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Introduction to Bose – Einstein condensation of microcavity polaritons

Le Si Dang

T = 20 K

N < N0 N0 N > N0

J. Kasprzak et al., 2006

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Introduction to Bose – Einstein condensation of microcavity polaritons

Le Si Dang

T = 20 K

N < N0 N0 N > N0

J. Kasprzak et al., 2006

Polaritons

Rb atoms

M.H. Anderson et al. 1995

Rb

mpolariton ~ 10 – 9 mRb

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Microcavity polaritons

Polariton BEC

Why not photon lasing?

Outline

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Microcavity polaritons

Photons in cavity

Excitons

In QW

Phonons Carriers

Mirror leakage R < 100%

Polaritons = Mixed (exciton – photon)

Strong (exciton – photon) coupling if >

QW ~ 10 nm

Optical cavity ~ 1 µm

HRmirror

Exciton → Photon → Exciton → Photon …

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Microcavity polaritons

QW ~ 10 nm

Optical cavity ~ 1 µm

HRmirror

-0,10 -0,05 0,00 0,05 0,10-20

0

20

40

exciton

cavity photon

In-plane wave vector k// (106cm-1)

Ene

rgy

(m

eV)

1730

1710

1690

1670

Ene

rgy

(meV

)

In-plane dispersion

Polaritons = Mixed (exciton – photon)

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Microcavity polaritons

QW ~ 10 nm

Optical cavity ~ 1 µm

HRmirror

Polaritons = Mixed (exciton – photon)

-0,10 -0,05 0,00 0,05 0,10-20

0

20

40

ΩRabi

lowerpolariton

upperpolariton

In-plane wave vector k// (106cm-1)

Ene

rgy

(m

eV)

1730

1710

1690

1670

Ene

rgy

(meV

)

In-plane dispersion

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-0,10 -0,05 0,00 0,05 0,10-20

0

20

40

lowerpolariton

upperpolariton

In-plane wave vector k// (106cm-1)

Ene

rgy

(m

eV)

1730

1710

1690

1670

Ene

rgy

(meV

)

In-plane dispersion

Parabolic well

mpol ~ 10– 5me

pol

2//

2

//m2

k)k(E

h=

BEC temperature ∝ 1 / mass

Polariton condensation at RT!

Microcavity polaritons

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-0,10 -0,05 0,00 0,05 0,10-20

0

20

40

lowerpolariton

upperpolariton

In-plane wave vector k// (106cm-1)

Ene

rgy

(m

eV)

1730

1710

1690

1670

Ene

rgy

(meV

)

In-plane dispersionpump

Injection of hot e-h pairs

Relaxation

Exciton reservoir

Microcavity polaritons

X – X scattering

Phonon scattering

N0 ~ 1

Stimulated scatterings

Massive occupation of ground state

How to observe microcavity polaritons?

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How to observe microcavity polaritons?

Microcavity polaritons

Microcavity emission measured as a function of emission angle

Polariton distribution in LPB

Polaritons → Photons

Conservation of E and k//

Microcavity emission (θ, φ) = Polaritons (k//)

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Microcavity polaritons

Polariton BECBimodal distributionMacroscopic spatial coherence

Why not photon lasing?

Outline

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M.H. Anderson et al. 1995

Rb

Bimodal distribution

Condensate

Thermal cloud

Phase transition driven by

decreasing T and/or increasing N

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kBT

N = constant Decreasing T

Bimodal distribution of CdTe polaritons

Bimodal distribution

Condensate

Thermal cloud

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

5 K 20 K

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

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kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons

Bimodal distribution

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Tbath = 5 K

Tbath = 5 K

Bimodal distribution of CdTe polaritons

Thermal cloud

Teff = 16 ± 1 K

Condensate

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GaAs polaritons

Bose-Einstein condensation of microcavity polaritons in a trap R. Balili et al., Science 316, 1007 (2007)

Stress induced harmonic potential trap

0.05 mW 0.4 mW

0.6 mW 0.8 mW

T = 4.2 K

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GaAs polaritons

Bose-Einstein condensation of microcavity polaritons in a trap R. Balili et al., Science 316, 1007 (2007)

T = 97 KPolariton temperature = 97 K

0.05 mW 0.4 mW

0.6 mW 0.8 mW

T = 4.2 K

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GaAs polaritons

Maxwell-Boltzmann

Bose-Einstein

T = 4.4 K

In thermal equilibrium with lattice at T = 4.2 K

Quantum degenerate exciton-polaritons in thermal equilibrium H. Deng et al., PRL 97, 146402 (2006)

Pumping into exciton reservoir

P = 4P0

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Macroscopic spatial coherence

~ 20 µm

Emission spot = Polariton system

B

Phase correlation between A and B

A0.5 mm

M.R. Andrews et al. 1997

Interference between twoBose condensates

Na

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Michelson interferometer

40 x emission spot

Arm 1 0 – 6 π

BS

Arm 2Retro-reflector

Overlapped images

Correlations between (x,y) and (-x,-y)

Arm 2

Flipped image

Arm 1

Macroscopic spatial coherence of CdTe polaritons

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Pumping = 1.9 P0

++++ ====

Delay between arms 1 and 2 → Interference contrast → g (1) (r, -r)

Macroscopic spatial coherence of CdTe polaritons

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Spatial correlation mapping

Below threshold Above threshold

40% correlation over 14 µmDistance between polaritons ≈ 0.5 µm

Macroscopic spatial coherence of CdTe polaritons

λdB ~ 2.6 µmTpol ~ 20 K

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GaAs polaritons

Spatial coherence of a polariton condensate H. Deng et al., PRL 99, 126403 (2007)

Double slit experiment at 4.2 K

Slit separation = 2.7 µm

7 P0

6.7 P0

0.5 P0

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GaAs polaritons

Bose-Einstein condensation of microcavity polaritons in a trap R. Balili et al., Science 316, 1007 (2007)

Condensates

Interference in thermal cloud

PL fromarm 1 arm 2

Interference in thermal cloud

Michelson interferometer

Below threshold Above threshold

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Microcavity polaritons

Polariton BEC

Why not photon lasing?

Outline

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Polariton BEC VS Photon lasing

Exciton – PhotonPolaritons

Microcavity

• Stimulated emission• Beam narrowing• Spontaneous coherence

and polarization

Polariton BEC

Vertical Cavity Surface Emitting Laser (VCSEL)

(e, h) – Photon Photon lasing

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Polariton BEC VS Photon lasing

Exciton – PhotonPolaritons

Microcavity

Vertical Cavity Surface Emitting Laser (VCSEL)

(e, h) – Photon

Polariton BEC

Photon lasing in GaAs microcavity

Bajoni et al.PRB 76, 201305 (2007)

Thermal cloud

Optical modes!

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Polariton BEC VS Photon lasing

Exciton – PhotonPolaritons

Vertical Cavity Surface Emitting Laser (VCSEL)

(e, h) – Photon

Polariton BEC

Photon lasing

Strongcoupling

Weakcoupling

Interactingbosons

Non interactingbosons

• Photon dispersion• Strong-weak

coupling crossover

• Blue shift withincreasing density

• Decoherence

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Strong – weak coupling crossover

Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP

Uncoupled X and cavity modes

Stimulation of polariton PL in semiconductor microcavity

Le Si Dang et al., PRL 81, 3920 (1998)

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Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP

Uncoupled X and cavity modes

Stimulation of polariton PL in semiconductor microcavity

Le Si Dang et al., PRL 81, 3920 (1998)

Strong coupling

Strong – weak coupling crossover

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Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP

Uncoupled X and cavity modes

Stimulation of polariton PL in semiconductor microcavity

Le Si Dang et al., PRL 81, 3920 (1998)

Strong coupling

Strong – weak coupling crossover

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Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP

Weak coupling

Uncoupled X and cavity modes

Stimulation of polariton PL in semiconductor microcavity

Le Si Dang et al., PRL 81, 3920 (1998)

Strong coupling

Strong – weak coupling crossover

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Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP

Uncoupled X and cavity modes

Weak coupling

Strong coupling

Stimulation of polariton PL in semiconductor microcavity

Le Si Dang et al., PRL 81, 3920 (1998)

Strong – weak coupling crossover

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Polariton = Interacting boson

Continuous blue shiftIncreasing density ≠ Photon laser !

Broadening

D. Porras and C. Tejedor, PRB 67, 161310 R (2003)

BEC VS Lasing in CdTe

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Polariton blueshift

F. Marchetti et al., PRB 2008

Phase diagram for condensation of microcavitypolaritons: from theory to practice

S. Utsunomiya et al., Nature Physics 2008

Observation of Bogoliubov excitations in exciton-polariton condensates

CdTe

GaAs

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k

E

Conclusion

"Phase transition" (N, T)

Massive occupation of ground state

Macroscopic spatial coherence

Polariton condensate

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< 10% > 90%

He atoms

Condensate fraction

Interaction

50%

polaritons

2006 Solids Polaritons < 50 K

1925 Prediction

1938 Liquids 4He superfluid 2.2 K

1995 Gases Atoms 10-6 K

Conclusion

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Interaction

Some polariton (hot) issues …

Polariton

Exciton – Photon

τ ~ 10 -12 s

Thermalization?

Thermodynamics? Kinetics?

Out of equilibriumBEC / BKT? Coherence?

Superfluidity?

Vortex?

Solid state Disorder Fragmentation?

RT BEC

Polariton "laser"

GaN, ZnO

Organics

WGM in microdisk

Slow Bloch modes in PC

0D, 1D

Josephson junction

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University of Crete (Nature 2008)

GaAs – based microcavity

Strong coupling up to 220 K

Polariton device

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Polariton BEC

J. Kasprzak (Cardiff)

M. Richard

R. André

Le Si Dang

F.M. Marchetti

M.H. Szymanska

J. Keeling

P. Littlewood

D. Solnyshkov

G. Malpuech

A. Baas

K. Lagoudakis

M. Wouters

I. Carusotto (Trento)

G. Nardin

B. Pietka

V. Savona

B. Deveaud-Plédran

A. Love

D. Krizhanovskii

D. Whittaker

M. Skolnick LPN Marcoussis J. Bloch, P. Senellart

U. A. Madrid C. Tejedor, L. Vina

U. Southampton A. Kavokin

U. Durham M. Kaliteevski