optically driven spins in semiconductor quantum dots: toward iii-v based quantum computing
DESCRIPTION
Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing. Duncan Steel - Lecture 1. DPG Physics School on "Nano- Spintronics ” Bad Honnef 2010. Requirements to build a QC (Divincenzo Criteria). Well defined qubits - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/1.jpg)
Optically Driven Spins in Semiconductor Quantum Dots:
Toward III-V Based Quantum Computing
DPG Physics School on "Nano-Spintronics”
Bad Honnef 2010
Duncan Steel - Lecture 1
![Page 2: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/2.jpg)
Requirements to build a QC(Divincenzo Criteria)
1. Well defined qubits 2. Universal set of quantum gates (highly
nonlinear) 3. Initializable4. Qubit specific measurements5. Long coherence time (in excess of 104
operations in the coherence time)
![Page 3: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/3.jpg)
Quantum Dots:Atomic Properties But Engineerable
• Larger oscillator strength (x104)• High Q (narrow resonances)• Faster• Designable• Controllable• Using ultrafast light, we have fast (200
GHz) switching with no ‘wires’. • Integratable with direct solid state photon
sources (no need to up/down convert)• Large existing infrastructure for nano-
fabrication• High temperature operation – Compared
to a dilution refrigerator• CHALLENGE: spatial placement and
size heterogeneity
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
![Page 4: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/4.jpg)
KEY REQUIREMEMT: CONTROLA logic device is highly nonlinear
Requires a two state system: 0 and 1
Semiconductor with periodic lattice
![Page 5: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/5.jpg)
The Principle Physics for Optically Driven Quantum Computing in semiconductors is
the Exciton
Semiconductor with periodic lattice
![Page 6: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/6.jpg)
Can the Exciton be Controlled in High Dimensional crystals?
Excitons in high dimenisonal crystals do not have a simple atomic like nonlinearity: Quantum gates are hard to imagine
Rabi oscillations in quantum wellsCundiff et al. PRL 1994Schulzgen et al., PRL 1999
Semiconductor with periodic lattice
hole
electron
With coulomb coupling, the e-h pair forms an exciton:Extended state of the crystal
![Page 7: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/7.jpg)
Is the Exciton a Well defined qubit in 1, 2, or 3 Dimensional Cystal?
The exciton in higher dimensional cyrstals is not a well defined qubit.
Bloch Theorem: for a periodic potential of the form The solution to Schrödinger’s equation has the form
€
Vr r +
r d ( ) = V
r r +
r d ( )
€
ψr r ( ) = e i
r k ⋅
r r u
r r ( ) where u
r r +
r d ( ) = u
r r ( )
hole
electron
![Page 8: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/8.jpg)
Can the Exciton be Controlled in High Dimensional cyrstals: i.e., can you build a universal set of quantum gates?
Rabi Oscillations:Qubit Rotations
Recall the spin paradigm for quantum computing:
€
↑
€
↓ €
↑
€
↓ €
↑
€
↓
![Page 9: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/9.jpg)
Coherent optical control•Coherent optical control of an electronic state means controlling the state of the spin or pseudo- spin Bloch vector on the Bloch sphere.
•It is a highly nonlinear optical process and is achieved with a combination of Rabi oscillations and precession.
€
↑ or excited
€
↓ or ground
x
y
z
€
↑ or excited
€
↓ or ground
x
y
z
Rabi Precession
![Page 10: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/10.jpg)
Simple Coherent Control in an Atom – Rabi Flops
Laser Pulse
€
↑
€
↓
x
y
z
€
H =hωo
2−1 00 1 ⎡ ⎣ ⎢
⎤ ⎦ ⎥+
h2
0 ΩRΩR
* 0 ⎡ ⎣ ⎢
⎤ ⎦ ⎥cosωt
€
ωo
€
↑
€
↓
Controlling t and/or ΩR allows control of the switching between up and down, creating states like:
€
ψ = 1 2( ) ↑ + ↓[ ]
€
ΩR =r μ ⋅
r E
h
![Page 11: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/11.jpg)
Rabi Oscillations
€
ih∂ ψ∂t
= H0 − μE0 sinωt[ ]ψ
H0 un = En un n =1,2; μ = u1 er u2
Pulse Area
€
θ =h2
μE0 ′ t ( )d ′ t 0
t∫0
C2 t( )2
1
2
6 7
![Page 12: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/12.jpg)
Can the Exciton be Controlled in High Dimensional cyrstals: i.e., can you build a universal
set of quantum gates?
Excitons in high dimenisonal crystals do not have a simple atomic like nonlinearity: Quantum gates are hard to imagine
![Page 13: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/13.jpg)
What does an atomic like nonlinearity look like in the laboratory: Saturation (Spectral Hole Burning) Spectroscopy
Absorption Saturated absorption
Differential absorption
Quantum computing is a highly nonlinear system (intrinsic feature of a two level system in contrast to a harmonic oscillator. Nonlinear spectroscopy quantifies the behavior.
€
α =αo
ω − ω0( )2 + γ 2 1+ I
I sat
⎛ ⎝ ⎜
⎞ ⎠ ⎟2
![Page 14: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/14.jpg)
Pump excitation reduces absorption on excited transition
Pump
ProbeTuning
Differential
Quantum Dot Spectrum
Nearly Degenerate Differential Transmission
![Page 15: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/15.jpg)
CW Nonlinear Spectroscopy Experimental Set-up
ENL ∝ Im[ χ ] Erobe IumIdetected ∝ ENL× Erobe
*
Epump
Eprobe
Eprobe
Esignal
Lock-in amplifier
Acousto-opticModulators ƒ≈100 Mhz
RF electronics
Detector
Frequency stabilizedlasers
![Page 16: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/16.jpg)
Many-Body Effects in High Dimensional Semiconductors
1.508 1.516
Absorbance (a.u.)
Energy (meV)
hh
lh
0
DT/T (a.u.)
1.5075 1.5125 1.5175
Energy (eV)
Wang et al. PRL 1993
Excitation Wavelength
![Page 17: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/17.jpg)
To Suppress Extended State Wave Function, consider a zero dimensional system: a Quantum Dot
ExcitonElectron based qubit
TrionSpin based qubit
|0>
|1>
|0>|1>
|i>
Figure of merit ~10 -10 4 6
e
h300 A
e
h300 A
Figure of merit ~10 -10 2 4
Dephasing time ~10 sec (in SAD’s)
-9 Dephasing time >>10 sec-9
Still a complex manybody system
![Page 18: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/18.jpg)
.
Detection energy (meV)
Exci
tatio
n en
ergy
(meV
)
1622
1624
1626
1628
1630
1621 1622 1623 1624 1625 1626 1627
Quantum Dot Photoluminescence as a Function of Laser Excitation Energy
Atomic-like spectrum – Discrete states followed by continuum
![Page 19: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/19.jpg)
• The luminescence and nonlinear spectra have many lines in common• The luminescence and
nonlinear techniques do not measure the same optical properties• The nonlinear response is
resonant and highly isolated
Photoluminescence and Nonlinear Spectra ComparisonPL
Int
ensi
tyN
onlin
ear S
igna
l In
tens
ity
![Page 20: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/20.jpg)
Use a Quantum Dot to Build a 2-Qubit Computer?
€
+12
€
+32
€
−12
€
−32
€
j = 32,m j
€
j = 12,m j
Filled valence band
Empty Conduction band
€
↓
€
↑
€
⇑↓↑
€
⇓↑↓
First break with atom picture: Lack of spherical symmetry means angular momentum is not a good quantum number
€
σ +
€
σ −
Ground and first excited states for neutral quantum dot
![Page 21: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/21.jpg)
How to Build a Two-Bit Quantum Computer
Need two quantum bitsNeed couplingNeed coherent control
Two spin-polarized excitonsCoulomb interactionResonant polarization- dependent optical coupling
|0>
|1>+
|0>
|1>
|00>
|10>Coulomb Interaction
B-Field|01>
|11>
σ+ σ-
![Page 22: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/22.jpg)
The Two-Bit System
GaAs
AlGaAs
AlGaAs
Optical Field
|00>
![Page 23: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/23.jpg)
The Two-Bit System
GaAs
AlGaAs
AlGaAs
Optical Field
σ+
|01>
![Page 24: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/24.jpg)
The Two-Bit System
GaAs
AlGaAs
AlGaAs
Optical Field
σ-
|10>
![Page 25: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/25.jpg)
Formation of the |11> state
GaAs
AlGaAs
AlGaAs
Optical Field
Biexciton
σ+ σ-
|11>
![Page 26: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/26.jpg)
Do quantum dots experience pure dephasing?
Detection of coherence is made by measuring an observable proportional to where
€
C2∗C1
€
ψ =C11 +C2 2The equation of motion for the coherence is
€
ddt
C2∗C1 = −γC2
∗C1 + other terms
€
γ arises from either loss of probability amplitude or pure dephasing due to a randomly fluctuating phase between the two probability amplitudes:
Relationship to NMR language
€
C2∗C1 = c2
∗c1e−
Γ2
+iω 0 ⎛ ⎝ ⎜
⎞ ⎠ ⎟t +θ R t( )
T1 = 1
Γ ; T2 =1γ = 1
2Γ +γ puredephasing
![Page 27: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/27.jpg)
Calculated Coherent Wavelength-Resolved Differential Transmission from a Two Level System
• The coherent contribution leads to an asymmetric lineshape in the absence of extra dephasing processes.• In the presence of strong
extra dephasing processes the lineshape develops into a sharp resonance on top of a broader resonance (Prussian helmet).
-2 -1 0 1 2-2 -1 0 1 2Probe detuning ( units)
ph =10 rel ph = 0
No pure dephasing Strong pure dephasing
Non
linea
r Sig
nal
Inte
nsity
(a.u
.)
![Page 28: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/28.jpg)
• “Coherent” and “incoherent” contributions •Homogeneously broadened• T1~ 19ps and T2~ 32ps (i.e. T2 ~ 2
T1 , absence of significant extra dephasing shows dots are robust against decoherence)
Measured Coherent Differential Transmissionfrom a Single Quantum Dot:
No extra dephasing =>quantum coherence is robust
Non
linea
r Sig
nal
Inte
nsity
(a.u
.)
![Page 29: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/29.jpg)
The Two-Bit System
GaAs
AlGaAs
AlGaAs
Optical Field
σ+
![Page 30: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/30.jpg)
The Two-Bit System
GaAs
AlGaAs
AlGaAs
Optical Field
σ-
![Page 31: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/31.jpg)
First Step Towards Semiconductor Based Quantum Computing:
Two Exciton-State Quantum Entanglement
Quantum entanglement in the wave function is a key feature in quantum computers. This is the property which allows them to surpass classical computers in computational ability.
( ) ( ) ( ) ( )23
21
21
23 +−++−−
+−+−−+ΨΨ+ΨΨ=Ψ
eeeeee cc
21-2
1+
23+
23-
21-2
1+
23+
23-
+σ-σ+c- c+
σ- polarized exciton state σ+ polarized exciton state
Quantum wave function shows entanglement of two exciton-states.
+
![Page 32: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/32.jpg)
The Exciton Based Two Qubit SystemBloch Spin Vector Basis (Feynman, Vernon, Hellwarth)
![Page 33: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/33.jpg)
Turn off the CoulombCorrelation
Turn on the Coulomb Correlation
No Signal !!
4 5 6 7 8 9
Ground state
depletion
Entanglement
Total Signal
-2 -1 0 1 2 3
σ- σ+
Pump: σ-
1==== −+−+
Pumpσ-
+-Probeσ+g Pump
σ-
- +Probeσ+g
Probe ( )4 5 6 7 8 9-2 -1 0 1 2 3Probe ( )
![Page 34: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/34.jpg)
Experiment : Coulomb Correlation Quantum Entanglement of two exciton-states
![Page 35: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/35.jpg)
Entanglement of Two Exciton States: Non Factorizable Wavefunction
ψ =C0 g +C+ σ + +C - σ - +Cb b
Non-interacting CaseFactorizable wavefunction:
With Coulomb CorrelationHow small Cb is depends on linewidth of state b and DE
b
σ+σ-
g
Cb =C+C−C0
b
σ+σ-
g
DE
Cb ≈0
![Page 36: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/36.jpg)
The Two (Exciton) Qubit System
GaAs
AlGaAs
AlGaAs
Optical Field
|00>
![Page 37: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/37.jpg)
The Two (Exciton) Qubit System
GaAs
AlGaAs
AlGaAs
Optical Field
σ+
|01>
![Page 38: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/38.jpg)
The Two (Exciton) Qubit System
GaAs
AlGaAs
AlGaAs
Optical Field
σ-
|10>
![Page 39: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/39.jpg)
The Two (Exciton) Qubit System
GaAs
AlGaAs
AlGaAs
Optical Field
Biexciton
σ+ σ-
|11>NOTE: In semiconductor systems the “Dipole Blockade” is a naturally occuring phenomena, but much stronger, usually, than the dipole term (Coulomb Blockade).
![Page 40: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/40.jpg)
Photoluminescence and Coherent Nonlinear Optical Spectra
• Superlinear excitation intensity dependence of photoluminescence from the biexciton-to-exciton transition
![Page 41: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/41.jpg)
The Bound Biexciton (Positronium Molecule)
• Higher order Coulomb correlations lead to 4-particle correlations and the bound biexciton
• An essential feature of optically induced entanglement and a quantum controlled not gate
m=-3/2 m=3/2
m=-1/2 m=1/2
DE=biexciton binding energy
![Page 42: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/42.jpg)
Cg C+ C- Cb
0.9 0.3 0.3 <<0.005
Quantification of Entanglement: Entropy*
b
σ+σ-
g
DE
For two-particle system, the entropy of entanglement goes between 0 and 1. Zero entropy means product state. Non-zero entropy indicating entanglement.From our experiment, using the upper limit for Cb, E =0.08±0.02*
*E~0.2 measured beyond chi-3 limit. Now up to E~1
C.H. Bennett,D. P. DiVincenzo, J. A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)
![Page 43: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/43.jpg)
Creation of the Bell State
21-2
1+
23+
23-
21-2
1+
23+
23-
+ σ-σ+c0 c+-
unexcited state Biexciton state
Quantum wave function shows entanglement of the ground state and the biexciton.
+
![Page 44: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/44.jpg)
The Two (Exciton) Qubit SystemRabi Oscillations
GaAs
AlGaAs
AlGaAs
Optical Field
|00>
![Page 45: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/45.jpg)
The Two (Exciton) Qubit SystemRabi Oscillations
GaAs
AlGaAs
AlGaAs
Optical Field
σ+
|01>
![Page 46: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/46.jpg)
Rabi Oscillations - qubit rotations
ih∂ ψ∂t = H0 −μE0sinωt[ ]ψ
H0 un =En un n=1,2; μ = u1 er u2
Pulse Area
€
θ =h2
μE0 ′ t ( )∫ d ′ t 0
t∫
0
C2 t( )2
1
2
![Page 47: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/47.jpg)
One Qubit Rotation in a Single Quantum DotThe Exciton Rabi Oscillation
• Rabi oscillations demonstrate an arbitrary coherent superposition of exciton and ground states,
• A pulse area of gives a complete single bit rotation,
/2-pulse -pulse -pulse
↑↓population:
Time (ps) Time (ps) Time (ps)
final quantumstate (beforedecoherence):
c↓↓↓↓ +c↑↓↑↓ or c↓↓↓↓ +c↓↑↓↑
↓↓→ ↑↓ or ↓↓ → ↓↑ ψ = 1
2 ↓↓ + 12 ↑↓ ψ = ↑↓ ψ = ↓↓
Excitonic energy levels Rabi oscillations
↓↓
Epump
↓↑↑↓
“Damping” is due to excitation induced increase in T1
![Page 48: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/48.jpg)
Physics for Optically Driven Spin
Semiconductor Quantum Coherence
Engineering
|0>
|X>
Neutral Exciton
Electronic Spin Qubit
Successful coherent optical manipulation of the optical Bloch vector necessary to manipulate
the spin vector
Negative Exciton
€
↑
€
↓€
T : trion
![Page 49: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/49.jpg)
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 g-factor and decays with time.
![Page 50: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/50.jpg)
CN
OS
(a. u
.)
Single Electron Spin Coherence:Raman Quantum Beats
X -
X
Charged Exciton System
Neutral Exciton System
0 500 1000 1500 2000 2500Delay (ps)
Single Charged Exciton
Ensemble Charged Excitons
Single Neutral Exciton
T2* >10 nsec at B=0
hs (m
eV)
Phys. Rev. Lett. - 2005
![Page 51: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/51.jpg)
Anomalous Variation of Beat Amplitude and Phase
(a) (b)
StandardTheory
• Plot of beat amplitude and phase as a function of the splitting.
![Page 52: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/52.jpg)
(a)
StandardTheory
Anomalous Variation of Beat Amplitude and Phase
• Plot of beat amplitude and phase as a function of the splitting.
![Page 53: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/53.jpg)
Spontaneously Generated Coherence (SGC)Trion
• 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.
![Page 54: Optically Driven Spins in Semiconductor Quantum Dots: Toward III-V Based Quantum Computing](https://reader038.vdocuments.us/reader038/viewer/2022110215/56816937550346895de09b79/html5/thumbnails/54.jpg)
Anomalous Variation of Beat Amplitude and Phase:The result of spontaneously generated Raman coherence
(a)
StandardTheory
• Plot of beat amplitude and phase as a function of the splitting.