Superfluidity of Polaritons in Engineered Potentials in Semiconductor Microcavities

Obergurgl 6 June 2010

Superfluidity of Polaritons in Engineered Potentials in

Semiconductor MicrocavitiesAlberto Amo, C. Adrados, J. Lefrère, E. Giacobino, A. Bramati

S. Pigeon, C. Ciuti

Laboratoire Kastler Brossel, UPMC, ENS, CNRS, Paris, FR

Laboratoire MPQ, Université Denis Diderot, CNRS, Paris, FR

I. CarusottoBEC-CNR-INFM and Dipartimento di Fisica, Universita di Trento, Povo, IT

R. HoudréInstitut de Physique de la Matière Condensée, EPFL, Lausanne CH


Outline

Polaritons in semiconductor microcavities

Observation of superfluidity of polaritons

Engineering the polariton landscape


Top DBR

Bottom DBR

Quantum Wells

Exciton

Photon

Angle θ (º)

kin-plane (μm-1)

Upper polariton

Lower polariton

θ

k in-plane

Semiconductor microcavities

Em

issi

on e

nerg

y (e

V)

Polaritons

~ 5meV

GaAs


Properties

Top DBR

Bottom DBR

Quantum Wells

Exciton

Photon

Angle θ (º)

kin-plane (μm-1)

Upper polariton

Lower polariton

θ

k in-plane

Composite bosons

Excitonic component strong interactions (non-linearities 3)

Semiconductor microcavities

Em

issi

on e

nerg

y (e

V)

Polaritons

~ 5meV

Photonic component low mass (10-5 me)

Short lifetime (~ps) out of equilibrium

GaAs


Kasprzak et al. Nature, 443, 409 (2006)

kin-plane (μm-1)

Lower polaritonE

mis

sion

ene

rgy

(eV

)

kx

ky

Polariton density

Polariton condensation

Polariton condensate

Atomic BEC

m/me

104

10-5

Tc

<1 K

20-300 K

T at Tc

1 m

1-10 m

T = 5 K CdTe

Excitation


Polariton quantum fluid effects

Interferogram Phase map

Quantized vortices (m=1)

Imprinted vortices (m=1,2)and persistent currents

Lagoudakis et al., Nature Phys. 4, 706 (2008)

Sanvitto et al., Nature Phys.DOI: 10.1038/NPHYS1668 (2010)


Polariton quantum fluid effects

Interferogram Phase map

Quantized vortices (m=1)

Imprinted vortices (m=1,2)and persistent currents

Lagoudakis et al., Nature Phys. 4, 706 (2008)

Sanvitto et al., Nature Phys.DOI: 10.1038/NPHYS1668 (2010)

Amo et al., Nature 457, 291 (2009)

Fluid dynamics

Real space

Momentum space


E

k

cs

Landau criteriom for superfluidity

Interacting Boson condensate linearized spectrum of excitations


E

k

cs

E

k

cs+vf

cs-vf

SUPERFLUID

Galileanboost

vf < cs

Landau criteriom for superfluidityF

LO

W



E

k

cs

E

k

cs+vf

cs-vf

SUPERFLUID

Galileanboost

vf < cs

Landau criteriom for superfluidity

E

k

cs+vf

cs-vf

FL

OW

ČERENKOV REGIME

E

k

cs

Galileanboost

vf > cs

FL

OW


I. Carusotto and C. Ciuti, phys. stat. sol. (b) 242, 2224 (2005)


Resonantly excited condensate withlow momentum

30 µm

FL

OW

Realspace

-1.0 -0.5 0.0 0.5k

x (m-1)

Momentumspace

Polariton density

Elastic scattering

-1 0 1

0.0

0.5

ky (m-1)

E -

Ep

22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e

Linear regime

Pump

Polariton superfluidity



30 µm

FL

OW

0

1

-1.0 -0.5 0.0 0.5k

x (m-1)

-1.0 -0.5 0.0 0.5

kx (m-1)

-1.0 -0.5 0.0 0.5 1.0

-0.5

0.0

0.5

k y (

m-1)

kx (m-1)

Polariton density

Collapse of the ring

-1 0 1

0.0

0.5

Pump

ky (m-1)

Elastic scattering

-1 0 1

0.0

0.5

ky (m-1)

E -

Ep

E -

Ep

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


Linear regime Superfluid

Pump

vf < cs


Realspace

Momentumspace


30 µm

FL

OW

0

1

Polariton density

Collapse of the ring

-1 0 1

0.0

0.5

Pump

ky (m-1)

Elastic scattering

-1 0 1

0.0

0.5

ky (m-1)

E -

Ep

E -

Ep


Linear regime Superfluid

Pump

30 µm FL

OW

Gross-Pitaevskiisimulations


Realspace


vf < cs



Superfluid regime


-1 0 1

0.0

0.5

40 µm

40 µm FL

OW

High momentum

Polariton density

Elastic scattering

ky (m-1)

E -

Ep


Linear regime Čerenkov

Pumpvf > cs

FL

OW


Čerenkov regime (supersonic)

Realspace

-1 0 1

0.0

0.5

Linear wavefronts

ky (m-1)

E -

Ep

supersonic

0

1



-1 0 1

0.0

0.5

40 µm

40 µm FL

OW

High momentum

0

1

Polariton density

Elastic scattering

ky (m-1)

E -

Ep



Pumpvf > cs

FL

OW



Realspace

-1 0 1

0.0

0.5

Linear wavefronts

ky (m-1)

E -

Ep

Supersonic atomic BEC

Carusotto et al. PRL 97, 260403 (2006)

s fsin c v 58 1 10sc . m / s

supersonic



Polariton landscape engineering 22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x t

t Pi x t D i V x t x t F e e

FL

OW

20 μm

probe σ +

Defect-free area




control

yPol

arit

on

ene

rgy

control σ -

Strong field:renormalization of the

polariton energy

polariton-polariton interaction

20 μmFL

OW

20 μm

probe σ +

Defect-free area

+




control

yPol

arit

on

ene

rgy

control σ -


polariton energy


20 μmFL

OW

20 μm

probe σ +

Defect-free area

probe σ + + control σ -

detection σ +

=

FL

OW

+

Amo et al., arXiv:1003.0131v1


scattered30 μm

inje

cted

inje

cted

scat

tere

d

No control horizontal control diagonal controlProbe only Probe + Probe +


Polariton landscape engineering

inje

cted


scattered30 μm

inje

cted

inje

cted

scat

tere

d




inje

cted


scattered30 μm

inje

cted

inje

cted

scat

tere

d




inje

cted

SUPERFLUID REGIME(high probe power)

inje

cted

no scattering


Summary

Observation of superfluidity of polaritons

Supersonic regime access to the sound speed

Polariton-polariton interactions landscape engineering

localization effects Josephson

oscillations

polariton circuits


Single polariton fluid: set-up

(d)(a)

XY

Near field CCDFar field

CCD

k

kz

k║

Microcavity sample

Excitation laser

Single laser excitation (CW, single mode)

Excitation close to the bottom of the lower polariton branch

resonant excitation of one polariton mode

Transmission experiment

-3 -2 -1 0 1 2 3

1.527

1.530

1.533

En

erg

y (e

V)

kx (m-1)

CW Pump

LPB

UPB



Other situations

40 µm

FL

OW

40 µm FL

OW

Polariton density

SUPERFLUID AROUND SEVERAL DEFECTS

SHADOW EFFECT AROUND BIG DEFECT


Superfluidity checklist

Resonantly pumped polariton condensates

Amo, Lefrère, et al., Nature Physics, (in press).

I Carusotto talk at ICSCE 4 conference (Cambridge, UK, 2008), available athttp://www.tcm.phy.cam.ac.uk/BIG/icsce4/talks/carusotto.pdf

Nature 457, 273 (2009)


Polariton fluid dynamics: set up

imag

ing

spec

trom

eter

Streak Camera

CCD

sampleLens F

Fourier plane

Lens Areal space imaging

Lens Bmomentum space

imaging

CW

2ps pulsed

PUMP

IDLER

fA

/2 cavity20 nm GaAs QW

Microcavity sample(grown at LPN)

ħΩRabi = 4.4 meV

kx

ky

X

Y

Energy selection




control

yPol

arit

on

ene

rgy

control σ -


polariton energy


20 μmFL

OW

20 μm

probe σ +

Defect-free area


detection σ +

=

FL

OW

Simulation GP

FL

OW

+





control

yPol

arit

on

ene

rgy

control σ -


polariton energy


20 μmFL

OW

20 μm

probe σ +

Defect-free area


detection σ +

=

FL

OW

30 µm FL

OW

Real defect

+



Polariton fluid dynamics

Study of the dynamics of polariton wavepacketst = 7 ps t = 28 ps t = 48 ps

Division in two in the presence of a big defectt = 8 ps t = 25 ps t = 45 ps

Amo et al., Nature 457, 291 (2009)

20 μm

20 μm

v = 1.2 m/ps (~1% light speed)

Original streak camera set-up

Obergurgl 6 June 2010Amo et al., Nature 457, 291 (2009)

TOPO

-3 -2 -1 0 1 2 3

1.527

1.530

1.533

En

erg

y (e

V)

kx (m-1)

CW PumpTOPO Signal

TOPO IdlerLPB

UPB

Pump polaritons

Signal polaritons

Coexistence of three fluids

• Steady state CW (pump) 100 m spot

• Triggered OPO (signal) 16 m spotfed by pump

• Idler

Pulse

Ene

rgy


Linear dispersion

0

1

E

-1 0 1

1.5265

1.5270

1.5275

Ene

rgy

(eV

)

kx (m-1)

2 2 22 / / /( , ) / 2 ( , ) ( , ) P P P P I I I t I Ix x i k x t x x t t i k x tt P Ii x t D i V x t x t F e e F e e e

CW Pump Pulsed probepol-pol interaction

decaynormal mode coupling

Amo et al., Nature 457, 291 (2009)


-60 -30 0 30 60

-60

-30

0

30

60

X (m)-60 -30 0 30 60

-60

-30

0

30

60

X (m)

t= 7ps t= 28ps t= 48psa

0.0

0.5

0.0

4.5

0.0

3.5

0.0

0.5

0.0

1.0

0.0

0.7b

-60 -30 0 30 60

-60

-30

0

30

60

Y (m

)

X (m)

Coherent propagation

Amo et al., Nature 457, 291 (2009)


-40 -20 0 20 40-40

-20

0

20

40

X (m)-40 -20 0 20 40

-40

-20

0

20

40

X (m)

t= 50pst= 36pst= 13pst= 8ps

-40 -20 0 20 40-40

-20

0

20

40

Y (m

)

X (m)-40 -20 0 20 40

-40

-20

0

20

40

X (m)

2.5

0.0

a

I

b

Flow through a defect

Amo et al., Nature 457, 291 (2009)


Frictionless flowPump polaritons

Signal polaritons

• Pump fluid: scattering waves

• Signal fluid no scattering with the defect Peaked momentum

compatible with superfluid behaviour

real spaceK-space

kX k Y

E=ħpump

E=ħsignal

Amo et al., Nature 457, 291 (2009)


Noise studies in the superfluid regime-20 -10 0 10 20

-2 -1 0 1 21.481

1.482

1.483

Emission angle (degrees)

En

erg

y (e

V)

ky (m-1)

Intensity noise polariton density statistics

Noise decreases in the superfluid regime

Superfluid threshold


a

-60 -40 -20 0 20 40-40

-20

0

20

40

X (m)b

t = 25 pst = 8 ps t = 45 psII

-60 -40 -20 0 20 40-40

-20

0

20

40

X (m)

Splitting in two

Amo et al., Nature 457, 291 (2009)


-20 -10 0 10 20

-2 -1 0 1 21.481

1.482

1.483

Emission angle (degrees)

En

erg

y (e

V)

ky (m-1)

Linear regime

Amo et al., Nature Physics 5, 805 (2009)

30 µm FLOW

Scattering with defects

Low density

30 µm FLOW 40 µm FLOW

Fluid without friction Linear wavefronts

Čerenkov

High density (quantum fluid regime)

Superfluid

vf<cs vf >cs

Polariton superfluidityT = 5 K


Linear regime

Amo et al., Nature Physics 5, 805 (2009)

30 µm FLOW


Scattering with defects

Low density T = 5 K

30 µm FLOW 40 µm FLOW

Fluid without friction Linear wavefronts

Čerenkov

High density (quantum fluid regime)

Superfluid

vf<cs vf >cs


-1 0 1

0.0

0.5

40 µm

40 µm FL

OW

High momentum

Polariton density

Elastic scattering

ky (m-1)

E -

Ep




Pumpvf > cs

FL

OW



Realspace

-1 0 1

0.0

0.5

Linear wavefronts

ky (m-1)

E -

Ep

0

1

supersonic

Documents

Superfluidity of Polaritons in Engineered Potentials in Semiconductor Microcavities