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Quantum fluid phenomena with Microcavity Polaritons

Alberto Bramati

Flux

Obstacle

20µµµµm

Flux

Obstacle

20µµµµm

⇒ An ideal system to study out

of equilibrium quantum fluids

Quantum fluid phenomena in polariton gases

Superfluidity, hydrodynamic dark solitons and vortices (Nature Physics 2009, Science 2011, Nature Photonics 2011)

Quantum Optics Team: topics

Logic gates, All Optical Spin Switches (Nature Physics 2007, PRL

2007, Nature Photonics 2010, PRL 2011)

Spin dependent non linearities in microcavities

⇒ Towards integrated optoelectronic devices

Quantum Effects in semiconductor nano and microcavities in strong coupling regime

⇒ Towards a compact, integrablenano- source of entangled beams

Microcavities, quantum wires, micropillars (PRL

2007, APL 2010,PRB 2011)

� Introduction

� Superfluidity and Čerenkov regime

� Hydrodynamic Vortices and Dark Solitons

� Towards Vortex Lattices

� Perspectives and conclusion

OutlineOutline

Quantum fluid phenomena

UPB

LPB

Exciton

PhotonTop DBR

Bottom DBR

Quantum Well

Linear combination ofexcitons and photons

-3 -2 -1 0 1 2 3

1.526

1.528

1.530

1.532

En

erg

y (

eV

)

kin plane

(µm-1)

P+ = -C a + X b

P- = X a + C b

MicrocavityMicrocavity PolaritonsPolaritons

Very small effective mass m ~ 10-5 me1

2 22

T

Bmk T

πλ

=

h

MicrocavityMicrocavity PolaritonsPolaritons

Polaritons are weakly interacting composite bosons

P+ = -C a + X b

P- = X a + C b

Large coherence length λT ~ 1-2 µm at 5K

and mean distance between polaritons d ~ 0,1-0,2 µm

This enables the building of many-body quantum coherent effects : condensation, superfluidity

5 K

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

Excitation CW laser 1.755 eV

• 2D system

• Out of equilibrium system :

- Creation and recombination (polariton life time ~5 ps)

Bose Einstein condensation of polaritonsBose Einstein condensation of polaritons

Boson quantum fluids: polaritons

50 µm

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

Coherent propagation

Energ

y(e

V)

Amo et al., Nature 457, 295 (2009)

Wertz et al., Nature Phys. 6, 860 (2010)

Long-range order phases

Real space Momentum space

Lai et al., Nature 450, 529 (2007)

Vortex and half vortex

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

and Science 326, 974 (2009)

Nardin et al., arXiv:1001.0846v3

Krizhanovskii et al., PRL 104, 126402 (2010)

Roumpos et al., Nature Phys. 7, 129 (2010)

1D BEC arrays

Cerda-Méndez et al., PRL 105, 116402 (2010)

Sanvitto et al., Nature Phys. 6, 527 (2010)

Persistent currents

Superfluidity

Hydrodynamics:

vortex

Hydrodynamics:

solitons

This talk

This talk

Wave equation for polaritonsWave equation for polaritons

with

Evolution of exciton and cavity fields, in the presence Evolution of exciton and cavity fields, in the presence Evolution of exciton and cavity fields, in the presence Evolution of exciton and cavity fields, in the presence

of excitonof excitonof excitonof exciton----exciton interaction exciton interaction exciton interaction exciton interaction

pol-polinteraction

decaynormal mode coupling

CW Pump

defects

Gross-Pitaevskii equation in the presence of defects

The Landau Criterion for superfluidity

E

k

cs

Quantum fluid effects: Quantum fluid effects: superfluiditysuperfluidity


E

k

cs

E

k

cs+vf

FLOW

SUPERFLUID

Galilean

boost

vf<cs


vf - cs


E

k

cs

E

k

cs+vf

vf - cs

FLOW

E

k

cs+vf

vf - cs

FLOW

SUPERFLUID

CERENKOV REGIME

Galilean

boost

vf<cs

E

k

cs

Galilean

boost

vf >cs

critical flow velocity for

the onset of excitations: cs


-1 0 1

0.0

0.5

ky (µm-1)

E -

Ep

(meV

)

(c)

P

Linear regime, interactions between polaritons are negligible

elastic scattering is possible

We probe the behaviour of the fluid through its interaction with defects

Near fieldFar field

Propagation of a polariton fluidPropagation of a polariton fluid

I. Carusotto and C. Ciuti, PRL (2004); Phys. Stat. Sol. (b). 242, 2224 (2005)

Nonlinear regimestrong interactions betweenpolaritons,dispersion curve modified

-1 0 1

0.0

0.5

ky (µm-1)

(d)

P

E -

Ep

(meV

)

If vf < cs and density large enough

SuperfluidSuperfluid regimeregime

2

sc g mψ= h

a sound velocity appears

Landau criterion for superfluidity is fulfilled: no states available any more for scattering

I. Carusotto and C. Ciuti, PRL (2004);Phys. stat. sol. (b). 242, 2224 (2005)

Observation of a linear spectrum of excitation for polaritons:

• Utsunomiya et al., Nature Phys. 4, 700 (2008)• Kohnle et al., PRL, 106, 255302 (2011)

Near fieldFar field

Landau criterium: ren

LP signalE E> signalk k≠

No elastic scattering

SuperfluidSuperfluid regimeregime

I. Carusotto and C. Ciuti, PRL (2004);phys. stat. sol. (b). 242, 2224 (2005)

(d)(a)

X

Y

Near field CCD

Far fieldCCD

θθθθk

kz

k║

Microcavitysample

Excitationlaser

AB

(b)

-20 -10 0 10 20

-2 -1 0 1 21.481

1.482

1.483

Emission angle (degrees)

En

erg

y (

eV

)

ky (µm

-1)

Control parameters

�Polariton density(pump intensity)

�Fluid velocity(excitation angle)

�Oscillation frequency(laser frequency)

Experimental schemeExperimental scheme

Point [A]low momentumvf < cs

Polariton flow around a defect :Polariton flow around a defect :

near field image = real spacenear field image = real space

experiment

theory

Experiment

Theory

0.0 0.5 1.0 1.5 2.0Excitation density (arb. units)

Po

lari

ton

-flu

id d

en

sity

(arb

. u

nits)

(a)

I II

III

vp = 5.2 105 m/sSuperfluidity appears for a polariton density of ~ 109/cm2

defect : 4 µm diameter

Polariton density

Polariton flow around a defect :Polariton flow around a defect :

far field image = momentum spacefar field image = momentum space

experiment

theory

-1 0 1

0.0

0.5

P

ky (µm-1)

Collapse of the ring

Polariton density

Point [A]low momentumvf < cs

Landau criterion� c

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

Transition to the Transition to the superfluidsuperfluid regimeregime

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

vf > csound supersonic regime

AB

(b)

-20 -10 0 10 20

-2 -1 0 1 21.481

1.482

1.483

Emission angle (degrees)

En

erg

y (

eV

)

ky (µm

-1)

ČČerenkoverenkov regimeregime

ky (µm-1)-1 0 1

0.0

0.5

P

E -

Ep

available states

Point [B]high momentum

Landau condition

E. Cornell’s talk at the KITP Conference on QuantumGases

http://online.itp.ucsb.edu/online/gases_c04/cornell/.

vf =13cs vf =24cs

Čerenkov shock waves of a BEC against an obstacle at supersonic velocities

FLOW

Observation of Čerenkov waves indicatesthe existence of a well defined soundvelocity in the system

ČČerenkoverenkov effect in an atomic BECeffect in an atomic BEC

40 µm

b-I b-II b-III

FL

OW

0

1

40 µm

c-I c-II c-III

ČČerenkoverenkov waves : near field imagewaves : near field image

Characteristic linear density wavefronts of the Čerenkov waves

experiment

theory

Experiment

Theory

0.0 0.5 1.0 1.5 2.0 2.5

0

5

10

15

20

Po

lari

ton

density (

µm

-2)

(fro

m e

xp

erim

en

t)

Excitation density (arb. units)

III

III

Polariton density

Transition to the Transition to the ČČerenkoverenkov regimeregime

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

The case of spatially extended defects; the size of the defect is largerthan the healing length

SuperfluiditySuperfluidity breakdown: vortices and breakdown: vortices and solitonssolitons

formation?formation?

The currents formed in the fluid passing around a large obstacle can give rise to turbulence in its wake

,c sv c∞ <fv v∞=

2f

v v∞=

Quantized vortices

Dark Solitons

Acceleration of the fluid near the defect: the Landau criterion is locally violated

Polariton densityS. Pigeon et al. PRB (2010)

DEFECT

Ejection ofvortices andanti-vortices

Dark solitons


Superfluidity



Polariton densityS. Pigeon et al. PRB (2010)

DEFECT

Ejection ofvortices andanti-vortices

Dark solitons


Superfluidity



phase

0

2π

Experimental setExperimental set--upup

Microcavity

Intermediatemask

Focalisationlens

Lens

Excitationlaser

Spot onsample

Flo

w

y

La

se

rin

ten

sity Flow

Key points

�CW laser (precise control of the fluid quantum state)

�Mask (free evolution for the superfluid phase)

� Possibility to generate topological excitations

Excitationgeometry

Big Big defectdefect (15(15µµm) >> m) >>

healinghealing lengthlength

1

-1

0

10 µµµµm

d e f

g h i

0

1

10 µµµµm

1

100

10 µµµµm

a b cSuperfluidity Vortex ejection Solitons

Flo

w

10Real space

Interferogram

First ordercoherence

25.0=sf cv 4.0=sf cv 6.0=sf cv

Superfluidity Turbulence Solitons

Constant phase Phase dislocations Phase jumpsPhase jumps

Polariton densityAmo et al., Science, 332, 1167 (2011)

Vortices and Vortices and SolitonsSolitons

First order coherence

∆y = 14 µm

∆y = 26 µm

Pola

rito

n d

ensity (

arb

. units)

-20 0 20

∆y = 36 µm

x (µm)

ns

40

20

0

-20 0 20

40

20

0

-20 0 20

Flo

wn

∆y

(µm

)

∆x (µm)

vf = 1.7 µm/psk= 0.73 µm-1

0 10 20

P

ola

rito

n d

ensity (

arb

. un

its)

∆x (µm)

∆φ

Relative

phase

π

0

Hydrodynamic Dark Hydrodynamic Dark SolitonsSolitons

1

2

12

sncos

n

φ = −

SolitonSoliton doublet and quadrupletdoublet and quadruplet

a b

20 µm Flo

w

0

1

a b

20 µm Flo

w

0

1

Big defect (17µm) >> healing length

Low momentum; k= 0.2 µm-1 High momentum; k= 1.1 µm-1

Amo et al., Science, 332, 1167 (2011)

Hydrodynamic Dark Hydrodynamic Dark SolitonsSolitons: theory: theory

Not yet observed in atomic BEC; the dissipation in polariton fluids helps in stabilizing dark solitons (Kamchatnov et al. arXiv:1111.4170)

Light engineering of the Light engineering of the polaritonpolariton landscape:landscape:

using using polaritonpolariton--polaritonpolariton interactionsinteractions

FL

OW

20 µm

probe σ + Defect-free area

Sample from R. Houdré

Engineered landscapeEngineered landscape

control

yPola

rito

n

energ

yF

LO

W

20 µm

probe σ + control σ -

strong field:renormalization of the

polariton energy

0.1g g↑↓ ↑↑

≈


control

yPola

rito

n

energ

y

probe

scattered

20 µm



polariton energy

probe σ + + control σ -

detection σ +

+ =F

LO

W

FL

OW

0.1g g↑↓ ↑↑

≈

Amo et al., PRB Rapid Comm. (2010)


20 µm



polariton energy

probe σ + + control σ -

detection σ +

+ =

30 µm

FL

OW

Real defect

FL

OW

FL

OW

control

yPola

rito

n

energ

y

probe

scattered0.1g g

↑↓ ↑↑≈

Amo et al., PRB Rapid Comm. (2010)


scattered30 µm inje

cte

d

inje

cte

d

inje

cte

d

sc

att

ere

d

No control Linear control Diagonal control

Probe only Probe + Probe +


pulsed

y

xE

ne

rgy

Artificial

Potential

(Gaussian shape)

Polariton Fluid

All-optical control of the quantum flow of a polariton condensate

D. Sanvitto, et al.,Nature Photonics 5, 610 (2011)

Optical control of vortex formationOptical control of vortex formation

Triangular Trapping Mask behind the

defect:

the vortices created in the wake of the

defect are trapped inside the trap

20 µµµµm

S. Pigeon, et al., Phys. Rev. B 83, 144513 (2011)

Flow

No mask frame readjusted

20 ∪∪∪∪m

100

1

10

(a) (b) (c) (d) (e)

0.4

-0.4

0

(g) (h) (i) (j) (k)

(f)

(l)

Low power

Tailoring the potential landscape to trap vorticesTailoring the potential landscape to trap vortices

D. Sanvitto, et al.,Nature Photonics 5, 610 (2011)

Towards spontaneous formation of vortex latticesTowards spontaneous formation of vortex latticesSmall triangular trap

Self-organization of vortices and anti-vortices in hexagonal lattices

Experiment Theory

Polariton density

Phase

Towards spontaneous formation of vortex latticesTowards spontaneous formation of vortex lattices

Increasing the size of the trap, a larger number of hexagonal unit cells is formed

�Polariton Quantum Fluids

• Superfluidity

• Čerenkov regime

• Hydrodynamic vortices and dark solitons

�Perspectives

• Engineering of polariton landscape: Dynamical

Potentials, Optical traps for polaritons

• Study and control of Quantum turbulence?

• Lattices of vortices?

• Spinor polariton condensates (Hivet et al. arXiv:1204.3564)

Conclusion and perspectives

University of TrentoUniversity of Trento

I. I. CarusottoCarusotto

Lab. MPQ, ParisLab. MPQ, Paris

C. C. CiutiCiuti

EPFL, LausanneEPFL, Lausanne

R. R. HoudrHoudréé

NNL Lab., LecceNNL Lab., LecceD. D. SanvittoSanvitto

Lab. LPN, Lab. LPN, MarcoussisMarcoussis

J. Bloch, A. J. Bloch, A. AmoAmo

Lab. LASMEA, Clermont Lab. LASMEA, Clermont FerrandFerrand

G. G. MalpuechMalpuech

CollaborationsCollaborations

EXPERIMENTS THEORY

PhD Students:G. Leménager

R. HivetV.G. SalaT. Boulier

The team

Post-Doc E.Cancellieri

Permanent Staff: Elisabeth Giacobino, Alberto Bramati

Former members:M. RomanelliC. LeyderJ. Lefrère

C. AdradosF. Pisanello

A. Amo

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