recent advances and issues on bose – einstein condensation ... · aussois 2008 institut néel -...
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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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 2
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
Recent advances and issues on Bose – Einstein condensation of microcavity polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 3
IntroductionBECExcitonsMicrocavity polaritons
Polariton BEC
Prospects
Outline
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 4
Particles
Mass, charge, spin
Integer
0, 1, …
Half integer
1/2, 3/2, …
Bosons
photon, exciton
Fermions
electron
Bose-Einstein condensation (1925)
PauliexclusionBEC
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 5
λdBa
N bosons at temperature T
Bose-Einstein condensation (1925)
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 6
N bosons at temperature T
Bose-Einstein condensation (1925)
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 7
Conduction 1/2
Valence 3/2
E
k
Gap ~ 1 eV
Exciton BEC in semiconductors (1962)
electron
Laser
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 8
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 9
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 …
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 10
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)
Microcavity polaritons (1992)
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 11
QW ~ 10 nm
Optical cavity ~ 1 µm
HRmirror
-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
Polaritons = Mixed (exciton – photon)
Microcavity polaritons (1992)
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 12
-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 ~ 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
Microcavity polaritons (1992)
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 13
-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
Polaritons at k// ~ 0
Condensation (T, N)
Microcavity polaritons (1992)
Polaritons → Photons
Polaritons (k//) = Photons (θ)
How to observe BEC?
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 14
-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
Polaritons at k// ~ 0
Condensation (T, N)
Microcavity polaritons (1992)
Polaritons → Photons
Polaritons (k//) = Photons (θ)Polaritons in momentum space
How to observe BEC?
Microcavity far-field emission
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 15
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 16
Introduction
Polariton BECBimodal distributionLong range spatial coherence
Prospects
Outline
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 17
M.H. Anderson et al. 1995
Rb
Bimodal distribution
Condensate
Thermal cloud
Phase transition driven by
decreasing T and/or increasing N
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 18
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 19
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 20
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 21
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 22
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 23
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 24
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 25
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 26
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 27
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Bimodal distribution
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 28
kBT
T = 5 K Increasing N
Bimodal distribution of CdTe polaritons
Bimodal distribution
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 29
kBT
N = constant Decreasing T
Bimodal distribution of CdTe polaritons
Bimodal distribution
Condensate
Thermal cloud
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 30
Tbath = 5 K
Tbath = 5 K
Bimodal distribution of CdTe polaritons
Thermal cloud
Teff = 16 ± 1 K
Condensate
λdB ≈ 3.6 µm
a ≈ 0.5 µm
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 31
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 32
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 33
++++ ====
Pumping = 1.9 P0
Macroscopic spatial coherence
Delay between arms 1 and 2 → Interference contrast → g (1) (r, -r)
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 34
λdB ~ 3 µm
Spatial correlation mapping
Below threshold Above threshold
Macroscopic spatial coherence
40% correlation over 14 µmDistance between polaritons ≈ 0.5 µm
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 35
Introduction
Polariton BEC
Prospects
Outline
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 36
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 37
Polariton "laser"
Condensate
Coherent photons
Polariton "laser"
Ultra low threshold
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 38
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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 39
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)
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 40
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))
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 41
Conclusion
"Phase transition" (N, T)
Massive occupation of ground state
Long range order
Polariton condensate
T = 20 K
N < N0 N0 N > N0
J. Kasprzak et al., 2006
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 42
< 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
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 43
University of Crete (Nature 2008)
GaAs – based microcavity
Strong coupling up to 220 K
Polariton device
Aussois 2008 I nstitut Néel - CNRS - UJF ht tp://neel.cnrs.fr/ 44
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