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

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