Recent advances and issues on Bose – Einstein condensation ... · Aussois 2008 Institut Néel -...

Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 1

Le Si Dang

T = 20 K

N < N0 N0 N > N0

J. Kasprzak et al., 2006

Recent advances and issues on Bose – Einstein condensation of microcavity polaritons


Le Si Dang

T = 20 K

N < N0 N0 N > N0


Polaritons

Rb atoms

M.H. Anderson et al., 1995

Rb

mpolariton ~ 10 – 9 mRb

Recent advances and issues on Bose – Einstein condensation of microcavity polaritons


IntroductionBECExcitonsMicrocavity polaritons

Polariton BEC

Prospects

Outline


Particles

Mass, charge, spin

Integer

0, 1, …

Half integer

1/2, 3/2, …

Bosons

photon, exciton

Fermions

electron

Bose-Einstein condensation (1925)

PauliexclusionBEC


λdBa

N bosons at temperature T


Tmk2

B

2

dB

hπ=λ

De Broglie wavelength

dBλ < a

T too high

N too small

3/1

NV

a

=

Inter particle distance

kBT

EMB gas


N bosons at temperature T


Tmk2

B

2

dB

hπ=λ

De Broglie wavelength

dBλ > a

Decreasing T

Increasing N

λdBa

Small mHigh T

Massive occupation of ground state

kBTNi << N

N0 ~ N

EBose gas

The theory is pretty, but is there also some truth to it?

(A. Einstein to P. Ehrenfest, 1924)

3/1

NV

a

=

Inter particle distance


Conduction 1/2

Valence 3/2

E

k

Gap ~ 1 eV

Exciton BEC in semiconductors (1962)

electron

Laser


Conduction 1/2

Valence 3/2

E

k

Exciton BEC in semiconductors (1962)

aB

e

h

_

+

Exciton = "H atom"

aB ~ 10 nm, mass ~ me

BEC expected at 1 K (1962)

No conclusive evidence

hole

electron

Exciton = boson


Microcavity polaritons (1992)

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 ~ 4 10– 5me

pol

2//

2

//m2

k)k(E

h=

BEC at 300 K!0.7 µm4 nm

6 µm40 nm4K

T300K

4 10-51Mass (me)

λdB

Exciton Polariton



-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

Polaritons at k// ~ 0

Condensation (T, N)


Polaritons → Photons

Polaritons (k//) = Photons (θ)

How to observe BEC?


-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

Polaritons at k// ~ 0

Condensation (T, N)


Polaritons → Photons

Polaritons (k//) = Photons (θ)Polaritons in momentum space

How to observe BEC?

Microcavity far-field emission


16 QWs CdTe/CdMnTe

Rabi splitting = 26 meV

EBX = 25 meV

Bragg mirrors

λ/4 CdMgTe

λ/4 CdMnTe

Far field emission (E, θ)

k//

θ

Molecular Beam Epitaxy

CdTe microcavity – 16 QWs


Introduction

Polariton BECBimodal distributionLong range spatial coherence

Prospects

Outline


M.H. Anderson et al. 1995

Rb

Bimodal distribution

Condensate

Thermal cloud

Phase transition driven by

decreasing T and/or increasing N


kBT

T = 5 K Increasing N

Bimodal distribution of CdTe polaritons


kBT




kBT




kBT




kBT




kBT




kBT




kBT




kBT




kBT





kBT





kBT

N = constant Decreasing T



Condensate

Thermal cloud


Tbath = 5 K

Tbath = 5 K


Thermal cloud

Teff = 16 ± 1 K

Condensate

λdB ≈ 3.6 µm

a ≈ 0.5 µm


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

Interferometry


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



++++ ====

Pumping = 1.9 P0


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


λdB ~ 3 µm

Spatial correlation mapping

Below threshold Above threshold


40% correlation over 14 µmDistance between polaritons ≈ 0.5 µm


Introduction

Polariton BEC

Prospects

Outline


Interaction

Some polariton (hot) issues …

Polariton

Exciton – Photon

τ ~ 10 -12 s

Thermalization?

Thermodynamics? Kinetics?

CW pumping

Out of equilibriumBEC / BKT? Coherence?

Superfluidity?

Vortex?

Solid state Disorder Fragmentation?

BEC at 300 K

Polariton "laser"

GaN, ZnO

Organics

New photonic structures

Microdisk, PC

0D, 1D

Josephson junction


Polariton "laser"

Condensate

Coherent photons

Polariton "laser"

Ultra low threshold


VCSEL

e-h population inversion

Polariton laser

exciton screening

GaAs CdTe ZnSe GaNZnO

Band gap / E BX

Pumping

polaritonstimulation

exciton saturation

e-h population inversion

VCSEL

Polariton"laser"

Low threshold UV laser

P0

50 P0


a

_

+

Excitons = "good" bosons if aB << a

Tmk2

B

2

dB

hπ=λ 3/1N1

a =>

T λdB a by increasing N

Exciton

Composite boson aB

e

h

_

+

BEC

Room temperature BEC

Wide band gap ZnSe, ZnO (2 nm), GaN (3 nm)


3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

-15-10

-5051015202530

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

-15-10

-5051015202530

Energy (eV)

Ang

le (d

egre

e)

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

-15-10

-5051015202530

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

-15-10

-5051015202530

Energy (eV)

Ang

le (d

egre

e)

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

1510

5051015202530

Energy (eV)

Ang

le (d

egre

e) P = 0.98 P0P = 1.03 P0 PhotonX

0 5 10 15 20 25 30

Teff

= 325 K

T = 300 K

Inte

grat

ed in

tens

ity (

arb.

uni

ts)

E-E0 (meV)

x10

1.1 P0

P0

0.02 P0

RT polariton lasing

Fabry-Perot microcavity GaN

EPFL (Christmann et al., APL 93, 051102 (2008))


Conclusion

"Phase transition" (N, T)

Massive occupation of ground state

Long range order

Polariton condensate

T = 20 K

N < N0 N0 N > N0



< 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

RTdevices


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

A. Baas M. Wouters

K. Lagoudakis G. Nardin

B. Pietka B. Deveaud-Plédran

F.M. Marchetti M.H. Szymanska

J. Keeling P. Littlewood

D. Solnyshkov

G. Malpuech

I. Carusotto

Date post:	21-Aug-2019
Category:	Documents
Upload:	duongthuan
View:	213 times
Download:	0 times

Recent advances and issues on Bose – Einstein condensation ... · Aussois 2008 Institut Néel -...

Documents