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Optically Driven Quantum Dot Based Quantum Computation. NSF CENTER - Frontiers of Optical Coherence and Ultrafast Science (FOCUS). NSF Workshop on Quantum Information Processing and Nanoscale Systems. Duncan Steel, Univ. Michigan L.J. Sham, UC-SD Dan Gammon, Naval Research Laboratories.

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optically driven quantum dot based quantum computation

Optically Driven Quantum Dot Based Quantum Computation

NSF CENTER - Frontiers of Optical Coherence and Ultrafast Science(FOCUS)

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-

Optically Controlled Spin

Optical control of spin:

  • Use spin as qubit
  • Use exciton for control and measurement

T2 > 1 ms

Operation time ~ 10 ps

( p-pulse)

T2 / Op. time > 105

requirements to build a qc divincenzo criteria
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

InAs

GaAs

Coupled QD’s

[001]

Coupled QD’s

GaAs

72 nm x 72 nm

Cross sectional STM

Boishin, Whitman et al.

Quantum Dots: The Solid State version of the ion approach

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

taken from R. Notzel

slide5

The Quantum Toolbox

Initialization (optical pumping)

Rotations (coherent Raman)

Entanglement (ORKKY or Coulomb)

Measurement (recycling transitions)

entanglement and two qubit operation
Entanglement and two qubit operation
  • Coherent tunneling provides a kinetic exchange interaction between dots.
  • 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)]
  • 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:
  • Hamiltonian for two spins
  • Exchange interactions
  • Excited state spectrum
  • Biexciton spectrum
  • B-field dependence
quantum dots atomic properties but better

InAs

GaAs

Coupled QD’s

[001]

Coupled QD’s

GaAs

72 nm x 72 nm

Cross sectional STM

Boishin, Whitman et al.

“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 nano-fabrication

AFM Image of Al0.5Ga0.5As QD’s formed on GaAs (311)b substrate. Figure taken from R. Notzel

slide8

PL imaging

First layer self-assembly

Growth Direction

Partial cap with GaAs

Indium flush

4 nm

Grow GaAs barrier.

2nd layer QD self-assembly

BOTTOM

QD

TOP

QD

QD PL image

Coupled dot spectroscopy

Repeat flush and cap

Processing for Diode

and Optical Mask

2

Intensity (arb. units)

QDs

1

Energy

-1V

EF

0

0V

C.B.

900

950

1000

1050

Electric Field

PL wavelength (nm)

V.B.

Schottky diode

Sample Development

MBE of InAs/GaAs

Self-Assembled Dots

Microscopy

slide9

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’

a

b

b’

Truth Tables based on quantum state probabilities

for Ideal and Optically Controlled Quantum Dot

(Science ‘03)

slide10
Anomalous Variation of Beat Amplitude and Phase:The result of spontaneously generated Raman coherence

Standard

Theory

(a)

  • Plot of beat amplitude and phaseas a function of the splitting.

Phys. Rev. Lett. - 2005

fast spin initialization in a single charged quantum dot theory
Fast spin initialization ina single charged quantum dot: theory

|T->

|t+>=|3/2>

|t->=|-3/2>

|T+>

H1

H2

-

V1

+

dark transitions

bright transitions

|z+>=|1/2>

|z->=|1/2>

|X+>

|X->

Bx

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.

After the magnetic field is applied in

Voigt geometry, the dark transitions

become bright.

Theory: Theory Phys. Rev. Lett. Jan. 2007

slide12

Fast spin initialization ina single charged quantum dot: experiment

VM absorption map as

a function of the applied bias

|T->

|T+>

I

pump

V1

H1

H2

V2

0.20

t

V1

II

0.15

|X+>

|X->

DC(V)

s

0.10

t>>s

Magnetic Field 0.88T

0.05

Bx

1324.41

1324.53

1324.47

Laser Energy (meV)

Blue circle region is transparent due to the laser beam depleting the spin ground states

Experiment: Phys. Rev. Lett. Aug. 2007

slide13

Fast spin initialization ina single charged quantum dot: experiment

|T->

|T->

|T+>

|T+>

re-pump

probe

probe

re-pump

V2

V1

H2

V2

V1

H1

s

s

|X+>

|X+>

|X->

|X->

absorption (a.u)

absorption (a.u)

re-pumpoff

re-pumpoff

H1

V1

H2

V2

recovered

absorption

re-pump on

absorption (a.u)

re-pump on

absorption (a.u)

1324.44

1234.48

1324.44

1234.48

Laser Energy (meV)

Laser Energy (meV)

fast spin initialization in a single charged qd
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).

dressed state picture
Dressed State Picture

The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion

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>

Strong pump

Weak probe

|2>

Power Spectrum of the Rabi Oscillations:Gain without inversionThe Mollow Spectrum of a Single QD

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

Impact of the High Speed Rabi experiment
optical control of two dot spins
Optical control of two dot-spins

Current work

PRB 07

Two trions with Coulomb interaction

Optical RKKY

time

Coulomb

e

dot #2

hole

dot #1

dot #2

<=== dot # 1 ===>

position

Four optical fields

Two optical fields

e wfs confined to each dot

Excited e wf covers both dots

Less demand on dot fabrication, more on optics

where s the frontier
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