Quantum fluid phenomena with Microcavity Polaritons
Alberto Bramati
Flux
Obstacle
20µµµµm
Flux
Obstacle
20µµµµm
⇒ An ideal system to study out
of equilibrium quantum fluids
Quantum fluid phenomena in polariton gases
Superfluidity, hydrodynamic dark solitons and vortices (Nature Physics 2009, Science 2011, Nature Photonics 2011)
Quantum Optics Team: topics
Logic gates, All Optical Spin Switches (Nature Physics 2007, PRL
2007, Nature Photonics 2010, PRL 2011)
Spin dependent non linearities in microcavities
⇒ Towards integrated optoelectronic devices
Quantum Effects in semiconductor nano and microcavities in strong coupling regime
⇒ Towards a compact, integrablenano- source of entangled beams
Microcavities, quantum wires, micropillars (PRL
2007, APL 2010,PRB 2011)
� Introduction
� Superfluidity and Čerenkov regime
� Hydrodynamic Vortices and Dark Solitons
� Towards Vortex Lattices
� Perspectives and conclusion
OutlineOutline
Quantum fluid phenomena
UPB
LPB
Exciton
PhotonTop DBR
Bottom DBR
Quantum Well
Linear combination ofexcitons and photons
-3 -2 -1 0 1 2 3
1.526
1.528
1.530
1.532
En
erg
y (
eV
)
kin plane
(µm-1)
P+ = -C a + X b
P- = X a + C b
MicrocavityMicrocavity PolaritonsPolaritons
Very small effective mass m ~ 10-5 me1
2 22
T
Bmk T
πλ
=
h
MicrocavityMicrocavity PolaritonsPolaritons
Polaritons are weakly interacting composite bosons
P+ = -C a + X b
P- = X a + C b
Large coherence length λT ~ 1-2 µm at 5K
and mean distance between polaritons d ~ 0,1-0,2 µm
This enables the building of many-body quantum coherent effects : condensation, superfluidity
5 K
Kasprzak et al. Nature, 443, 409 (2006)
Excitation CW laser 1.755 eV
• 2D system
• Out of equilibrium system :
- Creation and recombination (polariton life time ~5 ps)
Bose Einstein condensation of polaritonsBose Einstein condensation of polaritons
Boson quantum fluids: polaritons
50 µm
t =7ps t =28ps t =48ps
Coherent propagation
Energ
y(e
V)
Amo et al., Nature 457, 295 (2009)
Wertz et al., Nature Phys. 6, 860 (2010)
Long-range order phases
Real space Momentum space
Lai et al., Nature 450, 529 (2007)
Vortex and half vortex
Lagoudakis et al., Nature Phys. 4, 706 (2008),
and Science 326, 974 (2009)
Nardin et al., arXiv:1001.0846v3
Krizhanovskii et al., PRL 104, 126402 (2010)
Roumpos et al., Nature Phys. 7, 129 (2010)
1D BEC arrays
Cerda-Méndez et al., PRL 105, 116402 (2010)
Sanvitto et al., Nature Phys. 6, 527 (2010)
Persistent currents
Superfluidity
Hydrodynamics:
vortex
Hydrodynamics:
solitons
This talk
This talk
Wave equation for polaritonsWave equation for polaritons
with
Evolution of exciton and cavity fields, in the presence Evolution of exciton and cavity fields, in the presence Evolution of exciton and cavity fields, in the presence Evolution of exciton and cavity fields, in the presence
of excitonof excitonof excitonof exciton----exciton interaction exciton interaction exciton interaction exciton interaction
pol-polinteraction
decaynormal mode coupling
CW Pump
defects
Gross-Pitaevskii equation in the presence of defects
The Landau Criterion for superfluidity
E
k
cs
Quantum fluid effects: Quantum fluid effects: superfluiditysuperfluidity
The Landau Criterion for superfluidity
E
k
cs
E
k
cs+vf
FLOW
SUPERFLUID
Galilean
boost
vf<cs
Quantum fluid effects: Quantum fluid effects: superfluiditysuperfluidity
vf - cs
The Landau Criterion for superfluidity
E
k
cs
E
k
cs+vf
vf - cs
FLOW
E
k
cs+vf
vf - cs
FLOW
SUPERFLUID
CERENKOV REGIME
Galilean
boost
vf<cs
E
k
cs
Galilean
boost
vf >cs
critical flow velocity for
the onset of excitations: cs
Quantum fluid effects: Quantum fluid effects: superfluiditysuperfluidity
-1 0 1
0.0
0.5
ky (µm-1)
E -
Ep
(meV
)
(c)
P
Linear regime, interactions between polaritons are negligible
elastic scattering is possible
We probe the behaviour of the fluid through its interaction with defects
Near fieldFar field
Propagation of a polariton fluidPropagation of a polariton fluid
I. Carusotto and C. Ciuti, PRL (2004); Phys. Stat. Sol. (b). 242, 2224 (2005)
Nonlinear regimestrong interactions betweenpolaritons,dispersion curve modified
-1 0 1
0.0
0.5
ky (µm-1)
(d)
P
E -
Ep
(meV
)
If vf < cs and density large enough
SuperfluidSuperfluid regimeregime
2
sc g mψ= h
a sound velocity appears
Landau criterion for superfluidity is fulfilled: no states available any more for scattering
I. Carusotto and C. Ciuti, PRL (2004);Phys. stat. sol. (b). 242, 2224 (2005)
Observation of a linear spectrum of excitation for polaritons:
• Utsunomiya et al., Nature Phys. 4, 700 (2008)• Kohnle et al., PRL, 106, 255302 (2011)
Near fieldFar field
Landau criterium: ren
LP signalE E> signalk k≠
No elastic scattering
SuperfluidSuperfluid regimeregime
I. Carusotto and C. Ciuti, PRL (2004);phys. stat. sol. (b). 242, 2224 (2005)
(d)(a)
X
Y
Near field CCD
Far fieldCCD
θθθθk
kz
k║
Microcavitysample
Excitationlaser
AB
(b)
-20 -10 0 10 20
-2 -1 0 1 21.481
1.482
1.483
Emission angle (degrees)
En
erg
y (
eV
)
ky (µm
-1)
Control parameters
�Polariton density(pump intensity)
�Fluid velocity(excitation angle)
�Oscillation frequency(laser frequency)
Experimental schemeExperimental scheme
Point [A]low momentumvf < cs
Polariton flow around a defect :Polariton flow around a defect :
near field image = real spacenear field image = real space
experiment
theory
Experiment
Theory
0.0 0.5 1.0 1.5 2.0Excitation density (arb. units)
Po
lari
ton
-flu
id d
en
sity
(arb
. u
nits)
(a)
I II
III
vp = 5.2 105 m/sSuperfluidity appears for a polariton density of ~ 109/cm2
defect : 4 µm diameter
Polariton density
Polariton flow around a defect :Polariton flow around a defect :
far field image = momentum spacefar field image = momentum space
experiment
theory
-1 0 1
0.0
0.5
P
ky (µm-1)
Collapse of the ring
Polariton density
Point [A]low momentumvf < cs
Landau criterion� c
Amo et al., Nat. Phys.,5, 805 (2009)
Transition to the Transition to the superfluidsuperfluid regimeregime
Amo et al., Nat. Phys.,5, 805 (2009)
vf > csound supersonic regime
AB
(b)
-20 -10 0 10 20
-2 -1 0 1 21.481
1.482
1.483
Emission angle (degrees)
En
erg
y (
eV
)
ky (µm
-1)
ČČerenkoverenkov regimeregime
ky (µm-1)-1 0 1
0.0
0.5
P
E -
Ep
available states
Point [B]high momentum
Landau condition
E. Cornell’s talk at the KITP Conference on QuantumGases
http://online.itp.ucsb.edu/online/gases_c04/cornell/.
vf =13cs vf =24cs
Čerenkov shock waves of a BEC against an obstacle at supersonic velocities
FLOW
Observation of Čerenkov waves indicatesthe existence of a well defined soundvelocity in the system
ČČerenkoverenkov effect in an atomic BECeffect in an atomic BEC
40 µm
b-I b-II b-III
FL
OW
0
1
40 µm
c-I c-II c-III
ČČerenkoverenkov waves : near field imagewaves : near field image
Characteristic linear density wavefronts of the Čerenkov waves
experiment
theory
Experiment
Theory
0.0 0.5 1.0 1.5 2.0 2.5
0
5
10
15
20
Po
lari
ton
density (
µm
-2)
(fro
m e
xp
erim
en
t)
Excitation density (arb. units)
III
III
Polariton density
Transition to the Transition to the ČČerenkoverenkov regimeregime
Amo et al., Nat. Phys.,5, 805 (2009)
The case of spatially extended defects; the size of the defect is largerthan the healing length
SuperfluiditySuperfluidity breakdown: vortices and breakdown: vortices and solitonssolitons
formation?formation?
The currents formed in the fluid passing around a large obstacle can give rise to turbulence in its wake
,c sv c∞ <fv v∞=
2f
v v∞=
Quantized vortices
Dark Solitons
Acceleration of the fluid near the defect: the Landau criterion is locally violated
Polariton densityS. Pigeon et al. PRB (2010)
DEFECT
Ejection ofvortices andanti-vortices
Dark solitons
The case of spatially extended defects; the size of the defect is largerthan the healing length
Superfluidity
SuperfluiditySuperfluidity breakdown: vortices and breakdown: vortices and solitonssolitons
formation?formation?
Polariton densityS. Pigeon et al. PRB (2010)
DEFECT
Ejection ofvortices andanti-vortices
Dark solitons
The case of spatially extended defects; the size of the defect is largerthan the healing length
Superfluidity
SuperfluiditySuperfluidity breakdown: vortices and breakdown: vortices and solitonssolitons
formation?formation?
phase
0
2π
Experimental setExperimental set--upup
Microcavity
Intermediatemask
Focalisationlens
Lens
Excitationlaser
Spot onsample
Flo
w
y
La
se
rin
ten
sity Flow
Key points
�CW laser (precise control of the fluid quantum state)
�Mask (free evolution for the superfluid phase)
� Possibility to generate topological excitations
Excitationgeometry
Big Big defectdefect (15(15µµm) >> m) >>
healinghealing lengthlength
1
-1
0
10 µµµµm
d e f
g h i
0
1
10 µµµµm
1
100
10 µµµµm
a b cSuperfluidity Vortex ejection Solitons
Flo
w
10Real space
Interferogram
First ordercoherence
25.0=sf cv 4.0=sf cv 6.0=sf cv
Superfluidity Turbulence Solitons
Constant phase Phase dislocations Phase jumpsPhase jumps
Polariton densityAmo et al., Science, 332, 1167 (2011)
Vortices and Vortices and SolitonsSolitons
First order coherence
∆y = 14 µm
∆y = 26 µm
Pola
rito
n d
ensity (
arb
. units)
-20 0 20
∆y = 36 µm
x (µm)
ns
40
20
0
-20 0 20
40
20
0
-20 0 20
Flo
wn
∆y
(µm
)
∆x (µm)
vf = 1.7 µm/psk= 0.73 µm-1
0 10 20
P
ola
rito
n d
ensity (
arb
. un
its)
∆x (µm)
∆φ
Relative
phase
π
0
Hydrodynamic Dark Hydrodynamic Dark SolitonsSolitons
1
2
12
sncos
n
φ = −
SolitonSoliton doublet and quadrupletdoublet and quadruplet
a b
20 µm Flo
w
0
1
a b
20 µm Flo
w
0
1
Big defect (17µm) >> healing length
Low momentum; k= 0.2 µm-1 High momentum; k= 1.1 µm-1
Amo et al., Science, 332, 1167 (2011)
Hydrodynamic Dark Hydrodynamic Dark SolitonsSolitons: theory: theory
Not yet observed in atomic BEC; the dissipation in polariton fluids helps in stabilizing dark solitons (Kamchatnov et al. arXiv:1111.4170)
Light engineering of the Light engineering of the polaritonpolariton landscape:landscape:
using using polaritonpolariton--polaritonpolariton interactionsinteractions
FL
OW
20 µm
probe σ + Defect-free area
Sample from R. Houdré
Engineered landscapeEngineered landscape
control
yPola
rito
n
energ
yF
LO
W
20 µm
probe σ + control σ -
strong field:renormalization of the
polariton energy
0.1g g↑↓ ↑↑
≈
Engineered landscapeEngineered landscape
control
yPola
rito
n
energ
y
probe
scattered
20 µm
probe σ + control σ -
strong field:renormalization of the
polariton energy
probe σ + + control σ -
detection σ +
+ =F
LO
W
FL
OW
0.1g g↑↓ ↑↑
≈
Amo et al., PRB Rapid Comm. (2010)
Engineered landscapeEngineered landscape
20 µm
probe σ + control σ -
strong field:renormalization of the
polariton energy
probe σ + + control σ -
detection σ +
+ =
30 µm
FL
OW
Real defect
FL
OW
FL
OW
control
yPola
rito
n
energ
y
probe
scattered0.1g g
↑↓ ↑↑≈
Amo et al., PRB Rapid Comm. (2010)
Engineered landscapeEngineered landscape
scattered30 µm inje
cte
d
inje
cte
d
inje
cte
d
sc
att
ere
d
No control Linear control Diagonal control
Probe only Probe + Probe +
Engineered landscapeEngineered landscape
pulsed
y
xE
ne
rgy
Artificial
Potential
(Gaussian shape)
Polariton Fluid
All-optical control of the quantum flow of a polariton condensate
D. Sanvitto, et al.,Nature Photonics 5, 610 (2011)
Optical control of vortex formationOptical control of vortex formation
Triangular Trapping Mask behind the
defect:
the vortices created in the wake of the
defect are trapped inside the trap
20 µµµµm
S. Pigeon, et al., Phys. Rev. B 83, 144513 (2011)
Flow
No mask frame readjusted
20 ∪∪∪∪m
100
1
10
(a) (b) (c) (d) (e)
0.4
-0.4
0
(g) (h) (i) (j) (k)
(f)
(l)
Low power
Tailoring the potential landscape to trap vorticesTailoring the potential landscape to trap vortices
D. Sanvitto, et al.,Nature Photonics 5, 610 (2011)
Towards spontaneous formation of vortex latticesTowards spontaneous formation of vortex latticesSmall triangular trap
Self-organization of vortices and anti-vortices in hexagonal lattices
Experiment Theory
Polariton density
Phase
Towards spontaneous formation of vortex latticesTowards spontaneous formation of vortex lattices
Increasing the size of the trap, a larger number of hexagonal unit cells is formed
�Polariton Quantum Fluids
• Superfluidity
• Čerenkov regime
• Hydrodynamic vortices and dark solitons
�Perspectives
• Engineering of polariton landscape: Dynamical
Potentials, Optical traps for polaritons
• Study and control of Quantum turbulence?
• Lattices of vortices?
• Spinor polariton condensates (Hivet et al. arXiv:1204.3564)
Conclusion and perspectives
University of TrentoUniversity of Trento
I. I. CarusottoCarusotto
Lab. MPQ, ParisLab. MPQ, Paris
C. C. CiutiCiuti
EPFL, LausanneEPFL, Lausanne
R. R. HoudrHoudréé
NNL Lab., LecceNNL Lab., LecceD. D. SanvittoSanvitto
Lab. LPN, Lab. LPN, MarcoussisMarcoussis
J. Bloch, A. J. Bloch, A. AmoAmo
Lab. LASMEA, Clermont Lab. LASMEA, Clermont FerrandFerrand
G. G. MalpuechMalpuech
CollaborationsCollaborations
EXPERIMENTS THEORY
PhD Students:G. Leménager
R. HivetV.G. SalaT. Boulier
The team
Post-Doc E.Cancellieri
Permanent Staff: Elisabeth Giacobino, Alberto Bramati
Former members:M. RomanelliC. LeyderJ. Lefrère
C. AdradosF. Pisanello
A. Amo