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```March 29, 2011, Aussois, France
David Gershoni
The Physics Department, Technion-Israel Institute of Technology,
Haifa, 32000, Israel
and
Joint Quantum Institute, NIST and University of Maryland, USA
Technion – Israel Institute of Technology
Physics Department and Solid State Institute
Motivation
Coherent control of anchored qubits – spins of
carriers.
Coherent control of flying qubits – polarization of
photons.
Semiconductor Quantum dots provide a unique
stage for controlling the interactions between both
type of qubits, and they are compatible with the
technology of light sources and detectors.
Outline
• Two level system: Spin and Light Polarization
• Introduction to energy levels and optical transitions in
SCQDs
• The bright and dark excitons as matter two level systems
– Writing the exciton spin state by a polarized light pulse tuned
into excitonic resonances.
– Reading its spin state by a second polarized light pulse,
resonantly tuned into biexcitonic resonances.
– Manipulating its spin state by a third polarized and/or detuned
pulse.
Two level system and the Bloch
Sphere
   | 0    |1 
|
   |   |
 ,  are complex amplitudes
|  |2  |  |2  1
 is described by a po int
on the Bloch sphere
(| i |) 1/ 2
1/ 2(|  |)
(|  |) 1/ 2
1/ 2(| i |)
|
classical bit (0 or 1)– quantum bit (qubit – Bloch sphere)
• Jones vector:
x   y
x 

2
y
• General solution to
Maxwell equations for the
direction of the electric
field vector of a photon is
an ellipse
Linear
Circular
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Elliptical
5
Polarization – Poincare’ sphere
Poincare sphere
Stokes parameters
s0 , s1 , s2 , s3
H V
s1 
H V
s2 
DD
DD
s3 
RL
RL
s0  H  V  R  L  D  D
Information can be encoded in
the photon’s polarization state.
4 measurements are
required to determine
the full polarization state
of light:
a 2x2 density matrix
V
H
Selection rules for optical transitions in
semiconductor QDs
1
2
;
Conduction Band
atomic s  like
1
2

~1.25 eV
3
2
3
2
3 e
; 2
;
;
1
27
e
1
2
e
1
2
e
e
e
e
he

e
e e e
e e e
e
e
e
e
e
Valence Band
atomic p  like
hh
~0.05 eV
lh
e
~0.3 eV
so
0,0,00 
 1212, ,12 12


1,1,1
1 

3
2
, 32 32
promoting electron
leaving hole of
opposite ch arg e and spin

  32 ,32 , 3232
 


STM (scanning tunneling microscope)
images self assembled dots
Not all the same, but live
forever and can be put
into high Q microcavities, easily
Single Quantum Dot - Photoluminescence
2nm GaAs
GaAs
1.5 monolayer InAs (PCI)
GaAs
GaAs
Off resonance
excitation
P
S
h
emission due to
Spin interaction of charge carriers
• Two electrons (holes) non-interacting spin
states:
1
2
1
2
 32 
 32 
 12  32 
,
Total spin:  1(3)
1
2
 12  32 
 32 
,
1
2
 1(3)
 32 
,  12  32 
1
2
 32 
0
30 (15)
meV
0
• Electrons (holes) singlet state:
Energy

S
S
• Electrons (holes) triplet states:
Spin
,
T+1(+3)
,
T-1(-3)

T0
e-e (h-h)
exchange
~5meV
Quantum dot e-h pair (exciton) states
Non
interacting
Isotropic
electron-hole
exchange
Anisotropic
electron-hole
exchange
a
Bright Exciton
3
3
1
1
2  2  1  2  2  1

3
2
   
Δ1 ≈ 0.03meV
V
s    

Δ0 ≈ 0.3meV
 12  2  23  12  2
Dark Exciton
Dark exciton: Ground- state,
Optically inactive,
quantum two level system
H
a
s
Δ2 ≈ 0.001meV
• Its lifetime is long – comparable to that of a single electron or
hole.
• It is neutral and therefore less sensitive than charged particles to
fluctuating electric fields.
• Due to its fine structure and smaller g-factor, it is more protected
than the electron or hole from fluctuating magnetic fields,
especially where no external magnetic field is applied.
as an in-matter qubit
But how can it be addressed?
E. Poem et al., Nature Physics ( November 2010)
Biexciton excitation spectrum
R 
Se
Te

V

 P

S

Th
Sh

 i 
X S0
  1
  
 i 
D
  
H


S


 P
I
D
L 
XX P0
Te1Th 3
Te S h S eTh
Te 0Th 0
We can generate any of these biexciton spin
states by tuning the energy and polarization
of the laser.
Se S h
X P0
E
Experimental setup
Polarizing
beam splitter
First monochromator
and CCD camera/Detector
Spectral Two channel arbitrary
polarization rotator
Filter
H
V
Second monochromator
And detector
Beam combiner
Second pulse laser
He
Objective
Quantum Dot
Quantum Dot
Wetting layer
Quantum Dot
First pulse laser
Substrate
Sample
Delay line

   

XX 0*
XX 0

2nd pulse
1
2
1
2
H
  
  
V
D
H
X
θ
0*
R
    
1
2
    
1st pulse
V
X
V
0
H
0
L

D
1st pulse
1
2
P0(θ,)
‘Writing’ the spin with the 1st photonA
1i
R
R -LLL
V R R
H
2
2
X0
i
∆=30µev
2
1
2
S
A
Poincare sphere
Bloch sphere
  
S
  
‘Reading’ the spin with the 2nd photon
Se T h
Poincare
XX 0*
Se
I(XX0)
R
Th

Bloch
X0
Time resolved, two-photon PL
measurement XX0TT, X0P excitation
600
5
500
t [ps]
300
3
200
2
100
0
[integated
Counts/min]
-100
XX0T0
XX0
XX0T3
5
2 0
6
x 10
XX
T3
2 XX0T0
1
0
1.2805
1.281
2
XX0 5
X-1
X0
6
X0
X+1
1.2815
1.282
1.2825
E [eV]
1.283
1.2835
1.2865
1.287
1
[103 counts/min]
4
400
Quasi-resonant
Resonant
Conclusions so far…
• We demonstrate for the first time that the exciton
spin can be ‘written’ in any arbitrary coherent
superposition of its symmetric and anti-symmetric
spin eigenstates by an elliptically polarized short laser
pulse.
• We showed that by tuning a second polarized laser
pulse to a biexcitonic resonance, the exciton spin can
• Y. Benny, et al, "Coherent optical writing and reading of the
exciton spin state in single quantum dots " (arXiv:1009.5463v1
[quant-ph]28 Sep 2010), PRL 2011.
March 31, 2011, Aussois, France
E. Poem, Y. Kodriano, Y. Benny, C. Tradonsky, N. H.
Lindner, J. E. Avron and D. Galushko
The Physics Department and The Solid State Institute, Technion-Israel
Institute of Technology, Haifa, 32000, Israel
B. D. Gerardot and P. M. Petroff
Materials Department, University of California Santa Barbara, CA,
93106, USA
Technion – Israel Institute of Technology
Physics Department and Solid State Institute
Summary:
```
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