PROBING THE BOGOLIUBOV EXCITATION SPECTRUM OF A POLARITON SUPERFLUID BY HETERODYNE FOUR-

WAVE-MIXING SPECTROSCOPY

Verena Kohnle, Yoan Leger, Maxime Richard, Michiel Wouters, Marcia Portella-Oberli,

Benoit Deveaud-Pledran

o Introduction

o strong coupling: polaritonso sample

o Motivation: excitation spectrum of a polariton superfluid

o Heterodyne Four Wave Mixing (FWM) experiment

o Experimental Results

o Conclusion

Outline

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Strong coupling regime: Polaritons• Polariton: quasi particle composed

by a photon coupled to an exciton• Microcavity 2D system for photons; Quantum well 2D system for excitons• Polaritons are the new eigenstates

of the system in the strong coupling regime

Picture: Kasprzak et al. Nature (2006)

Polaritons are composed bosons:

Photonic content: provides high degree of coherenceExcitonic content: interaction between polaritons

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Sample

Substrate (GaAs)

•••

•••

8nm QWIn0.04Ga0.96As

λ-cavity

bott

om D

BRto

p D

BR• AlAs/GaAs – cavity which contains a 8 nm In0.04Ga0.96As quantum well (QW)

• Bragg mirrors: contain 26.5 and 20 pairs of alternated /4 layers of AlGaAs and AlAs

• wedged cavity spacer layer the resonator frequency of

the resonator can be varied by moving the laser spot over the sample

• rabi splitting: 3.4 meV

1.491

1.490

1.489

1.488

1.487

1.486

1.485

1.484

1.483

en

erg

y (e

V)

43210-1-2 detuning (meV)

upper Polariton lower Polariton E_cavity (calculated) E_exciton (calculated)

space

Polariton superfluid: Bogoliubov dispersion

feature of interactions: blueshift of dispersion BOGOLIUBOV Dispersion:

• linear at small k• „ghost“ branch

In experiment: up to now nobody was able to show the „ghost“ branch

Polaritons : weakly interacting bose gas

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

State of the art

Utsunomiya et al. Nature, 4, 700 (2008)

No Bogoliubov ghost branch observed:

A proposal as an answer:

Wouters et al. Phys Rev B,79, 125311 (2009)

Wouters et al. Phys Rev B,79, 125311 (2009)

FWM I010 I0

en

erg

y

wavevector k

0-k0 +k0

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

our method:• using heterodyne Four-Wave-Mixing (FWM) setup • fs-laser broad energy spectrum (~12meV) normal and gohst branch are probed with the same laser pulse

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Heterodyne FWM setup

balanced detection

• best sensitivity• spectral interferometry

– amplitude & phase resolution

• balanced detection– background

suppression

Ref (0,0)

Pump (0,w1)

Trigger (k,w2)FWM(-k,2w1-w2)

Sample

AOM @ 2w1-w2

HeterodyneChannels: A (j=0)

B (j=p)

LensPinhole Miror

to CCD

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Bogoliubov: tracking the ghost branch

ghost branch

normal branch

k=0

k = 1 µm-1

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Dispersion of the Bogoliubov excitationsevolution in k of the different branches: (delay integration between 5 – 6 ps)

Gross-Pitaevskii equations:

Equation for excitons:

Equation for cavity photons:

Yx/p= exciton/photon wavefunctiong = exciton-exciton interaction potentialgx/p= decay rate of excitons/photons2WR= Rabi splittingF(r,t)= pump laser field

2 22x x

x x x x R px

Ψ iγi Ψ Ψ g Ψ Ψ Ω Ψ

t 2 2m

( )p pp p p R x

Ψ iγi Ψ ε Ψ Ω Ψ F(r,t)

t 2

k = 1 µm-1

Arb. Int. = 16

evolution in excitation power: (@ delay time t=5.7ps)

Bogoliubov: excitation power dependence

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

k = 1 µm-1

Arb. Int. = 16

ng

2 ng

evolution in excitation power: (@ delay time t=5.7ps)

Bogoliubov: excitation power dependence

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

k = 1 µm-1

Arb. Int. = 16

evolution in excitation power: (@ delay time t=5.7ps)

Bogoliubov: excitation power dependence

Introduction

Motivation

FWMexperiment

Experimentalresults

Conclusion/Outlook

conclusion & outlook Observation of the Bogoliubov excitation

spectrum of a polariton superfluid using heterodyne FWM spectroscopy

we demonstrate unambigously the excistence of the negative energy „ghost“ branch

Outlook: 2D FT allows to characterice th apperence of the different resonances

THANK YOU !