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Optically Driven Spins in
Semiconductor Quantum Dots
Duncan Steel - Lecture 2
DPG Physics School 2010 on
"Nano-Spintronics"
The qubit for real systems is the electron or hole spin:
The key to optically driven quantum computing in semiconductors is the
negatively charged exciton (trion) in a quantum dot
|1>
|0>
Optical Bloch
Vector Qubit
|0>
Semiconductor Quantum
Coherence Engineering
Successful coherent optical
manipulation of the optical
Bloch vector necessary to
manipulate the spin vector
|1>
Electronic
Spin Qubit
The electron spin vector
AlGaAs
(GaAs)
GaAs
(InAs)
AlGaAs
(GaAs)
|0>
|1>
The electron spin vector
AlGaAs
(GaAs)
GaAs
(InAs)
AlGaAs
(GaAs)
l
|0>
|1>
The electron spin vector
AlGaAs
(GaAs)
GaAs
(InAs)
AlGaAs
(GaAs)
l
|0>
|1>
The electron spin vector
Long coherence time
AlGaAs
(GaAs)
GaAs
(InAs)
AlGaAs
(GaAs)
|0>
|1>
Optical Excitation of Spin Coherence:
Two-photon stimulated Raman
• Circularly polarized
pump pulse creates
coherent superposition of
spin up and down state.
• Raman coherence
oscillates at frequency of
the Zeeman splitting due
to electron in-plane gfactor and decays with
time.
Single Electron Spin Coherence:
Single Charged Exciton
Raman Quantum Beats
Charged Exciton System
X-
Neutral Exciton System
CNOS (a. u.)
G
G
Ensemble Charged Excitons
Single Neutral Exciton
X
Phys. Rev. Lett. - 2005
500
1000
1500
2000
2500
Delay (ps)
hgs (meV)
G
0
G
T2* >10 nsec at B=0
Anomalous Variation of Beat Amplitude and Phase
Standard
Theory
(a)
• Plot of beat amplitude and phase as a function of the splitting.
(b)
Anomalous Variation of Beat Amplitude and Phase
Standard
Theory
(a)
• Plot of beat amplitude and phase as a function of the splitting.
Spontaneously Generated Coherence (SGC)
Trion
G
G
• Coupling to electromagnetic vacuum modes can create coherence* !!
• Modeled in density matrix equations by adding a relaxation term:
Normally forbidden in atomic systems or extremely weak.
Anomalous Variation of Beat Amplitude and Phase:
The result of spontaneously generated Raman coherence
Standard
Theory
(a)
• Plot of beat amplitude and phase as a function of the splitting.
Phys. Rev. Lett. - 2005
Two-Photon Spin Rabi
Trion
Laser Pulse
Trion
ˆ
X
ˆ Rotations with
a nd Y
Zˆ Precession
y
Initialization
x
y
x
0

 2  0
Rx 

Rz  
R x   0

2
2


 
R  y    R z   R x  R z 
2
2
Phase Gate - Demonstration of
Geometric Phase (Aharonov & Anandan)
Tz 
Optical Control of
Trion Optical Bloch
Vector

Z
Z
Optical Control of
Spin Bloch Vector


Fo r
0
the state v ecto r fo r th e sp in ,
th e trio n 2  xˆ rotatio n transfo rm s 

 Uˆ 
0
 1
ˆ
w here U  
 0
0
to
0 
ˆ
 and U C  z   C  z 
1 
  C

z   C z 

Coherent Generation of a Geometrical Phase
Demonstration of the Phase Control
• Modulation effect clearly seen
• Frequency of the modulations
depends on the strength of the
CW field
• Phase change after
modulation points consistent
with theory for 0.2, 5 and 10
mW scans
• Action of CW field can be
likened to a spin phase gate
The Mollow Absorption Spectrum, AC Stark effect, and Autler
Townes Splitting: Gain without Inversion
Dressed State Picture
Mollow Spectrum:
New physics in
absorption
Autler Townes Splitting
S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955)
B. R. Mollow, Phys. Rev. 188, 1969 (1969).
B. R. Mollow, Phys. Rev. A. 5, 2217 (1972)..
Power Spectrum of the Rabi Oscillations:
Gain without inversion
The Mollow Spectrum of a Single QD
|3>
|2>
Weak probe
Strong pump
X. Xu, B. Sun, P. R. Berman, D.G.
Steel, A. Bracker, D. Gammon, L. J.
Sham, “Coherent optical
spectroscopy of a strongly driven
quantum dot,” Science, 317 p 929
(2007).
Autler-Townes Splitting in a Single Quantum Dot
Dressed state Picture
|1>
|2>
30 Io
20 Io
10 Io
5 Io
0 Io
321594
321591
Probe Frequency (GHz)
|3>
|b(N)>
|a(N)>
|b(N-1)>
40 Io
Rabi Splitting (GHz)
Absorption (a.u.)
Probe Abosorption as a
Function of the Pump Intensity (on resonance)
Pump intensity
(Io=0.03w/cm2)
50 Io
|a(N-1)>
1
0
0
4
Pump Field Strength(1 /
Io
8
)
} WR
} WR
Probe Absorption as a Function of Pump Frequency Detuning
Theoretical Plot
Experimental Data
Pump Detuning
(GHz)
Absorption (a.u.)
Pump Intensity
30Io
1.7
0.6
0.3
0.0
-0.3
-0.6
-1.7
321591
321594
Probe Frequency (GHz)
-5.0 -2.5
0
2.5
5.0
Probe Detuning Gunits
Thy Physical Model of the Dark State Experiment
|T->
|T->
|T+>
H1
Wp
V2
V1
H1
V2
Wd
H2
|X+>
|X+>
|X->
|X->
Bx
D arkstate 
DT/T (10-4)
The Quartet Transition Pattern
V1 H1
H2 V2
1
W p X   Wd X 
W 2p  W 2d
Theoretical plot of the CPT including
electron spin dephasing
B=1.32 T
0
-8
0
Laser Detuning (GHz)
8
-3
-3
0
Laser Detuning (G units)
The Observation of the Coherent Population Trapping of an Electron Spin
1
0
1
The probe absorption spectrum
scanning across transition H1
Wd/2p(GHz)
1.38
1.26
|T->
DT/T (10-4)
0
1
0.83
p
0
1
0.78
V2
d
|X+>
0
1
H1
|X->
Solide lines are the fits, which yield
electron spin T2* of 4 ns.
0.56
0
0
0
-5
0
Probe Detuning (GHz)
5
Nature - Physics, 2008
Ωpump
|X+>
Ωprobe
Relative Absorption x 10
ehe |T->
-4
Probing Dynamic Nuclear Spin
Polarization by Dark State Spectroscopy
3
Probe absorption spectra
by varying the laser
scanforward
rate
Black:
Red: backward
2
1
e
e
|X->
0
319074
319077
Probe Frequency (GHz)
Broadened & rounded trion peak
Scan direction dependence:
hysteresis & dark state shift
Large trion excitation
(absorption) is favored
Dynamic control of nuclear field
(Dark state position reflect Zeeman Splitting)
Time Dependent Probe Absorption Spectrum
B=2.6 T
ehe |T->
Ωpump
|X+> e
Ωprobe
e
|X->
Time Dependent Probe Absorption Spectrum
Laser
Partialfrequency
backwardparked
scan here
ehe |T->
Ωpump
|X+> e
Ωprobe
e
|X->
Stable configuration:
maximum trion excitation (absorption)
Time Dependent Probe Absorption Spectrum
Relative Abs. x 10
-4
(e)
(f)
L
R
1.5
R
L
D
0
319083
319089
Probe Frequency (GHz)
ehe |T->
Ωpump
|X+> e
Ωprobe
e
|X->
D
0
300
Time (S)
600
Dark State is a meta-stable
state for nuclear field
Trion Induced Dynamic Nuclear Spin Polarization
anisotropic hyperfine from hole
|T>
Z

Sh Ik
nuclear Zeeman << trion linewidth
Flip up rate:
 
Flip down rate:
 
f
Z
h
S I

k
f
Z
h

k
S I
i
i
2
  t ,i  t , f   t     t     
2
  t ,i  t , f   t     t     
Whichever increases t dominates!
Nuclear field dynamics:
d
dt
DNP rate
   g N   a t
 t

 t
 t

Dynamic Nuclear Spin Polarization Induced Spectral Servo
Two photon detuning
Nuclear
field
Absorption
Probe laser frequency
Probe detuning ( = 2-ph detuning - nuclear field )
Numerical Simulation Results : Slow Scan
Experime
nt
Theor
y
Nuclear field dynamics:
d
dt
   g N   a t
 t

Parameters:
g N  1.5 s
1
a  2.4 (M H z)
3
Nuclear T1 ~ sec
Ah ~ 3 m eV
Numerical Simulation Results : fast Scan
Experime
nt
Theor
y
Parameters:
g N  0.4 s
1
a  50 (M H z)
3
Nuclear T1 ~ sec Ah ~ 20 m eV
Microscopic theory: Weng Yang et al., Q14.00002; http://arxiv.org/ab
Nuclear Field Locking Effect
Metastable
configurations
Stable
configurations
for DNP
 t 
DNP rate:
 t

 t

     pum p
Two-photon detuning
Nuclear field locked to stable value
 
 W pum p
2
  prob
 (  pum p   probe )
Dynamic Nuclear Spin Feedback Suppresses Fluctuations
DNP by trion
Nuclear field
self-focus to
stable value
Nuclear field
unstable
against DNP
Single QD
arbitrary
nuclear spin
config
CW laser
excitation
Medium
trion excitation
2-photon
resonance
shifts
C. Latta et al., Nature Phys. 5,
758 (2009)
Maximum
trion excitation
Nuclear spin fluctuation
Stable-config
nuclear field
locked to
frequencies
Suppression of Nuclear Field Inhomogeneous Broadening
More enhancement on spin T2* with larger pump strength
larger pump
larger slope in  t
 t
tighter locking

0
(b)
Pump intensity
Absorption
40
90
70
60
20
Slope (a.u.)
–
Probe detuning
spin T2*

peak-to-dip ratio
-0.5
0
1.5
0.5
1.0
Pump Rabi (GHz)
Suppression of Nuclear Field Inhomogeneous Broadening
Thermal
value
–
Spin decoherence rate
extracted from dip-to-peak
ratio
–
T2* extended well above
thermal value
Deficiency: locking position
changes with probe scan
–
ehe |T->
Ωpump
|X+> e
Ωprobe
e
|X->
Coherent Spin Manipulations without Hyperfine Induced Dephasing
Pump 1
>>
Pump 2
>>
Probe
(fixed freq)
(fixed freq)
(freq scan)
–
Pump 1 + pump 2 locks nuclear field to a constant value
–
Pump 1 + probe measures spin T2*
Three Beam Measurement
Clean line shape
Spin decoherence rate ~ 1 MHz,
reduced by a factor of 400
Xu, X. et al., Nature 59, 1105 (2009)
Where’s the Frontier?
• Engineering coupled dot system with one electron in
each dot with nearly degenerate excited states.
• Demonstration of optically induced entanglement.
• Integration into 2D photonic bandgap circuits.
• Understanding of decoherence.
• Possible exploitation of nuclear coupling.
Semiconductor Nano-Optics:
An Interdisciplinary Collaboration
Dan Gammon
Naval Research Lab
Lu Sham
UC-San Diego
Paul Berman
Luming Duan
Roberto Merlin
U. Mich.
Outstanding Graduate Students**
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Nicolas Bonadeo (graduated)
Jeff Guest (graduated)
Gang Chen (graduated)
Todd Stievater (graduated)
Anthony Lenihan (graduated)
Elizabeth Tabak (graduated)
Elaine Li (graduated)
Gurudev Dutt (graduated)
Jun Cheng (graduated)
Yanwen Wu (graduated)
Qiong Huang (graduated)
Xiaodong Xu
Erik Kim
Katherine Smirl
Bo Sun
John Schaible
Vasudev Lai
**Alberto Amo - Autonoma University of Madrid

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