Strong coupling
(teoria classica)
Trasmissione FP con risonanza
TC  tC 
2
T 2 e 
1 R e
i  2 r     2
e
e 

1  F sin 2 ( r   / 2)
4R
F
2
1  R 
Trascurando r
la condizione di risonanza è
 2n


  nB  nR 
2

c
m

nB  nR   m
Posizione picco  r 
c


Calcolo posizione risonanze
 2 nB  nR ( ) 


2

nB
-1,0
Posizione picco
-0,5
 2

 nB  nR ( )    m
 

n
B
nB  nR ( )  
nB 
R
2
m

2
m
2
R  nB
m

nB  nR ( )   nB
R
Cavità ben accordata
Metodo grafico
0,0
R
0,5
1,0
Metodo grafico, cavità vuota
0,8
Transmission

nB  0  nB
R
1,0
0,6
0,4
0,2
0,0
829
R
830
831
832
Lambda (nm)
833
834
1,0
Transmission
Metodo grafico, cavità con eccitone

nB  nR ( )   nB
3 soluzioni
R
0,8
0,6
0,4
0,2
0,0
829
830
831
832
Lambda (nm)
833
834
Spettri cavità con eccitone
TC 
T 2 e 
1 R e
i  2 r     2
e
2 modi normali
Resta un
piccolo
assorbimento
sulle code
della banda
eccitonica
Picco centrale
trova un forte
assorbimento e
non compare negli
spettri
Se la cavità è fuori sintonia
R
3,64
eccitone
cavità vuota
n
3,62
3,60
3,58
829
830
831
832
Lambda (nm)
833
834
Al variare del tuning
 eccitone nudo
3,64
n
3,62
3,60
3,58
829
830
831
832
Lambda (nm)
833
834
Transmission (a.u)
Al variare del tuning
826
828
830
Lamba (nm)
832
834
Anticrossing
  (  0 ) 2  2 00G / nB  ( X   Ph ) 2
bare photon
bare exciton
0  2 00G / nB
Polariton
Half-photon, half-exciton
0
Al crescere della forza di oscillatore (ovvero del coupling)
3,66
G
3,64
n
3,62
3,60
3,58
3,56
829
830
831
832
Lambda (nm)
833
834
Eccitone nudo
Al crescere della
forza di oscillatore
lo splitting aumenta
Modi normali
Al crescere dell’ allargamento
3,64
3,62
n

3,60
3,58
829
830
831
832
Lambda (nm)
833
834
Eccitone nudo
Al crescere dello
allargamento lo
splitting diminuisce
fino a sparire
Modi normali
Fononi distruggono strong coupling
Exciton scattering distrugge
strong coupling
Esistenza polaritone
Coupling regimes
WC:VCSEL
SC:Polariton
Broadening
distrugge
Strong
coupling
Teoria quantistica:
Polaritone
Teoria quantistica: Polaritone
Photon state in second quantization and k space
Electromagnetic Vacuum
VPh  nPh  0

a VPh  nPh  1, k 

ak nPh  1, k  nPh  0


k
a , a   

k


k'
 
k ,k '
H phot
 
 a
a
)
k
(



cav
k
k

k
Exciton state in second quantization and k space
Exciton Vacuum
VX  n X  0

b VX  n X  1, k 

bk n X  1, k  n X  0


k
b , b   

k


k'
 
k ,k '
H exc
 
 b
b
)
k
(



exc
k
k

k
Half-photon, half-exciton
Anticrossing k//=0
Accordo in frequenza
Controllo deterministico
del tuning a posteriori
Cavità con gradiente
GaAs
Effetti quantistici
BEC polaritoni
Anticrossing k//=0
Bose-Einstein condensation (BEC) of an ideal Bose gas1
•The Bose-Einstein distribution function:



f B k ,T ,  
1
, 0

 E k  E 0    
exp 
1

k BT



•In a d-dimensional system with a parabolic dispersion around k=0:
2 2 / d
)  nc (T )  Tc (n)  4
n (d / 2) 2 / d
2m
•In a 3D (d=3) system with a parabolic dispersion around k=0:
2
2
2/3
Tc 
n
1.897mkb
1 S.N.
Bose, Z. Phys. 26, 178 (1924), A. Einstein, Sitzber. Kgl. Preuss. Akad. Wiss (1924).
Esistenza polaritone
Coupling regimes
Broadening
distrugge
Strong
coupling
Trappola in k space per polaritoni
Phase diagram of exciton-polaritons
Weak coupling
Weak coupling
Strong coupling
Solid lines show the critical concentration Nc versus temperature of the polariton
KT phase transition. Dotted and dashed lines show the critical concentration Nc
for quasi condensation in 100 µm and 1 meter lateral size systems, respectively.
Phase diagrams of exciton-polaritons in different materials
Solid lines show the critical concentration Nc versus temperature of the polariton KT phase transition. Dotted and dashed lines
show the critical concentration Nc for quasi condensation in 100 µm and 1 meter lateral size systems, respectively.
CdTe T=5K
GaN
Polaritons
at T=300K
BEC in GaN
@ 300K
Polariton laser
Laser history...
1917 Einstein derived the Plank formula, spontaneous + stimulated emission
1950 W. Lamb: idea of light amplification
1950 A. Kastler, optical pumping
1953 Weber, Twones, Basov, Prokhorov, maser
1959 T.H.Maiman, laser on rubis
1960s gaz lasers
1969 first semiconductor lasers (pn-junction)
1972 Zh. Alferov, laser on heterostructures
1990s lasers on semiconductor nanostructures, VCSELs
1996, Imamoglou, idea of polariton lasing
2007, RT polariton laser
To make a polariton laser one should have a microcavity
in the strong-coupling regime
Coherent spontaneous
emission from
polariton BEC
Optically or electronically excited exciton-polaritons relax towards the ground
state and Bose-condense there. Their relaxation is stimulated by final state
population. The condensate emits spontaneously a coherent light
“Normal”
semiconductor laser:
“Polariton” laser:
 The threshold to lasing is
given by the inversion of
population condition.
 The threshold condition:
population of the k=0 state
larger than 1.
 The absorption must be
balanced by stimulated
emission.
 The emission occurs at the
energy lower than the
absorption edge.
 Photon Bose condensation.
 Bose condensation of a half
matter-half light particle.
 Stimulated
light
 Spontaneous emission of
light
emission
of
Escape of polaritons from
cavity