Optical control of electrons
in single quantum dots
Semion K. Saikin
University of California, San Diego
Optical Control
of electrons in QDs
Single Electron
Devices
Spintronics
Quantum Information
Processing
Photonics
Devices: D. Gammon, NRL
Spectroscopy: group of D. G. Steel, U. Michigan
Theory & Modeling: group of L. J. Sham, UCSD
V
Support:
2
Content
• Semiconductor quantum dot structures:
Design and Applications
• Properties of single dots:
Energy levels structure, Spin states
Interaction with light, excitons
• Optical Control:
Goal and device design
Optical cooling
Single dot switch
Operations with coupled dots
• Conclusions
3
Semiconductor QDs
Artificial Atoms
Vertical QD
Gated QD
Interface
fluctuation QDs
Self-assembled
dots
1 mm
Koichiro Zaitsu, et al.,
APL 92, 033101 (2008)
Elzerman et al.
Nature 430, 431(2004)
D.Gammon, et al.,
PRL 76, 3005 (1996)
NIST website
0.1 mm
InAs
AlGaAs
GaAs
Etching
Gate
depletion
Interface
imperfections
GaAs
Lattice mismatch
4
QD devices
Present and Future
Past
Lasers & Optical Amplifiers
Photodetectors
Low threshold current
Weak temperature dependence
Adjustable frequency range
Broad frequency spectrum
High responsivity
High T operation
Solar Cells
High efficiency of
photon to electron
conversion
Thermoelectric elements
Control for electron
and phonon mobility
Single photon sources & modulators
Quantum Information Processing
Slow relaxation
Long coherence time
Future
Single Electron Memory
Ability to control
Long relaxation time
5
Content
• Semiconductor quantum dot structures:
Design and Applications
• Properties of single dots:
Energy levels structure, Spin states
Interaction with light, excitons
• Optical Control:
Goal and device design
Optical cooling
Single dot switch
Operations with coupled dots
• Conclusions
6
Energy Levels
quantization
EC
E3e
E2e
E1e
electron
~ 1-100 meV
Infra Red Range
DEC
Eg~1.25 eV
Near Infra Red/Visible
Range
hole
DEV
EV
frequency  2
E1h
E2h
Visible light
Spacing between the energy levels can controlled
using different materials or by design!
7
Spin states
Spin up
Spin down
e-
EC
Ee( )
E1e
Ee( )
e-
• An intrinsic angular momentum of a quantum particle
• Associated magnetic momentum μ   gmBS
• Interaction with a magnetic field H  μB
Spin relaxation time:
Ts  20 ms at T = 1 K and B = 4 T
~ 0.1 - 0.5 meV
Bx
Eh( )
E1h
Eh( )
EV
Spin states are long lived!
8
Spin blockade device
Example
EF
EF
Delft University of Technology
Different
spins
– Current
not zero
Same spins
– Current
is is
blocked
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Optical Absorption/Emission
exciton
Exciton relaxation time ~ 0.1 – 1 ns
EC
E3e
DEC
E2e
E1e
Photon hnDE
DE
DEV
EV
E1h
E2h
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Selection Rules
negative exciton
EC
V
E3e
DEC
E2e
E1e
Bx
Photon
Linear polarization, V[1,0,0]
DEV
EV
E1h
E2h
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Selection Rules
negative exciton
s+
EC
E3e
DEC
E2e
E1e
Photon hnDE
Circular polarization
s+
DEV
EV
E1h
E2h
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Content
• Semiconductor quantum dot structures:
Design and Applications
• Properties of single dots:
Energy levels structure, Spin states
Interaction with light, excitons
• Optical Control:
Goal and device design
Optical cooling
Single dot switch
Operations with coupled dots
• Conclusions
13
Goal
Control the spin of an electron spin in a single quantum dot
FAST, EFFICIENTLY, PRECISELY.
EC
Ee( )
Ee( )
Eh( )
Eh( )
EV
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Setup
Quantum dot is empty
AlGaAs
Laser beam
InAs QD
AlGaAs
n+ GaAs
EF
V
mask
QD layer
Quantum dot is filled
VB
EF
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Optical probe of single dot
Photoluminescence
pump
2+
X
X+
capture
X0
X-
recombination
X2-
X. Xu, et. al., PRL 99, 097401 (2007)
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Selection Rules
H1
V2
V1
Bx
H2
H and V – orthogonal linear polarizations
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Optical cooling
Whenever an electron is in the
Pump
state flip it to the
state.
Relaxation
Frequency and polarization selection
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Optical cooling
EC
E1e
Photon hnDE
VE1h
EV
Z
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Optical cooling
Model
System evolution:
Relaxation rate:
G  1.2 meV
Precision, P
Operation precision
Relaxation rate, G
Cooling rate, g

 (t )  i [H,  ]  L{  }
t
Cooling Rate
Rabi frequency, W
Relaxation rate, G
Prepared state:
P(t )  P() + (P(0)  P())eγt
C. Emary, X. Xu, D. Steel, S.Saikin, L. J.
Sham, Phys. Rev. Lett. 98, 047401 (2007)
time, ns
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Optical cooling
Pump-probe measurement
H2
Pump
V2
Probe
State preparation efficiency 98.9%
H1
Probe
Pump
V1
X. Xu, et. al., PRL 99, 097401 (2007)
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Single Quantum Dot Switch
If an electron in the
state then flip it to the
state and reverse.
d detuning
Pump1
Pump2
Use frequency and polarization selection
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Model
Optimization of detuning
Effects of pulse length
B=8T
B=2T
B=4T
B=8T
T = 20 ps
T = 50 ps
T = 100 ps
C. Emary, L. J. Sham J. Phys.:
Cond. Matter 19, 056203 (2007)
Dynamics of an electron state
Classical vs. Quantum
1.0
Electron state
0.8
0.6
0.4
0.2
0.0
-600
-400
-200
0
time (ps)
200
400
600
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Operation with electrons
in two dots
If two electrons are in a same state
flip both of them.
or
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Origin of interaction
Bi-trion binding energy D
D ~ 1 meV
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Energy levels
H(dot2)
H(dot1)
V(dot2)
V(dot1)
26
Model
Dynamics of electrons
Pulse timing
1.0
energy
H(t)
0.8
Electrons state
V(t)
0
energy
E4
E2
d
0.4
0.2
E1
0
0.6
E3
E5
t1
t2
time
t3
t4
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
pulse width (ns)
To minimize incoherent pumping
and losses due to relaxation
S.Saikin, et. al., arXiv:0802.1527
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Conclusions
• An electron in a single quantum dot can be prepared to a given
state with precision ~99% on the timescale of 1 nanosecond using
resonant optical pumping.
• States of a single electron in a QD can be switched coherently on
a timescale of 0.1 nanosecond using a Raman process.
• Simple logical operations can be designed with coupled quantum
dots. The operation timescale is ~ 0.5 nanosecond
Thank you!
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