Optical control of electronsin single quantum dots

Semion K. Saikin

University of California, San Diego

2

Optical Control of electrons in QDs

Quantum InformationProcessing

PhotonicsSingle Electron Devices

Spintronics

V

Devices: D. Gammon, NRL

Spectroscopy: group of D. G. Steel, U. Michigan

Theory & Modeling: group of L. J. Sham, UCSD

Support:

3

Content• Semiconductor quantum dot structures:

Design and Applications

• Properties of single dots:

Energy levels structure, Spin states

Interaction with light, excitons

• Optical Control:

Goal and device design

Optical cooling

Single dot switch

Operations with coupled dots

• Conclusions

4

Semiconductor QDsArtificial Atoms

Vertical QD

Elzerman et al. Nature 430, 431(2004)

Gated QDSelf-assembled

dots

1 m

Interfacefluctuation QDs

D.Gammon, et al.,PRL 76, 3005 (1996)

NIST websiteKoichiro Zaitsu, et al.,APL 92, 033101 (2008)

Lattice mismatch

GaAs

InAs

GaAs

AlGaAs

Interfaceimperfections

GatedepletionEtching

0.1 m

5

QD devicesPresent and Future

Lasers & Optical Amplifiers Photodetectors

Solar Cells

Thermoelectric elements

Single Electron Memory

Single photon sources & modulators

Quantum Information Processing

Future

Past

Low threshold currentWeak temperature dependenceAdjustable frequency range

Broad frequency spectrumHigh responsivityHigh T operation

High efficiency ofphoton to electronconversion

Slow relaxationLong coherence time

Control for electron and phonon mobility

Ability to controlLong relaxation time

6

Content• Semiconductor quantum dot structures:

Design and Applications

• Properties of single dots:Energy levels structure, Spin states

Interaction with light, excitons

• Optical Control:

Goal and device design

Optical cooling

Single dot switch

Operations with coupled dots

• Conclusions

7

Energy Levelsquantization

E1e

E2e

E1h

E2hEV

EC

EC

EV

E3e~ 1-100 meV

Spacing between the energy levels can controlledusing different materials or by design!

electron

hole

Eg~1.25 eV Near Infra Red/Visible Range

frequency 2

Visible light

Infra Red Range

8

Spin states

e-

Spin up

e-

Spin down

• An intrinsic angular momentum of a quantum particle

• Associated magnetic momentum

• Interaction with a magnetic field

E1e

E1h

EV

EC

Bx

Sμ Bg

μBH

~ 0.1 - 0.5 meVEe( )

Ee( )

Eh( )

Eh( )Spin relaxation time:

20sT ms at T = 1 K and B = 4 T

Spin states are long lived!

9

Spin blockade deviceExample

EF

EF

Different spins – Current is not zeroDelft University of Technology Same spins – Current is blocked

10

Optical Absorption/Emission

E1e

E3e

E2e

E1h

E2hEV

EC

EC

EV

Photon hEE

Exciton relaxation time ~ 0.1 – 1 nsexciton

11

Selection Rules

E1e

E3e

E2e

E1h

E2hEV

EC

EC

EV

Photon

V

Linear polarization, V[1,0,0]

Bx

negative exciton

12

Selection Rules

E1e

E3e

E2e

E1h

E2hEV

EC

EC

EV

Photon hE

Circular polarization

negative exciton

13

Content• Semiconductor quantum dot structures:

Design and Applications

• Properties of single dots:

Energy levels structure, Spin states

Interaction with light, excitons

• Optical Control:Goal and device design

Optical cooling

Single dot switch

Operations with coupled dots

• Conclusions

14

Goal

EV

EC

Ee( )

Eh( )

Ee( )

Eh( )

Control the spin of an electron spin in a single quantum dot FAST, EFFICIENTLY, PRECISELY.

15

Setup

AlGaAs

n+ GaAsEF

AlGaAs

InAs QD

Quantum dot is empty

EF

Quantum dot is filled

VB

QD layer

mask

Laser beam

V

16

Optical probe of single dot

X0X+

X- X2-

X2+

X. Xu, et. al., PRL 99, 097401 (2007)

Photoluminescence

pump

capture

recombination

17

V2V1

H1

H2

H and V – orthogonal linear polarizations

Selection Rules

Bx

18

Optical cooling

RelaxationPump

Whenever an electron is in the state flip it to the state.

Frequency and polarization selection

19Z

E1e

E1h

EV

EC

Photon hE

V-

Optical cooling

20

Optical coolingModel

Rel

axat

ion

rate

, C

oolin

g ra

te,

Rabi frequency, Relaxation rate,

Pre

cisi

on, P

time, ns

System evolution:

}{],[)( LHitt

tePPPtP γ))()(()()( 0Prepared state:

C. Emary, X. Xu, D. Steel, S.Saikin, L. J. Sham, Phys. Rev. Lett. 98, 047401 (2007)

Relaxation rate: 21. eV

Cooling Rate

Operation precision

21

Optical coolingPump-probe measurement

State preparation efficiency 98.9%

PumpH2 V2

Probe

PumpH1

V1Probe

X. Xu, et. al., PRL 99, 097401 (2007)

22

Single Quantum Dot Switch

If an electron in the state then flip it to the state and reverse.

Pump1 Pump2

detuning

Use frequency and polarization selection

23

ModelOptimization of detuning Effects of pulse length

B = 8 T

T = 20 psT = 50 psT = 100 ps

B = 2 TB = 4 TB = 8 T

-600 -400 -200 0 200 400 600

0.0

0.2

0.4

0.6

0.8

1.0

Ele

ctro

n st

ate

time (ps)

Dynamics of an electron stateClassical vs. Quantum

C. Emary, L. J. Sham J. Phys.: Cond. Matter 19, 056203 (2007)

24

Operation with electrons in two dots

If two electrons are in a same state or flip both of them.

25

Origin of interaction

Bi-trion binding energy

meV

26

Energy levels

V(dot1)

H(dot2) H(dot1)

V(dot2)

27

t4t3t2t1

E4

E5

E3

E1

0

ener

gy

time

0

E2

H(t)V(t)

ener

gy

Pulse timing

Model

To minimize incoherent pumping and losses due to relaxation

Dynamics of electrons

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

Ele

ctro

ns s

tate

pulse width (ns)

S.Saikin, et. al., arXiv:0802.1527

28

Conclusions

• An electron in a single quantum dot can be prepared to a given state with precision ~99% on the timescale of 1 nanosecond using resonant optical pumping.

• States of a single electron in a QD can be switched coherently on a timescale of 0.1 nanosecond using a Raman process.

• Simple logical operations can be designed with coupled quantum dots. The operation timescale is ~ 0.5 nanosecond

Thank you!