Polariton-polariton interaction constants

M. Vladimirova S. CronenbergerD. Scalbert

A. Miard, A. LemaîtreJ. Bloch

A. V. Kavokin

K. V. Kavokin

G. MalpuechD. Solnyshkov

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

Physics and Astronomy School, University of Southampton, UK

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

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

LASMEA, Clermont-Ferrand, France

Energy

Polariton nonlinearities

•Interaction between excitons ↔ energy shift

•Phase space filling

C XR

Energy

Transmission

UPB

LPB

R

UPB

LPB

k

Excitonic component is responsible for polariton non-linear effects

R

R

EX

C CXR

Energy renormalization vs

saturation

Energy shift Saturation

•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

Polariton nonlinearities: polarization effects

Energy shift in linear polarization EL=n(1+2)/2

Interaction depends on spin

energy shift depends on the spin of polaritons

Energy shift in circular polarization EC=n1

>0 ↔ repulsion, blue shift

<0 ↔ attraction, red shift

+ 1 + 2

+ + +

Polariton energy shift from transmission experiments

100 fs Spectral filtering

sample

f

demolulation

10 meV25 meV

Babinet-Soleil

compensator

spectrometer+PM

1 ps

chopper

1.470 1.475 1.480Tra

nsm

issi

on

(a

rb. u

nits

)

Energy (eV)1.465 1.470 1.475 1.480T

ran

smis

sio

n (

arb

. un

its)

Energy (eV)

depolarising fiber

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

Or EOM

T

and/or

Tc-Tl

GaAs cavity, In0.5Ga0.95As QW,

GaAs/Ga0.9Al0.1As Bragg mirrors

23 pairs/29pairs R=3.5 meV

30 m spot

“Mixed” dichroism

~0 •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

“Mixed” dichroism at very low powers : P >15 W

1.472 1.474 1.476 1.478 1.480-0.4

0.0

0.4

Energy (eV)

"Mixed" dichroism

Transmission (arb. units)

(TC-T

L)/(T

C+T

L)

circular linear 200 W

“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

1.47 1.481.47 1.48

P=200 µW

Tra

nsm

issi

on (

arb.

uni

ts)

P=18 µW

linear circular

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)

1.465 1.470 1.475 1.480Tra

nsm

issi

on (

arb.

uni

ts)

Energy (eV)

Normalize the intensity and look at the differential spectra

Measuring LPB shift

1.467 1.468 1.469-0.1

0.0

0.1

1.468 1.469 1.470

0.0

0.3

1.467 1.468 1.469-0.1

0.0

0.1

1.468 1.469 1.470

0.0

0.3

1.467 1.468 1.469-0.1

0.0

0.1

1.468 1.469 1.470

0.0

0.3 =-0.25 meV

300 µW

550 µW

400 µW

=-1.9 meV

Nor

mal

ized

diff

eren

tial t

rans

mis

sion

Energy (eV)Blue shift, almost no broadening in both

polarizationsNegligible shift and broadening in

linear polarization

Red → linear Black → circular

(T-T18 W) / (T+T18 W)

Ratio between interaction constants

Large dispersion=poor precision at zero and strong negative detunig

2 and 1 have different sign

|2| increases when detuning changes from negative to zero

-0.05

0.00

0.05

0.10

-3 -2 -1 0 1

-1

0

1

550 µW400 µW L L L C C C

Sh

ift (

me

V)

300 µW

P=0.3 mWP=0.4 mW P=0.55 mW

2/1

Detuning (meV)

Red → linear Black → circular

EL=n(1+2)/2

EC=n1

Tentative explanation

Different contribution to the interaction constants 1 (↑ ↑) and 2 (↑ ↓)

Spin independent contributions:

1) Mean field electrostatic energy (Repulsion)

2) Van-der-Waals (dipole-dipole) interaction (Attraction)

Spin dependent contributions:

1) Exchange interaction (Repulsion for ↑ ↑ and Attraction for ↑ ↓)

2) Bi-exciton state (Attraction) ↑ ↓

1n=UCoulomb+UVdW+Uex↑↑

2n=UCoulomb+UVdW+Uex↑↓+Ubi

-2 0

1472

1476 sp

bd

LPB 1s exciton 1s dark exciton 2p exciton bi-exciton

Ene

rgy

(meV

)

Detuning (meV)

be

EC=1n EL=(1+2)n

-2 0

1472

1476 sp

bd

LPB 1s exciton 1s dark exciton 2p exciton bi-exciton

En

erg

y (m

eV

)

Detuning (meV)

be

-0.1

0.0

En

erg

y sh

ift (

me

V)

UCoulomb

Ubi

Uex↑↓UVdW

Uex↑↑

2n = UCoulomb+UVdW + Uex↑↓ + Ubi

1n = UCoulomb+UVdW + Uex↑↑

calculated

Fit of ECmeasured

Fit of

-0.05

0.00

0.05

0.10

-3 -2 -1 0 1

-1

0

1

550 µW400 µW L L L C C C

Sh

ift (

me

V)

300 µW

P=0.3 mWP=0.4 mW P=0.55 mW

2/1

Detuning (meV)

Conclusions The question remains open,

whether only 2 polariton interaction constants are sufficient. Experiment aswers YES and theory NO.

0 200 4000.0

0.1

0.2

Shi

ft (m

eV)

Power (W)

C

L

If |2|~|1| and 2<0 this can have important

implications

-1 0 1-1

0

1

I

collapseBEC

BEC

2 (

arb.

uni

ts)

1 (arb. units)

BEC

collapse

I

II

III IV

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