David GershoniThe Physics Department, Technion-Israel Institute of Technology,

Haifa, 32000, Israeland

Joint Quantum Institute, NIST and University of Maryland, USA

Technion – Israel Institute of TechnologyPhysics Department and Solid State Institute

March 29, 2011, Aussois, France

MotivationCoherent control of anchored qubits – spins of

carriers.Coherent control of flying qubits – polarization of

photons. Semiconductor Quantum dots provide a unique

stage for controlling the interactions between both type of qubits, and they are compatible with the technology of light sources and detectors.

Outline• Two level system: Spin and Light Polarization

• Introduction to energy levels and optical transitions in SCQDs

• The bright and dark excitons as matter two level systems – Writing the exciton spin state by a polarized light pulse tuned

into excitonic resonances.

– Reading its spin state by a second polarized light pulse,

resonantly tuned into biexcitonic resonances.

– Manipulating its spin state by a third polarized and/or detuned pulse.

Two level system and the Bloch Sphere

2 2

| 0 |1

| |

,

| | | | 1

int

are complex amplitudes

is described by a po

onthe Bloch sphere

|

|

(| | ) 1/ 2

1/ 2(| | ) (| | ) 1/ 2i

1/ 2(| | )i

classical bit (0 or 1)– quantum bit (qubit – Bloch sphere)

5Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Linear Circular Elliptical

• General solution to Maxwell equations for the direction of the electric field vector of a photon is an ellipse

x y 2x y

• Jones vector:

Polarization – Poincare’ sphere

H

V

Poincare sphere

0 1 2 3, , ,s s s sStokes parameters

1

H Vs

H V

2

D Ds

D D

3

R Ls

R L

Information can be encoded in the photon’s polarization state.

4 measurements are required to determine the full polarization

state of light:

a 2x2 density matrix

0s H V R L D D

Selection rules for optical transitions in semiconductor QDs

7

hehh

Conduction Band

atomic s like

3 3

2 2;

1 1

2 2;

eeee ee

e

lh3 1

2 2;

ee

e

eee

e

so1 1

2 2;

ee

e

eee

Valence Band

atomic p like

3 3

2 21,1 ,

1 1

2 20,0 ,

3 3

2 2,

arg

promoting electron

leaving holeof

oppositech e and spin

~0.3 eV

~0.05 eV

~1.25 eV

3 3

2 21, 1 ,

1 1

2 20,0 ,

3 3

2 2,

STM (scanning tunneling microscope) images self assembled dots

Not all the same, but live forever and can be put into high Q - microcavities, easily

Single Quantum Dot - Single Quantum Dot - PhotoluminescencePhotoluminescence

GaAs

GaAs1.5 monolayer InAs (PCI)2nm GaAs

GaAs

h

emission due to radiative recombination

S

Off resonanceexcitation

P

• Two electrons (holes) non-interacting spin states:

• Electrons (holes) singlet state:

• Electrons (holes) triplet states:

Spin interaction of charge carriers

S

,, T0T-1(-3)T+1(+3)

,, , 2

321

23

21

23

21

23

21

23

21

23

21

23

21

23

21

Total spin: )3(1 )3(1 0 0

e-e (h-h) exchange ~5meV

Energy

S

Non-

radiatively

Spin blockaded

30 (15)

meV

Bright ExcitonBright Exciton

Dark ExcitonDark Exciton

Isotropic electron-hole

exchange

Anisotropic electron-hole

exchange

a

as

s

Δ0 ≈ 0.3meV

Δ1 ≈ 0.03meV

Δ2 ≈ 0.001meV

Non interacting

3 12 2 2 3 1

2 2 2

3 12 2 1 3 1

2 2 1

V

H

Quantum dot e-h pair (exciton) states

Dark exciton: Ground- state, Optically inactive,

quantum two level system

The dark exciton’s advantages • Its lifetime is long – comparable to that of a single electron or

hole.

• It is neutral and therefore less sensitive than charged particles to fluctuating electric fields.

• Due to its fine structure and smaller g-factor, it is more protected than the electron or hole from fluctuating magnetic fields, especially where no external magnetic field is applied.

as an in-matter qubitBut how can it be addressed?But how can it be addressed?

E. Poem et al., Nature Physics ( November 2010)

E

I

Biexciton excitation spectrum

S

SP

P

0PX

h

h

T

S

e

e

S

T

e hS S

L

R

H

V

i

D

D

i 1

0SX

0 0e hT T e hS Te hT S

1 3e hT T

0PXX

We can generate any of these biexciton spin states by tuning the energy and polarization of the laser.

Experimental setup

SubstrateSubstrate

Wetting layerWetting layerQuantum DotQuantum Dot

Quantum DotQuantum Dot

Quantum DotQuantum Dot

First pulse laser

Second pulse laser

First monochromator and CCD camera/Detector

Delay line

Beam combiner

Spectral Filter

Two channel arbitrarypolarization rotator

Sample

Objective

He

Second monochromator And detector

Polarizingbeam splitter

1st pulse

12

12

12

12

2nd pulse

0X

*0X

0XX

V

H

H

V

*0XX

0

R

θ

2A/I0

D

H

V

L

D

P0(θ,)

1st pulse

Poincare sphere Bloch sphere

LR2

1H

2

1

2

i L-R2

iV R LR

‘Writing’ the spin with the 1st photon0X

∆=30µev

A

S

A

S

‘Reading’ the spin with the 2nd photon

0X

*0XX

Bloch

heTS

R

eS

hT

Poincare

I(XX0)

2 6 2 6

-100

0

100

200

300

400

500

600

1

2

3

4

5

1.2805 1.281 1.2815 1.282 1.2825 1.283 1.2835 1.2865 1.2870

1

2x 10

5

Time resolved, two-photon PL measurement XX0

TT, X0P excitation

t [

ps]

E [eV]

XX0T3XX0

T0

X-1 XX0 X0

X+1

XX0

XX0T0

5

[103 c

oun

ts/m

in]

]in

tega

ted

Cou

nts

/min

[

XX0T3

X0

Quasi-resonant Resonant

Conclusions so far…• We demonstrate for the first time that the exciton

spin can be ‘written’ in any arbitrary coherent superposition of its symmetric and anti-symmetric spin eigenstates by an elliptically polarized short laser pulse.

• We showed that by tuning a second polarized laser pulse to a biexcitonic resonance, the exciton spin can be faithfully ‘readout’.

• Y. Benny, et al, "Coherent optical writing and reading of the exciton spin state in single quantum dots " (arXiv:1009.5463v1

[quant-ph]28 Sep 2010), PRL 2011.

Technion – Israel Institute of TechnologyPhysics Department and Solid State Institute

March 31, 2011, Aussois, France

E. Poem, Y. Kodriano, Y. Benny, C. Tradonsky, N. H. Lindner, J. E. Avron and D. Galushko

The Physics Department and The Solid State Institute, Technion-Israel Institute of Technology, Haifa, 32000, Israel

B. D. Gerardot and P. M. PetroffMaterials Department, University of California Santa Barbara, CA,

93106, USA

Summary: