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Polariton-polariton interaction constants

M. Vladimirova

S. Cronenberger

D. Scalbert

A. Miard,

A. Lemaître

J. Bloch

A. V. Kavokin

K. V. Kavokin

G. Malpuech

D. Solnyshkov

Groupe d’Etude des Semiconducteurs, CNRS, Montpellier, France

Laboratoire de Photonique et de Nanostructures, CNRS, Marcoussis, France

Physics and Astronomy School, University of Southampton, UK

A. F. Ioffe Institute, St-Petersburg, Russia

LASMEA, Clermont-Ferrand, France

UPB

WR

LPB

LPB

Saturation

Energy shift

X

C

C

X

Energy renormalization vs

saturation

WR

Polariton nonlinearitiesEnergy

Excitonic component is responsible for polariton non-linear effects

X

C

WR

WR

WR

- Interaction between excitons ↔ energy shift
- Phase space filling

Transmission

Energy

- LPB and UPB are expected to shift in the same or in the opposite direction, depending on the mechanism of the non-linearity
- Experimentally : energy shift appears well before saturation

k

+

a2

+

+

+

+

Polariton nonlinearities: polarization effectsInteraction depends on spin

energy shift depends on the spin of polaritons

Energy shift in circular polarization DEC=na1

Energy shift in linear polarization DEL=n(a1+a2)/2

a>0 ↔ repulsion, blue shift

a<0 ↔ attraction, red shift

Polariton energy shift from transmission experiments

100 fs

1 ps

Babinet-Soleil compensator

depolarising fiber

sample

demolulation

T

and/or

Tc-Tl

Spectral filtering

f

10 meV

25 meV

Or EOM

spectrometer

+PM

30 mm spot

chopper

GaAs l/2 cavity, In0.5Ga0.95As QW,

GaAs/Ga0.9Al0.1As Bragg mirrors

23 pairs/29pairs WR=3.5 meV

We look for the power dependence of transmission in linear and circular polarizations

“Mixed” dichroism

- Corcular polarisation spectrum is blue shifte with respect to circular polarization spectrum
- UPB : smaller effect, but blue shift
- LPB: MC is more transparent in circular polarization!
- UPB: the effect is inversed

d~0

“Mixed” dichroism at very low powers :

P >15 mW

“Mixed” dichroism : explanation

Question: Why at LPB the trasmission increases with power?

Answer: Because of the exciton energy shift!

When exciton energy increases LPB acquire more photonic character and thus better transmitted through the sample

The situation is inversed at UPB

Any tiny shift of the exciton energy is accompanied by the modification of transmission

This is not the saturation of absorption!

How to measure the power and polarization dependent polariton shift

- This shift is very small
- It is masked by the strong variation of intensity
- We can not go up to high power
- Seems to depend on the detuning and excitation type (LPB or LPB+UPB)

Normalize the intensity and look at the differential spectra

Measuring LPB shift

(T-T18 mW) / (T+T18 mW)

Red → linear Black → circular

Blue shift, almost no broadening in both polarizations

Negligible shift and broadening in linear polarization

Ratio between interaction constants

Red → linear Black → circular

- Large dispersion=poor precision at zero and strong negative detunig
- a2 and a1 have different sign
- |a2| increases when detuning changes from negative to zero

DEL=n(a1+a2)/2

DEC=na1

a2n=UCoulomb+UVdW+Uex↑↓+Ubi

DEL=(a1+a2)n

DEC=a1n

Tentative explanationDifferent contribution to the interaction constants a1 (↑ ↑) and a2 (↑ ↓)

- Spin independent contributions:
- Mean field electrostatic energy (Repulsion)
- Van-der-Waals (dipole-dipole) interaction (Attraction)

- Spin dependent contributions:
- Exchange interaction (Repulsion for ↑ ↑ and Attraction for ↑ ↓)
- Bi-exciton state (Attraction) ↑ ↓

a1n = UCoulomb+UVdW + Uex↑↑

measured

calculated

Fit of a2/a1

a2n = UCoulomb+UVdW + Uex↑↓ + Ubi

Uex↑↑

UCoulomb

UVdW

Uex↑↓

Ubi

Conclusions

- The question remains open, whether only 2 polariton interaction constants are sufficient. Experiment aswers YES and theory NO.

- If |a2|~|a1| and a2<0 this can have important implications

I. A. Shelykh et al, SST (2010)

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