david gershoni the physics department, technion-israel institute of technology, haifa, 32000, israel...
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David GershoniThe Physics Department, Technion-Israel Institute of Technology,
Haifa, 32000, Israeland
Joint Quantum Institute, NIST and University of Maryland, USA
Technion – Israel Institute of TechnologyPhysics Department and Solid State Institute
March 29, 2011, Aussois, France
MotivationCoherent 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
2 2
| 0 |1
| |
,
| | | | 1
int
are complex amplitudes
is described by a po
onthe Bloch sphere
|
|
(| | ) 1/ 2
1/ 2(| | ) (| | ) 1/ 2i
1/ 2(| | )i
classical bit (0 or 1)– quantum bit (qubit – Bloch sphere)
5Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Linear Circular Elliptical
• General solution to Maxwell equations for the direction of the electric field vector of a photon is an ellipse
x y 2x y
• Jones vector:
Polarization – Poincare’ sphere
H
V
Poincare sphere
0 1 2 3, , ,s s s sStokes parameters
1
H Vs
H V
2
D Ds
D D
3
R Ls
R L
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
0s H V R L D D
Selection rules for optical transitions in semiconductor QDs
7
hehh
Conduction Band
atomic s like
3 3
2 2;
1 1
2 2;
eeee ee
e
lh3 1
2 2;
ee
e
eee
e
so1 1
2 2;
ee
e
eee
Valence Band
atomic p like
3 3
2 21,1 ,
1 1
2 20,0 ,
3 3
2 2,
arg
promoting electron
leaving holeof
oppositech e and spin
~0.3 eV
~0.05 eV
~1.25 eV
3 3
2 21, 1 ,
1 1
2 20,0 ,
3 3
2 2,
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 - Single Quantum Dot - PhotoluminescencePhotoluminescence
GaAs
GaAs1.5 monolayer InAs (PCI)2nm GaAs
GaAs
h
emission due to radiative recombination
S
Off resonanceexcitation
P
• Two electrons (holes) non-interacting spin states:
• Electrons (holes) singlet state:
• Electrons (holes) triplet states:
Spin interaction of charge carriers
S
,, T0T-1(-3)T+1(+3)
,, , 2
321
23
21
23
21
23
21
23
21
23
21
23
21
23
21
Total spin: )3(1 )3(1 0 0
e-e (h-h) exchange ~5meV
Energy
S
Non-
radiatively
Spin blockaded
30 (15)
meV
Bright ExcitonBright Exciton
Dark ExcitonDark Exciton
Isotropic electron-hole
exchange
Anisotropic electron-hole
exchange
a
as
s
Δ0 ≈ 0.3meV
Δ1 ≈ 0.03meV
Δ2 ≈ 0.001meV
Non interacting
3 12 2 2 3 1
2 2 2
3 12 2 1 3 1
2 2 1
V
H
Quantum dot e-h pair (exciton) states
Dark exciton: Ground- state, Optically inactive,
quantum two level system
The dark exciton’s advantages • 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 qubitBut how can it be addressed?But how can it be addressed?
E. Poem et al., Nature Physics ( November 2010)
E
I
Biexciton excitation spectrum
S
SP
P
0PX
h
h
T
S
e
e
S
T
e hS S
L
R
H
V
i
D
D
i 1
0SX
0 0e hT T e hS Te hT S
1 3e hT T
0PXX
We can generate any of these biexciton spin states by tuning the energy and polarization of the laser.
Experimental setup
SubstrateSubstrate
Wetting layerWetting layerQuantum DotQuantum Dot
Quantum DotQuantum Dot
Quantum DotQuantum Dot
First pulse laser
Second pulse laser
First monochromator and CCD camera/Detector
Delay line
Beam combiner
Spectral Filter
Two channel arbitrarypolarization rotator
Sample
Objective
He
Second monochromator And detector
Polarizingbeam splitter
1st pulse
12
12
12
12
2nd pulse
0X
*0X
0XX
V
H
H
V
*0XX
0
R
θ
2A/I0
D
H
V
L
D
P0(θ,)
1st pulse
Poincare sphere Bloch sphere
LR2
1H
2
1
2
i L-R2
iV R LR
‘Writing’ the spin with the 1st photon0X
∆=30µev
A
S
A
S
‘Reading’ the spin with the 2nd photon
0X
*0XX
Bloch
heTS
R
eS
hT
Poincare
I(XX0)
2 6 2 6
-100
0
100
200
300
400
500
600
1
2
3
4
5
1.2805 1.281 1.2815 1.282 1.2825 1.283 1.2835 1.2865 1.2870
1
2x 10
5
Time resolved, two-photon PL measurement XX0
TT, X0P excitation
t [
ps]
E [eV]
XX0T3XX0
T0
X-1 XX0 X0
X+1
XX0
XX0T0
5
[103 c
oun
ts/m
in]
]in
tega
ted
Cou
nts
/min
[
XX0T3
X0
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 be faithfully ‘readout’.
• 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.
Technion – Israel Institute of TechnologyPhysics Department and Solid State Institute
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. PetroffMaterials Department, University of California Santa Barbara, CA,
93106, USA
Summary: