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NSF CENTER - Frontiers of Optical Coherence and Ultrafast Science (FOCUS)
Optically Driven Quantum Dot
Based Quantum Computation
NSF Workshop on Quantum Information
Processing and Nanoscale Systems.
Duncan Steel, Univ. Michigan
L.J. Sham, UC-SD
Dan Gammon, Naval Research Laboratories
ARO/NSA, AFSOR, DARPA, ONR, NSF
Optically Controlled Spin
x-
Optical control of spin:
– Use spin as qubit
T2
> 1 ms
Operation time ~ 10 ps
( p-pulse)
T2 / Op. time
> 105
– Use exciton for
control and
measurement
Requirements to build a QC
(Divincenzo Criteria)
Well defined qubits (no extended states)
Initializable
Universal set of quantum gates (highly
nonlinear)
Qubit specific measurements
Long coherence time (in excess of 104
operations in the coherence time)
The III-V Semiconductor-Optics Approach to QC
Quantum Dots: The Solid State version of the ion approach
• 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
taken from R. Notzel
GaAs
InAs
Coupled QD’s
Coupled QD’s
72 nm x 72 nm
GaAs
Cross sectional STM
Boishin, Whitman et al.
The Quantum Toolbox
Initialization (optical pumping)
Measurement (recycling transitions)
Rotations (coherent Raman)
Entanglement (ORKKY or
Coulomb)
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.
2.
3.
4.
5.
Hamiltonian for two spins
Exchange interactions
Excited state spectrum
Biexciton spectrum
B-field dependence
“Quantum computation with quantum dots” Daniel Loss and
David P. DiVincenzo, Phys. Rev. A. 57 p120 (1998)
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 nanofabrication
•
•
•
•
•
•
GaAs
InAs
Coupled QD’s
Coupled QD’s
AFM Image of Al0.5Ga0.5As QD’s
formed on GaAs (311)b substrate.
Figure taken from R. Notzel
72 nm x 72 nm
GaAs
Cross sectional STM
Boishin, Whitman et al.
Sample Development
Intensity (arb. units)
MBE of InAs/GaAs
Self-Assembled Dots
First layer self-assembly
Partial cap with GaAs
Indium flush
Grow GaAs barrier.
2nd layer QD self-assembly
TOP
QD
PL imaging
BOTTOM
QD
QD PL image
2
1
0
900
950
1000
1050
PL wavelength (nm)
Repeat flush and cap
Coupled dot spectroscopy
Microscopy
QDs
EF
Growth
Direction
4 nm
0V
C.B.
V.B.
-1V
Schottky diode
Energy
Processing for Diode
and Optical Mask
Electric Field
First Demonstration of an all Optically Driven
Semiconductor Based Conditional Quantum Logic Gate
If ‘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’
a
a’
b
b’
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
Truth Tables based on quantum state probabilities
for Ideal and Optically Controlled Quantum Dot
Ideal Truth Table
Physical Truth Table
1
1
1
1
1
1
0.9
1
0.9
0.8
0.8
0.8
0.7
0.63
0.7
0.6
0.67
0.6
Population 0.5
Population 0.5
0.4
0.4
0.3
0
0.2
0
0
|10>
0
0
0
|00>
|01>
Input States
|11>
0
0
0.1
0.3
0
0
0
|10>
0
0
|01>
Output States
|00>
0
0.2
0
0.1
(Science ‘03)
0
0
0.13
0.17
|11>
0.06
0.11
0.14
0
|00>
|11>
0
0.2
0.09
|01>
|10>
Input State
|10>
|01> Output State
|00>
|11>
Anomalous Variation of Beat Amplitude and Phase:
The result of spontaneously generated Raman coherence
Bea t ampli tude (a.u .)
Standard
Theory
(a)
(a)
0
20
40
Spl itti ng ( meV)
• Plot of beat amplitude and phase as a function of the splitting.
Phys. Rev. Lett. - 2005
Fast spin initialization in
a single charged quantum dot: theory
|T->
|t+>=|3/2>
+
dark
|t->=|-3/2>
transitions -
|T+>
V1
H1
H2
bright transitions
|z+>=|1/2>
|z->=|1/2>
|X+>
|X->
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.
Bx
After the magnetic field is applied in
Voigt geometry, the dark transitions
become bright.
Theory: Theory Phys. Rev. Lett. Jan. 2007
Fast spin initialization in
a single charged quantum dot: experiment
VM absorption map as
a function of the applied bias
|T->
|T+>
I
pump
V1
V1
0.20
t
0.15
|X+>
H1
H2
V2
II
|X->
s
0.10
t>>s
Magnetic Field 0.88T
0.05
Bx
1324.41
1324.47
Laser Energy (meV)
1324.53
Blue circle region is transparent due to the
laser beam depleting the spin ground
states
Experiment: Phys. Rev. Lett. Aug. 2007
Fast spin initialization in
a single charged quantum dot: experiment
|T->
|T+>
re-pump
V1
H2
probe
V2
V1
V2
H1
s
|X+>
|X+>
|X->
absorption (a.u)
|X->
re-pump off
H2
re-pump on
1324.44
1234.48
Laser Energy (meV)
re-pump off
V1
V2
recovered
absorption
absorption (a.u)
absorption (a.u)
re-pump
probe
s
absorption (a.u)
|T->
|T+>
H1
re-pump on
1324.44
1234.48
Laser Energy (meV)
Fast Spin Initialization in a Single Charged QD
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.
THEORY: C. Emary et al. Phys. Rev. Lett. 98, 047401 (2007).
EXPERIMENT: Xiaodong Xu et al. Phys. Rev. Lett. in press (2007).
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>
Weak probe
Strong pump
|2>
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
Optical control of two dot-spins
Current work
PRB 07
Two trions with Coulomb interaction
Optical RKKY

time


e


Coulomb
dot #2
hole


dot #1
dot #2
position
Four optical fields
e wfs confined to each dot
Less demand on dot fabrication, more on optics

<=== dot # 1 ===>
Two optical fields
Excited e wf covers both dots
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