iy  x  iy   
e
Valence band Spin orbit: Ising coupling
SHAPE MATTERS:
Quenching the Hole-Mn spin flip
  
M I  S h ( xI ) 
M I z S z ( xI )
GSM and XSM spectrum
H 0  H1  X
 EX X
H 0  H1  X
 EX X
Magnetic Field (0,0,5)
1 Mn
NG=6
NX=24
2 Mn
NG=36
NX=244
3Mn
NG=216
NX=864
E(meV)
E(meV)
Photoluminescence
(PL) Theory
PL: results
PL, theory
PL, experiment
Spontaneous Emission from X to G
2
X 


X p G  E X  EG   
2
 ( )
G
Optical
Selection rules
SPIN BLOCKADE
Energy
conservation
 ( )
PL SPECTRUM
e  E X / k BT
PL( )   P( E X )X  
X
ZX
X
X
Energy (meV)
Occupation
of excited state
Thermal like
occupation
OPTICAL SPIN BLOCKADE
2


X pG
X p G  E X  EG   
2
G
2
 G ( S1 ,..., S _ N ) S ( S1 ,..., S _ N )
2
g pX
2
Franck Condon=
Spin Blockade
GSM
X 
Standard
optical selection
rule
Photon QUANTUM
MEASUREMENT
XSM
N=3. Narrowing and shift
PL, experiment
0T
2T
4T
6T
8T
10T
 ( )
 ( )
P. S. Dorozhkin,
Phys. Rev. B 68,
195313 (2003)
Bell States in DMS?
    
HIGLY ENTANGLED
    
    h  e    h 


e
Lowest energy state
Of XSM
GSM
Intriguing question: can the detection of a
linearly polarized photon yield a Bell state?
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