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Optically Driven Quantum Dot Based
Quantum Computation NSF Workshop on Quantum
Information Processing and Nanoscale Systems. Duncan Steel, Univ. Michigan
L.J. Sham, UC-SDDan Gammon, Naval Research Laboratories
NSF CENTER - Frontiers of Optical Coherence and
Ultrafast Science (FOCUS)
ARO/NSA, AFSOR, DARPA, ONR, NSF
Optically Controlled Spin
Optical control of spin:
– Use spin as qubit
– Use exciton for control and measurement
T2 > 1 s
Operation time ~ 10 ps
( -pulse)
T2 / Op. time > 105
x-
Requirements to build a QC
(Divincenzo Criteria)Well defined qubits (no extended states)
InitializableUniversal set of quantum gates (highly nonlinear)
Qubit specific measurementsLong coherence time (in excess of 104 operations in the coherence time)
The III-V Semiconductor-Optics Approach to QC
• Direct bandgap semiconductor allows for optical control
• Small effective mass => large Bohr radius => large optical coupling
• Ease of doping allows single electron spin manipulation
• Epitaxial growth and fabrication technology in place for large scale integration
• System is robust against pure dephasing
• Optics and electronics easily integrated
• Optical manipulation can have clock speeds greater than 10 THz
• Adaptive optics allows high speed spatial and temporal pulse shaping
InAs
GaAs
GaAs
Cross sectional STMBoishin, Whitman et al.
Coupled QD’s
Coupled QD’s [001]
72 nm x 72 nm
taken from R. Notzel
Quantum Dots: The Solid State version of the ion approach
Rotations (coherent Raman)Initialization (optical pumping)
Entanglement (ORKKY or Coulomb)
Measurement (recycling transitions)
The Quantum Toolbox
Entanglement and two qubit operation
1. Coherent tunneling provides a kinetic exchange interaction between dots.
2. A DC bias can be chosen so that kinetic exchange exists only in the optically excited state i.e. only during the laser pulse.[Stinaff et al., Science (2006)]
3. A theoretical scheme has been worked out for a swap gate using this resonant exchange process[Emary and Sham, Phys. Rev. B (2007)] Need to determine:
1. Hamiltonian for two spins2. Exchange interactions3. Excited state spectrum4. Biexciton spectrum5. B-field dependence
Quantum Dots: Atomic Properties But Better
• Larger oscillator strength (x104)• High Q (narrow resonances)• Faster• Designable• Controllable• Integratable with direct solid state photon sources (no need to up/down convert)
• Large existing infrastructure for nano-fabrication
InAs
GaAs
GaAs
Cross sectional STMBoishin, Whitman et al.
Coupled QD’s
Coupled QD’s [001]
72 nm x 72 nmAFM Image of Al0.5Ga0.5As QD’s formed on GaAs (311)b substrate. Figure taken from R. Notzel
“Quantum computation with quantum dots” Daniel Loss and David P. DiVincenzo, Phys. Rev. A. 57 p120 (1998)
Sample Development
First layer self-assembly
Repeat flush and cap
Indium flush
Partial cap with GaAs
Grow GaAs barrier.2nd layer QD self-assembly
4 nm
Growth Direction
MBE of InAs/GaAsSelf-Assembled Dots
Microscopy
900 950 1000 1050
0
1
2
Inte
nsity
(ar
b. u
nits
)
PL wavelength (nm)
TOPQD
BOTTOMQD
QD PL image
PL imaging
-1VQDs
0V
V.B.
C.B.
EF
Schottky diode
Processing for Diodeand Optical Mask
Coupled dot spectroscopy
Ene
rgy
Electric Field
|00>|01>
|10>|11>
|00>
|01>
|10>
|11>
0 0
1
000
0
1
0
1
00
1
00
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Population
Input States
Output States
Ideal Truth Table
|00>|01>
|10>|11>
|00>
|01>
|10>
|11>
0 0
0.63
0.130 0
0.17
0.67
0
0.8
0.06
0.11
1
0.2
0.14
0.090
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Population
Input State
Output State
Physical Truth Table
Truth Tables based on quantum state probabilitiesfor Ideal and Optically Controlled Quantum Dot
(Science ‘03)
First Demonstration of an all Optically Driven Semiconductor Based Conditional
Quantum Logic GateIf ‘a’ is the control bit and ‘b’ is the target bit, the wiring diagram is on the left and the truth table is given by
a b a’ b’0 0 0 00 1 0 11 0 1 11 1 1 0
a a’
b b’
Anomalous Variation of Beat Amplitude and Phase:
The result of spontaneously generated Raman coherence
(a)0 20 40
(a)
Splitting ( )eV
-0.4
-0.2
0.0
0 20 40
Phase (
)
(Splitting )eV
(b)
StandardTheory
• Plot of beat amplitude and phase as a function of the splitting.
Phys. Rev. Lett. - 2005
Fast spin initialization ina single charged quantum dot: theory
After the magnetic field is applied in Voigt geometry, the dark transitionsbecome bright.
If the magnetic field is applied in Faraday geometry, the transition from |t+> (|t->) to |z-> (|z+>) is dipole forbidden transition. So the speed of the spin initialization is limited by the weak decay from |t+> (|t->) to |z-> (|z+>) induced by the heavy-light hole mixing.
|z->=|1/2>|z+>=|1/2>
|t+>=|3/2> |t->=|-3/2>
+ -dark transitions
|T+>
|T->
V1 H1 H2
bright transitions
Bx
|X+>|X->
Theory: Theory Phys. Rev. Lett. Jan. 2007
Fast spin initialization ina single charged quantum dot: experiment
Blue circle region is transparent due to the laser beam depleting the spin ground states
t>>s
Bx
VM absorption map as a function of the applied bias
pump
|T+>
|T->
|X+>|X->
s
tV1
I V1 H1 V2
1324.47 1324.531324.41
0.05
0.10
0.15
0.20
II
H2
Magnetic Field 0.88T
DC
(V)
Laser Energy (meV)
Experiment: Phys. Rev. Lett. Aug. 2007
Fast spin initialization ina single charged quantum dot: experiment
1324.44 1234.48
Laser Energy (meV)
re-pump off
re-pump on
H2 V2
re-pump off
1324.44 1234.48Laser Energy (meV)
V1 H1
re-pump onrecovered absorption
abso
rpti
on (
a.u)
abso
rpti
on (
a.u)
abso
rpti
on (
a.u)
abso
rpti
on (
a.u)
s
re-pump
H2 V2
probe
|T+>
|X+>|X->
|T->
s
re-pump
H1V1
probe
|T+>
|X+>|X->
|T->
V1 V2
Fast Spin Initialization in a Single Charged QD
THEORY: C. Emary et al. Phys. Rev. Lett. 98, 047401 (2007).EXPERIMENT: Xiaodong Xu et al. Phys. Rev. Lett. in press (2007).
Demonstrated initialization of the single spin in the lower state to 98% at 1.3 T.
Time scale for initialization ~ 0.25 ns. One of the fastest initialization implemented.
Equivalent to cooling a spin in ensemble of spins from 4 K to 0.2 K or, equivalently, letting the spin relax to the ground state in a magnetic field of 60 T at 4K.
The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion
Autler Townes Splitting
Mollow Spectrum: New physics in absorption
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)..
Dressed State Picture
Power Spectrum of the Rabi Oscillations:Gain without inversion
The Mollow Spectrum of a Single QD
|2>
|3>
Strong pumpWeak probe
Science, August 2007
Impact of the High Speed Rabi experiment
• Demonstrates high speed Rabi oscillations in excess of 1.4 GHz with <10 nano-Watts: Dot Switching with ~10-18Joules. 100GHz limit.
• Achievable with low power diode lasers
• Enables use of 960 nm band telecom switching technology
Coulomb
Optical control of two dot-Optical control of two dot-spinsspins
Two trions with Coulomb interaction Optical RKKY
PRB 07Current work
e wfs confined to each dot
Two optical fieldsFour optical fields
Excited e wf covers both dots
hole
time
position<=== dot # 1 ===>
dot #2
e
dot #2
Less demand on dot fabrication, more on optics
dot #1