Transcript Weizmann Institute of Science
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
1/ 2(| | ) (|
i
| ) 1/ 2 | | 2 | | 2 1 (| | ) 1/ 2 1/ 2(|
i
| )
is described by a po
int
on the Bloch sphere
|
classical bit (0 or 1) – quantum bit (qubit – Bloch sphere)
• General solution to Maxwell equations for the direction of the electric field vector of a photon is an ellipse • Jones vector:
x
y
x
2
y Linear Circular
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Elliptical
5
s
2
Polarization – Poincare’ sphere
4 measurements are
Poincare sphere
required to determine
Stokes parameters 0 , , 1 2 , 3
the full polarization state of light:
s
1
H H
V
V
a 2x2 density matrix
V
D
D D
D s
3
R R
L L
H
s
0
H R L D
Information can be encoded in the photon’s polarization state.
D
Selection rules for optical transitions in semiconductor QDs
1 2 ; 1 2
Conduction Band
1 1 , 2 2 , 1 2 1 2 ~1.25 eV 3 2 ; 3 2 3 2 ; 1 2
e e
1 2 7 ; 1 2
e e e e e
e e
e
h e e e e e e e e
Valence Band hh
~0.05 eV
lh
e e e
so
~0.3 eV , , 2
promoting electron
3 2
leaving hole of opposite ch
arg 3 2 2 , 3 ,
e and spin
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 - Photoluminescence
GaAs 2nm GaAs 1.5 monolayer InAs (PCI) GaAs GaAs
Off resonance excitation
P S
h emission due to radiative recombination
Spin interaction of charge carriers
• Two electrons (holes) non-interacting spin states: 1 2 1 2 2 2 Total spin: 1 ( 3 ) , 1 2 1 2 2 2 1 ( 3 ) , 1 2 1 2 2 2 0 , 1 2 1 2 2 2 0 30 (15) meV Energy • S S • Electrons (holes) triplet states: Spin blockaded , , T +1(+3) T -1(-3) T 0 e e ( h h ) exchange ~5meV
Quantum dot e-h pair (exciton) states
3 2
Bright Exciton
2
Non interacting
1 2 1 2 1
Isotropic electron-hole exchange
Δ 0 ≈ 0.3meV
Anisotropic electron-hole exchange
Δ 1
a
≈ 0.03meV
V
s
H
3 2 2 2 2 1 2
Dark Exciton
2
a s
Dark exciton : Ground- state,
Δ 2 ≈ 0.001meV
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 qubit
But how can it be addressed?
E. Poem
et al
.,
Nature Physics
( November 2010)
Biexciton excitation spectrum
R
S e T e
P S
D
1
H V
D T h S h
I
S P
X S
0
e h T T
0
e h
3
XX P
0
h L
h X P
0
We can generate any of these biexciton spin states by tuning the energy and polarization of the laser.
E
Experimental setup
Polarizing beam splitter Spectral Filter Two channel arbitrary polarization rotator First monochromator and CCD camera/Detector H V Second monochromator And detector Beam combiner Second pulse laser First pulse laser He Objective Sample Delay line
1 2 1 2
2 nd pulse
XX 0 * XX 0 V H X 0 * R D
1 st pulse
1 2 1 2
1 st pulse
X 0 V H 0 H
θ
P 0 (θ,
)
L D V
‘Writing’ the spin with the 1
st R i L X 0
photon
A
i
2 ∆=30µev 1 2 S S Poincare sphere Bloch sphere A
‘Reading’ the spin with the 2
nd
photon
S e T h
Poincare
XX 0 * I (XX 0 ) R S e T h X 0
Bloch
Time resolved, two-photon PL measurement XX
0 TT
, X
0 P
excitation
600 500 400 300 200 100 0 XX 0 T0 XX -100 2 x 10 5 XX 0 T0 1 0 T3 2 XX 0 T3 0 1.2805
6 1.281
6 1.2815
X -1 1.282
1.2825
E [eV] 1.283
XX 0 XX 0 2
5 1.2835
X +1 1.2865
X 0 X 0 1.287
5 4 3 2 1
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 .
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