POLARITON GAS EXCITATIONS:FROM SINGLE-PARTICLE TO SUPERFLUID

Yoan LégerLaboratory of Quantum Opto-electronicsEcole Polytechnique Fédérale de LausanneSwitzerland

Polariton Superfluidity

Heterodyne four wave mixing

From standard fluid to superfluidity

2d fourier spectroscopy

Polariton Superfluidity

Heterodyne four wave mixing

From standard fluid to superfluidity

2d fourier spectroscopy

Superfluidity & sound wave excitationsStriking properties of superfluidsZero viscosity, Rollin film, foutain effectQuantized vortices….

Bogoliubov theoryof the weakly interacting Bose gas

Elementary excitation are collective excitations! with sound wave behavior

Woods et al. Rep. Prog. Phys. 36 1135 (1973)

Superfluidity in the solid state

Microcavity polaritons

Spacing layerX Ph.

UP

LP

Cavityfield

ExcitonPolariton

DBR

QW

DBR

In-plane momentum~ Emission angle

Energy

LP

UP

Momentum dispersion

Superfluidity in the solid state

Bose Einstein condensation

Kasprzak et al. Nature 443, 409 (2006)

Coulomb interactions

Polaritons should be superfluid!!

Amo et al. Nat. Phys. 5, 805 (2009)

Spacing layerX Ph.

UP

LP

Cavityfield

ExcitonPolariton

DBR

QW

DBR

Microcavity polaritons

The superfluid dispersion

Linearization comes from the coupling of counter-propagating modesby interactions

Appearance of a ghost branch

Injecting polaritons at k=0

Naive picture of the ghost branch

Particle-hole superposition

Diluted polariton gas Sound wave in superfluid

Gross-Pitaevskii formalismWeakly interacting bosons:

qkk

kkqkqkkkk

k aaaagV

aaH,,

†††0

21

21212

1

Mean field theory:

).(*).(0

222

1,2

trkik

trkik

BB eveugmt

i

εk0

ωB uk2

vk2

Linearization of interaction term: )2( 000 gnkkB

2.5

2.0

1.5

1.0

0.5

0.0

En

erg

y (

me

V)

2.52.01.51.00.50.0k (m

-1)

1.5

1.0

0.5

0.0

Co

ntr

ibu

tio

n

2.52.01.51.00.50.0gn (meV)

k=1μm-1

gn=1meV

Normal branch

Ghost branch

Looking for the Ghost branch

PL measurements

Kind of linearizationNo ghost branch

Utsunomiya et al. Nat. Phys. 4, 700 (2008)

Accessing the ghost branch with FWM

In the proposal: non-resonant condensate

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

Polariton Superfluidity

Heterodyne four wave mixing

From standard fluid to superfluidity

2d fourier spectroscopy

Polariton FWMFour wave mixing and selection rules

*123

)3( EEEEFWM

Angular selection rule 123 kkkkFWM

Third order nonlinearity

123 FWMEnergy selection rule

Polariton FWMFour wave mixing and selection rules

*1

22

)3( EEEFWM

Angular selection rule 122 kkkFWM

Third order nonlinearity

122 FWMEnergy selection rule

Polariton FWM

2 fields : condensate field and probe field

Stimulated parametric scattering of 2 polaritons from the condensate

• Based on spectral interferometry

• requires : • a full control of the excitation fields• Pulsed excitation to cover the full emission spectrum

• provides:• best sensitivity, and selectivity• access to amplitude and phase of the nonlinear emission

Heterodyne FWM

How to extract useful signal when angular selection is not enough?

Problem: Condensate emission should largely dominate the spectrum

Heterodyne FWM

Heterodyne setup

Excitation fieldsLinear emission

FWMFWM

Coherent excitationSpectral interferometryEnergy selection

Pulsed resonantexcitation

Pump

Trigger

FWM

AOM

Spectro

AO

M

AO

M

75 MHz79 MHz

TriggerPump

71 MHz

ω0

LocalOsc..

Sample

Balanced detection

FWM 71 MHzRef. Pump 75 MHzRef. Trigger 79MHz

HeterodyningExcitationPulses

transmission

Inte

nsi

ty

Energy

Inte

nsi

ty

Energy

Inte

ns

ity

Energy

+ local osc. @ 71MHzIn

ten

sity

Energy

Inte

nsi

ty

Energy

Inte

ns

ity

Energy

80MHz

75MHz

pump

79MHz

trigger

71MHz

FWM

Energy

Frequency comb:

AOM

Spectro

AOMAOM

75 MHz79 MHz

TriggerPump

71 MHz

ω0

LocalOsc..

Sample

Balanced detection

FWM 71 MHzRef. Pump 75 MHzRef. Trigger 79MHzLP UP

extractedFWM

Inte

nsi

ty

Energy

Inte

nsi

ty

Energy

Inte

ns

ity

Energy

GB

NB

Polariton Superfluidity

Heterodyne four wave mixing

From standard fluid to superfluidity

2d fourier spectroscopy

Dispersion & dissipation…

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6E

-E0

(meV

)

1.21.00.80.60.40.20.0Wavevector (m

-1)

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6E

-E0

(me

V)

1.21.00.80.60.40.20.0Wavevector (m

-1)

Damping of polariton density!Normal & ghost branch

Low densityK=0

GB NB

t1

t2

t3

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6E

-E0

(me

V)

1.20.80.40.0Wavevector (m

-1)

Stating on the ghost branch?

Savvidis et al.Phys. Rev. B. 64, 075311 (2001)

OPO experiment

Linear dispersion

but off-resonances can always exist in FWM we have to go further!

Nature of the excitations1/2

Off-resonance or “real” ghost?

Dissipative Gross-Pitaevskii equation with:

r.kir.kiLP eveutr

*),( 0 r.kir.kiLP eveutr

*),( 0

r.kir.kiLP eveutr

*),( 0

pump FWM trigger

Always 2 energy modes:Ghost and normal branch

Change of intensity and linewidthWith polariton density

1/3 1

Standard fluidSingle particleexcitations

SuperfluidSound waves

12

10

8

6

4

2

Exc

. Po

wer

(m

W)

1.4871.4861.4851.4841.4831.482Energy (eV)

Nature of the excitations2/2

GB k=0 NB

0.8

0.6

0.4

0.2

Nor

mal

ized

Inte

nsit

y

12108642

Exc. Power (mW)

NormalGhost

Threshold!

Redistribution of intensityDensity of state on the ghost!

Intensity dependence

Polariton Superfluidity

Heterodyne four wave mixing

From standard fluid to superfluidity

2d fourier spectroscopy

Investigating the processes

1.5

1.0

0.5

0.0

-0.5

-1.0

-5 0 5

1.4860

1.4855

1.4850

1.4845

1.4840

1.4835

-5 0 5

Delay between pulses (ps)

En

erg

y (

eV

)

Exp. Th.

Delay<0

pump

Trig. FWM

t Delay>0

pump

Trig. FWM

t

Delay dependence

2D fourier transform spectroscopy

Delay dependence

1.5

1.0

0.5

0.0

-0.5

-1.0

-5 0 5

1.4860

1.4855

1.4850

1.4845

1.4840

1.4835

-5 0 5

Delay between pulses (ps)

En

erg

y (

eV

)

420-2

Trigger energy (meV)

LP UP

pump

Trig. FWM

t

delayFourier transform on delayE(ωdet ,τ) E(ωdet , ωexc)

ΩR

Conclusions & perspectives

Ghost branch of a superfluid• In solid state, for the first time• Transformation of the excitations

Sound like dispersion• Linear for the normal branch• Assymmetry due to dissipation

2D fourier transform spectroscopy• Highly powerful method • Starting the process investigation…

acknowledgements

To the audience!

To my collaborators:

Verena Kohnle, Michiel Wouters, Maxime Richard, Marcia Portella-Oberli, Benoit Deveaud-Plédran