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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
![Page 4: Introduction to Bose – Einstein condensation of ... · ICSCE4, Cambridge, Sept. 2008 Institut Néel - CNRS 36 Polariton BEC VS Photon lasing](https://reader030.vdocuments.net/reader030/viewer/2022040217/5d5ce79b88c9935a7e8b653b/html5/thumbnails/4.jpg)
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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
![Page 34: Introduction to Bose – Einstein condensation of ... · ICSCE4, Cambridge, Sept. 2008 Institut Néel - CNRS 36 Polariton BEC VS Photon lasing](https://reader030.vdocuments.net/reader030/viewer/2022040217/5d5ce79b88c9935a7e8b653b/html5/thumbnails/34.jpg)
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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