Garnett W. Bryant, N. Malkova, and J. Si

Atomic Physics Division and JQI, NIST, Gaithersbur

M. Zielinski and W. Jaskolski

NRC, Ottawa, Canada and UMK, Torun, Polan

J. Aizpurua

DIPC, San Sebastian, Spain

Reengineering the Optics of Qu

Dots Using Nanomechanical S
Introduction

Passive control of quantum dot (QD) optics is achieved by tailoshape and composition during growth. Dynamical control oQDs is highly desirable. For QDs embedded in nanstructures, dynamical control could be obtained by usinimposed mechanical strain to reengineer the QDs to degeneracies, polarize optical transitions, induce entanchange coupling between closely spaced dots, all capabilituse dots in optical nanodevices and quantum information proceTo exploit hybrid nanomechanical/QD devices, an understacoupling between internal strain due to lattice mismatcimposed mechanical strain, and excitons in the Qnanomechanical structure is needed.To identify the effects of mechanical strain, we present a thQDs in a GaAs nanomechanical bridge. The bridge is benexternal strain applied to reengineer the QDs.
• DC Stark field analog

– Biaxial deformation acts like an electric field Ez

• Electrons and holes shift the same way

– Shear bends act like Ex

• Electrons and holes shift the opposite way

– Internal relaxation and state distortion is critical

• Excitons

– Strain reengineers the anisotropic exchange coupling – This controls the phase of spin mixing in the exciton, 

leading to

– Fine structure level mixing and crossing and 

polarization rotation

• Coupled dots

– Strain-induced state crossing and inter-dot transfer

Nanomechanically Strained QDs: Summary

e h
s 

- atomistic tight-binding theory: spin-orbit interaction, no p- lattice relaxation: valence force field - external strain: bend bridge, hold boundaries fixed - internal relaxation of both lattice mismatch and applied st

- excitons: configuration interaction approach

Symmetric bend (biaxial deformation)‏ Antisymmetric ben

Theory of QDs in nanomechanical oscillators:Results for a pyramidal InAs QD in a GaAs nanobridge

Geometries and applied strain Geometries and applied strain

Theoretical approach Theoretical approach
Manipulating electron energies with nanomechani

Electrons

Biaxial deformation•“Rigid” shift with fixed level ordering andstate symmetries•Shift: 1-10 meV•Electron and hole shift the same wayShear•Quadratic increase•Mixing, pushed into the wetting layer•Electron and hole shift the opposite way

“Analog” to DC Stark effect with same or opposite charge 

1S

“1P”
Biaxial deformation

•“Rigid” shift with fixed level ordering andstate symmetries•Electron and hole shift the same wayShear•Quadratic decrease•Mixing

Holes

bend

bend down 

Manipulating hole energies with nanomechanica

H1
Internal relaxation determines level and charg

x=y=0.2

Conduction ba

δZ lattice sh

compression

Biaxial lattice relaxation in a flat bridge Biaxial lattice relaxation in a flat bridge

Δ

Vdef > 0

Δ

Vdef < 0

Lattice relaxation in a bent bridge Lattice relaxation in a bent bridge

with additional internal relaxation ( with additional internal relaxation (red)‏
Distorting the electron and hole stat

Strain

-induced charge shifts: induced charge shifts:

“analog

” to Stark effect with counterr

to Stark effect with counterr

e

h

Electron H

Asymmetric stretching or squeezing Asymmetric stretching or squeezing

BendChargeshift
Down 6a Down 2a

Manipulating inter-dot transferExample: electrons in a biaxially deformed double dot

Strain-induced charge shifting determines charge transfer in c

induced charge shifting determines charge transfer in c

Level crossing Level crossing

Single dot Cha

Cha

Double dot
Excitons: biaxial 

deformation

Exciton energy follows pair ground stateBinding can increase or decrease by bending (charge shifting)‏Fine structure: level splittingsEx1 and Ex

2 are dark

Ex

3 and Ex

4...exchange split 

bright statesEx

3 and Ex

4...asymmetric 

exchange Bend-induced anti-crossing and polarization rotation

e 

h 
Excitons: 

biaxial deformation

Pair ground state weakly polarized, strain polarizes along yEx3(4) polarized along x-y (x+y) in 

unbent structurePolarization rotates to x (y) by bending
Excitons: shear

Exciton energy follows pair ground stateBinding increases by bending (hole squeezing)‏Fine structure: level splittingsEx1 and Ex

2 are dark

Ex

3 and Ex

4...exchange split 

bright statesEx

3 and Ex

4...asymmetric 

exchange and strong coupling Bend-induced anti-crossing and polarization rotation
Excitons: shear

Pair ground state weakly polarized, strain polarizes along xEx3(4) polarized along x-y (x+y) in 

unbent structureRotates to y (x) by bending (reverse of biaxial deformation

‏(
Reengineering excitons: tuning the exchang

Biaxial deformation Shear deform

Strain

-induced tuning of the induced tuning of the magnitude magnitude of the exchange couplin

of the exchange coupli

S

z= 

±1 e/h pair states determines the splitting between brigh

1 e/h pair states determines the splitting between brigh

Strain

-induced tuning of the induced tuning of the phase

of the exchange coupling between of the exchange coupling between 

S

z= 

±1 e/h pair states determines 1 e/h pair states determines 

the polarization of bright states the polarization of bright states