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Obergurgl 6 June 2010
Superfluidity of Polaritons in Engineered Potentials in
Semiconductor MicrocavitiesAlberto Amo, C. Adrados, J. Lefrère, E. Giacobino, A. Bramati
S. Pigeon, C. Ciuti
Laboratoire Kastler Brossel, UPMC, ENS, CNRS, Paris, FR
Laboratoire MPQ, Université Denis Diderot, CNRS, Paris, FR
I. CarusottoBEC-CNR-INFM and Dipartimento di Fisica, Universita di Trento, Povo, IT
R. HoudréInstitut de Physique de la Matière Condensée, EPFL, Lausanne CH
Obergurgl 6 June 2010
Outline
Polaritons in semiconductor microcavities
Observation of superfluidity of polaritons
Engineering the polariton landscape
Obergurgl 6 June 2010
Top DBR
Bottom DBR
Quantum Wells
Exciton
Photon
Angle θ (º)
kin-plane (μm-1)
Upper polariton
Lower polariton
θ
k in-plane
Semiconductor microcavities
Em
issi
on e
nerg
y (e
V)
Polaritons
~ 5meV
GaAs
Obergurgl 6 June 2010
Properties
Top DBR
Bottom DBR
Quantum Wells
Exciton
Photon
Angle θ (º)
kin-plane (μm-1)
Upper polariton
Lower polariton
θ
k in-plane
Composite bosons
Excitonic component strong interactions (non-linearities 3)
Semiconductor microcavities
Em
issi
on e
nerg
y (e
V)
Polaritons
~ 5meV
Photonic component low mass (10-5 me)
Short lifetime (~ps) out of equilibrium
GaAs
Obergurgl 6 June 2010
Kasprzak et al. Nature, 443, 409 (2006)
kin-plane (μm-1)
Lower polaritonE
mis
sion
ene
rgy
(eV
)
kx
ky
Polariton density
Polariton condensation
Polariton condensate
Atomic BEC
m/me
104
10-5
Tc
<1 K
20-300 K
T at Tc
1 m
1-10 m
T = 5 K CdTe
Excitation
Obergurgl 6 June 2010
Polariton quantum fluid effects
Interferogram Phase map
Quantized vortices (m=1)
Imprinted vortices (m=1,2)and persistent currents
Lagoudakis et al., Nature Phys. 4, 706 (2008)
Sanvitto et al., Nature Phys.DOI: 10.1038/NPHYS1668 (2010)
Obergurgl 6 June 2010
Polariton quantum fluid effects
Interferogram Phase map
Quantized vortices (m=1)
Imprinted vortices (m=1,2)and persistent currents
Lagoudakis et al., Nature Phys. 4, 706 (2008)
Sanvitto et al., Nature Phys.DOI: 10.1038/NPHYS1668 (2010)
Amo et al., Nature 457, 291 (2009)
Fluid dynamics
Real space
Momentum space
Obergurgl 6 June 2010
E
k
cs
Landau criteriom for superfluidity
Interacting Boson condensate linearized spectrum of excitations
Obergurgl 6 June 2010
E
k
cs
E
k
cs+vf
cs-vf
SUPERFLUID
Galileanboost
vf < cs
Landau criteriom for superfluidityF
LO
W
Interacting Boson condensate linearized spectrum of excitations
Obergurgl 6 June 2010
E
k
cs
E
k
cs+vf
cs-vf
SUPERFLUID
Galileanboost
vf < cs
Landau criteriom for superfluidity
E
k
cs+vf
cs-vf
FL
OW
ČERENKOV REGIME
E
k
cs
Galileanboost
vf > cs
FL
OW
Interacting Boson condensate linearized spectrum of excitations
I. Carusotto and C. Ciuti, phys. stat. sol. (b) 242, 2224 (2005)
Obergurgl 6 June 2010
Resonantly excited condensate withlow momentum
30 µm
FL
OW
Realspace
-1.0 -0.5 0.0 0.5k
x (m-1)
Momentumspace
Polariton density
Elastic scattering
-1 0 1
0.0
0.5
ky (m-1)
E -
Ep
22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e
Linear regime
Pump
Polariton superfluidity
Obergurgl 6 June 2010
Resonantly excited condensate withlow momentum
30 µm
FL
OW
0
1
-1.0 -0.5 0.0 0.5k
x (m-1)
-1.0 -0.5 0.0 0.5
kx (m-1)
-1.0 -0.5 0.0 0.5 1.0
-0.5
0.0
0.5
k y (
m-1)
kx (m-1)
Polariton density
Collapse of the ring
-1 0 1
0.0
0.5
Pump
ky (m-1)
Elastic scattering
-1 0 1
0.0
0.5
ky (m-1)
E -
Ep
E -
Ep
Amo et al., Nature Phys. 5, 805 (2009)
22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e
Linear regime Superfluid
Pump
vf < cs
Polariton superfluidity
Realspace
Momentumspace
Obergurgl 6 June 2010
30 µm
FL
OW
0
1
Polariton density
Collapse of the ring
-1 0 1
0.0
0.5
Pump
ky (m-1)
Elastic scattering
-1 0 1
0.0
0.5
ky (m-1)
E -
Ep
E -
Ep
22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e
Linear regime Superfluid
Pump
30 µm FL
OW
Gross-Pitaevskiisimulations
Polariton superfluidity
Realspace
Resonantly excited condensate withlow momentum
vf < cs
Amo et al., Nature Phys. 5, 805 (2009)
Obergurgl 6 June 2010
Superfluid regime
Obergurgl 6 June 2010
-1 0 1
0.0
0.5
40 µm
40 µm FL
OW
High momentum
Polariton density
Elastic scattering
ky (m-1)
E -
Ep
22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e
Linear regime Čerenkov
Pumpvf > cs
FL
OW
Gross-Pitaevskiisimulations
Čerenkov regime (supersonic)
Realspace
-1 0 1
0.0
0.5
Linear wavefronts
ky (m-1)
E -
Ep
supersonic
0
1
Amo et al., Nature Phys. 5, 805 (2009)
Obergurgl 6 June 2010
-1 0 1
0.0
0.5
40 µm
40 µm FL
OW
High momentum
0
1
Polariton density
Elastic scattering
ky (m-1)
E -
Ep
22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e
Linear regime Čerenkov
Pumpvf > cs
FL
OW
Gross-Pitaevskiisimulations
Čerenkov regime (supersonic)
Realspace
-1 0 1
0.0
0.5
Linear wavefronts
ky (m-1)
E -
Ep
Supersonic atomic BEC
Carusotto et al. PRL 97, 260403 (2006)
s fsin c v 58 1 10sc . m / s
supersonic
Amo et al., Nature Phys. 5, 805 (2009)
Obergurgl 6 June 2010
Polariton landscape engineering 22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x t
t Pi x t D i V x t x t F e e
FL
OW
20 μm
probe σ +
Defect-free area
Obergurgl 6 June 2010
Polariton landscape engineering 22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x t
t Pi x t D i V x t x t F e e
control
yPol
arit
on
ene
rgy
control σ -
Strong field:renormalization of the
polariton energy
polariton-polariton interaction
20 μmFL
OW
20 μm
probe σ +
Defect-free area
+
Obergurgl 6 June 2010
Polariton landscape engineering 22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x t
t Pi x t D i V x t x t F e e
control
yPol
arit
on
ene
rgy
control σ -
Strong field:renormalization of the
polariton energy
polariton-polariton interaction
20 μmFL
OW
20 μm
probe σ +
Defect-free area
probe σ + + control σ -
detection σ +
=
FL
OW
+
Amo et al., arXiv:1003.0131v1
Obergurgl 6 June 2010
scattered30 μm
inje
cted
inje
cted
scat
tere
d
No control horizontal control diagonal controlProbe only Probe + Probe +
Amo et al., arXiv:1003.0131v1
Polariton landscape engineering
inje
cted
Obergurgl 6 June 2010
scattered30 μm
inje
cted
inje
cted
scat
tere
d
No control horizontal control diagonal controlProbe only Probe + Probe +
Amo et al., arXiv:1003.0131v1
Polariton landscape engineering
inje
cted
Obergurgl 6 June 2010
scattered30 μm
inje
cted
inje
cted
scat
tere
d
No control horizontal control diagonal controlProbe only Probe + Probe +
Amo et al., arXiv:1003.0131v1
Polariton landscape engineering
inje
cted
SUPERFLUID REGIME(high probe power)
inje
cted
no scattering
Obergurgl 6 June 2010
Summary
Observation of superfluidity of polaritons
Supersonic regime access to the sound speed
Polariton-polariton interactions landscape engineering
localization effects Josephson
oscillations
polariton circuits
Obergurgl 6 June 2010
Single polariton fluid: set-up
(d)(a)
XY
Near field CCDFar field
CCD
k
kz
k║
Microcavity sample
Excitation laser
Single laser excitation (CW, single mode)
Excitation close to the bottom of the lower polariton branch
resonant excitation of one polariton mode
Transmission experiment
-3 -2 -1 0 1 2 3
1.527
1.530
1.533
En
erg
y (e
V)
kx (m-1)
CW Pump
LPB
UPB
Obergurgl 6 June 2010
Obergurgl 6 June 2010
Other situations
40 µm
FL
OW
40 µm FL
OW
Polariton density
SUPERFLUID AROUND SEVERAL DEFECTS
SHADOW EFFECT AROUND BIG DEFECT
Obergurgl 6 June 2010
Superfluidity checklist
Resonantly pumped polariton condensates
Amo, Lefrère, et al., Nature Physics, (in press).
I Carusotto talk at ICSCE 4 conference (Cambridge, UK, 2008), available athttp://www.tcm.phy.cam.ac.uk/BIG/icsce4/talks/carusotto.pdf
Nature 457, 273 (2009)
Obergurgl 6 June 2010
Polariton fluid dynamics: set up
imag
ing
spec
trom
eter
Streak Camera
CCD
sampleLens F
Fourier plane
Lens Areal space imaging
Lens Bmomentum space
imaging
CW
2ps pulsed
PUMP
IDLER
fA
/2 cavity20 nm GaAs QW
Microcavity sample(grown at LPN)
ħΩRabi = 4.4 meV
kx
ky
X
Y
Energy selection
Obergurgl 6 June 2010
Polariton landscape engineering 22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x t
t Pi x t D i V x t x t F e e
control
yPol
arit
on
ene
rgy
control σ -
Strong field:renormalization of the
polariton energy
polariton-polariton interaction
20 μmFL
OW
20 μm
probe σ +
Defect-free area
probe σ + + control σ -
detection σ +
=
FL
OW
Simulation GP
FL
OW
+
Amo et al., arXiv:1003.0131v1
Obergurgl 6 June 2010
Polariton landscape engineering 22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x t
t Pi x t D i V x t x t F e e
control
yPol
arit
on
ene
rgy
control σ -
Strong field:renormalization of the
polariton energy
polariton-polariton interaction
20 μmFL
OW
20 μm
probe σ +
Defect-free area
probe σ + + control σ -
detection σ +
=
FL
OW
30 µm FL
OW
Real defect
+
Amo et al., arXiv:1003.0131v1
Obergurgl 6 June 2010
Polariton fluid dynamics
Study of the dynamics of polariton wavepacketst = 7 ps t = 28 ps t = 48 ps
Division in two in the presence of a big defectt = 8 ps t = 25 ps t = 45 ps
Amo et al., Nature 457, 291 (2009)
20 μm
20 μm
v = 1.2 m/ps (~1% light speed)
Original streak camera set-up
Obergurgl 6 June 2010Amo et al., Nature 457, 291 (2009)
TOPO
-3 -2 -1 0 1 2 3
1.527
1.530
1.533
En
erg
y (e
V)
kx (m-1)
CW PumpTOPO Signal
TOPO IdlerLPB
UPB
Pump polaritons
Signal polaritons
Coexistence of three fluids
• Steady state CW (pump) 100 m spot
• Triggered OPO (signal) 16 m spotfed by pump
• Idler
Pulse
Ene
rgy
Obergurgl 6 June 2010
Linear dispersion
0
1
E
-1 0 1
1.5265
1.5270
1.5275
Ene
rgy
(eV
)
kx (m-1)
2 2 22 / / /( , ) / 2 ( , ) ( , ) P P P P I I I t I Ix x i k x t x x t t i k x tt P Ii x t D i V x t x t F e e F e e e
CW Pump Pulsed probepol-pol interaction
decaynormal mode coupling
Amo et al., Nature 457, 291 (2009)
Obergurgl 6 June 2010
-60 -30 0 30 60
-60
-30
0
30
60
X (m)-60 -30 0 30 60
-60
-30
0
30
60
X (m)
t= 7ps t= 28ps t= 48psa
0.0
0.5
0.0
4.5
0.0
3.5
0.0
0.5
0.0
1.0
0.0
0.7b
-60 -30 0 30 60
-60
-30
0
30
60
Y (m
)
X (m)
Coherent propagation
Amo et al., Nature 457, 291 (2009)
Obergurgl 6 June 2010
-40 -20 0 20 40-40
-20
0
20
40
X (m)-40 -20 0 20 40
-40
-20
0
20
40
X (m)
t= 50pst= 36pst= 13pst= 8ps
-40 -20 0 20 40-40
-20
0
20
40
Y (m
)
X (m)-40 -20 0 20 40
-40
-20
0
20
40
X (m)
2.5
0.0
a
I
b
Flow through a defect
Amo et al., Nature 457, 291 (2009)
Obergurgl 6 June 2010
Frictionless flowPump polaritons
Signal polaritons
• Pump fluid: scattering waves
• Signal fluid no scattering with the defect Peaked momentum
compatible with superfluid behaviour
real spaceK-space
kX k Y
E=ħpump
E=ħsignal
Amo et al., Nature 457, 291 (2009)
Obergurgl 6 June 2010
Noise studies in the superfluid regime-20 -10 0 10 20
-2 -1 0 1 21.481
1.482
1.483
Emission angle (degrees)
En
erg
y (e
V)
ky (m-1)
Intensity noise polariton density statistics
Noise decreases in the superfluid regime
Superfluid threshold
Obergurgl 6 June 2010
a
-60 -40 -20 0 20 40-40
-20
0
20
40
X (m)b
t = 25 pst = 8 ps t = 45 psII
-60 -40 -20 0 20 40-40
-20
0
20
40
X (m)
Splitting in two
Amo et al., Nature 457, 291 (2009)
Obergurgl 6 June 2010
-20 -10 0 10 20
-2 -1 0 1 21.481
1.482
1.483
Emission angle (degrees)
En
erg
y (e
V)
ky (m-1)
Linear regime
Amo et al., Nature Physics 5, 805 (2009)
30 µm FLOW
Scattering with defects
Low density
30 µm FLOW 40 µm FLOW
Fluid without friction Linear wavefronts
Čerenkov
High density (quantum fluid regime)
Superfluid
vf<cs vf >cs
Polariton superfluidityT = 5 K
Obergurgl 6 June 2010
Linear regime
Amo et al., Nature Physics 5, 805 (2009)
30 µm FLOW
Polariton superfluidity
Scattering with defects
Low density T = 5 K
30 µm FLOW 40 µm FLOW
Fluid without friction Linear wavefronts
Čerenkov
High density (quantum fluid regime)
Superfluid
vf<cs vf >cs
Obergurgl 6 June 2010
-1 0 1
0.0
0.5
40 µm
40 µm FL
OW
High momentum
Polariton density
Elastic scattering
ky (m-1)
E -
Ep
Amo et al., Nature Phys. 5, 805 (2009)
22 /( , ) / 2 ( , ) ( , ) P P P Px x i k x tt Pi x t D i V x t x t F e e
Linear regime Čerenkov
Pumpvf > cs
FL
OW
Gross-Pitaevskiisimulations
Čerenkov regime (supersonic)
Realspace
-1 0 1
0.0
0.5
Linear wavefronts
ky (m-1)
E -
Ep
0
1
supersonic