Introduction to Bose – Einstein condensation of ... · ICSCE4, Cambridge, Sept. 2008 Institut Néel - CNRS 36 Polariton BEC VS Photon lasing

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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


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


Microcavity polaritons

Polariton BEC

Why not photon lasing?

Outline



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 …



QW ~ 10 nm


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




QW ~ 10 nm


HRmirror


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

0

20

40

ΩRabi

lowerpolariton

upperpolariton


Ene

rgy

(m

eV)

1730

1710

1690

1670

Ene

rgy

(meV

)

In-plane dispersion


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

0

20

40

lowerpolariton

upperpolariton


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!



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

0

20

40

lowerpolariton

upperpolariton


Ene

rgy

(m

eV)

1730

1710

1690

1670

Ene

rgy

(meV

)

In-plane dispersionpump

Injection of hot e-h pairs

Relaxation

Exciton reservoir


X – X scattering

Phonon scattering

N0 ~ 1

Stimulated scatterings

Massive occupation of ground state

How to observe microcavity polaritons?


How to observe 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//)



Polariton BECBimodal distributionMacroscopic spatial coherence


Outline


M.H. Anderson et al. 1995

Rb

Bimodal distribution

Condensate

Thermal cloud

Phase transition driven by

decreasing T and/or increasing N


kBT

N = constant Decreasing T

Bimodal distribution of CdTe polaritons


Condensate

Thermal cloud


kBT

T = 5 K Increasing N


5 K 20 K


kBT




kBT




kBT




kBT




kBT




kBT




kBT




kBT




kBT





Tbath = 5 K

Tbath = 5 K


Thermal cloud

Teff = 16 ± 1 K

Condensate


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


GaAs polaritons


T = 97 KPolariton temperature = 97 K

0.05 mW 0.4 mW

0.6 mW 0.8 mW

T = 4.2 K


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


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


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


Pumping = 1.9 P0

++++ ====

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



Spatial correlation mapping

Below threshold Above threshold

40% correlation over 14 µmDistance between polaritons ≈ 0.5 µm


λdB ~ 2.6 µmTpol ~ 20 K


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


GaAs polaritons


Condensates

Interference in thermal cloud

PL fromarm 1 arm 2

Interference in thermal cloud

Michelson interferometer

Below threshold Above threshold



Polariton BEC


Outline


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




Microcavity


(e, h) – Photon

Polariton BEC

Photon lasing in GaAs microcavity

Bajoni et al.PRB 76, 201305 (2007)

Thermal cloud

Optical modes!





(e, h) – Photon

Polariton BEC

Photon lasing

Strongcoupling

Weakcoupling

Interactingbosons

Non interactingbosons

• Photon dispersion• Strong-weak

coupling crossover

• Blue shift withincreasing density

• Decoherence


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)


Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP




Strong coupling



Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP




Strong coupling



Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP

Weak coupling




Strong coupling



Energy (meV)

PL

int.

/ pum

p po

wer

(ar

b. u

nits

)

LP UP


Weak coupling

Strong coupling





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


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


k

E

Conclusion

"Phase transition" (N, T)

Massive occupation of ground state

Macroscopic spatial coherence

Polariton condensate


< 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


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


University of Crete (Nature 2008)

GaAs – based microcavity

Strong coupling up to 220 K

Polariton device


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

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Introduction to Bose – Einstein condensation of ... · ICSCE4, Cambridge, Sept. 2008 Institut Néel - CNRS 36 Polariton BEC VS Photon lasing