Jacqueline Bloch
Centre de Nanosciences et de NanotechnologiesC2N, CNRS/Universités Paris Sud/ Paris Saclay
Palaiseau, France
Quantum fluids of light
[email protected]://www.polaritonquantumfluid.fr
Jacqueline Bloch
Centre de Nanosciences et de NanotechnologiesC2N, CNRS/Universités Paris Sud/ Paris Saclay
Marcoussis, France
[email protected]://www.polaritonquantumfluid.fr
General motivations Why cavity polaritons?
How do we perform experiments?
Band structure?
Why non-linearities?Where do we go??
Quantum fluids of light?
Fractional Quantum Hall effect
Graphene Topological insulators
Superfluidity
Quantum fluids of light as an analogous system
ℏ
Same Hamiltonian => Same physical properties
System « easier » to probe, manipulate
Create new geometries, new properties => Applications
Realize experiments impossible to predict because of complexity of numerical simulations (many body physics): quantum simulations
Why use synthetic quantum material?
Nature 14 November 2012
Original idea: [R. Feynman., Int. J. Theor. Phys. 21, 467 (1982)]
Quantum fluids of light as an analogous system
Photons have no mass !
Photons have no charge !
Photons do not interact (or so weakly) !
Photons are bosons (not fermions like electrons !)
Photons have no mass ! Effective mass in a cavity
Photons have no charge ! ! Artificial gauge field(see for neutral atoms J. Dalibard et al., RMP 83, 1523 2011)
Photons do not interact (or so weakly) ! Yes when coupled to electronic excitations
Photons are bosons (not fermions like electrons !) Nobody is perfect!
Quantum fluids of light as an analogous system
UJ
Bose-Hubbard
Driven-dissipative photonic Bose-Hubbard model
Ciuti & Carusotto, Rev. Mod. Phys. 85, 299 (2013)
M.J. Hartman, Journal of Optics (2016)
C.Noh and DG Angelakis, Report on progress in Physics (2016)
A. Biella et al., Phys. Rev. A 96, 023839 (2017)
F. Vincentini et al., Phys. Rev. A 97, 013853 (2018)
Out of equilibrium quantum physics
Emulation with light
Topologicaledge states Si
Chiral edge states
Zheng Wang et al.,Nature 461 772 (2009)
M. Hafezi, Nat. Phot. 7 1001 (2013)
Synthetic Landau levels
N. Shine et al.Nature 354, 671 (2016)
B.Bahari et al., Science10.1126/science.aao4551(2017)
M. A. Bandres et al. Science 10.1126/science.aar4005 (2018)
Non reciprocal lasing
Randon quantum walk
A. Crespi, Nature Photonics 7, 322 (2013)
P. Vignolo et al., New J. Phys. 16 (2014) 043013
Quasicrystal
Semiconductor microcavities : cavity polaritons
2 µµµµm
T = 10 KNature 443, 409 (2006)
Kasprzak et al. Nature, 443, 409 (2006)kx
ky
Polariton density
T = 5 K CdTe
Benoid Deveaud
Le Si Dang
Polariton superfluidity
A. Amo et al. Nature Physics 5, 805 (2009)
C. Ciuti & I. Carusotto, Rev. Mod. Phys. 85, 299 (2013)
C. Ciuti and I. Carusotto PRL 242, 2224 (2005)
Cristiano CiutiIacopo Carusotto Alberto Amo Alberto Bramati Elisabeth Giacobino
4 µµµµm
Pillar diameter = 3 µm
Interpillar distance a = 2.4 µm
Emulating Dirac Physics
y
k/(2
ππ/3a
)
-20
2-4 -2 0 2 4
kx/(2π/3a)
ky/(
2π
/3√3a)
En
erg
y(m
eV
–1
57
7)
Dirac cones
Jacqmin et al., PRL 112, 116402 (2014)
See also Yamamot (Stanford), Krizhanovskii (Sheffield)
Propagation of light in a non-linear medium
C. Michel et al. Nature Com 2018
Quentin Glorieux
Propagation of light in a non-linear medium
D. Faccio Edimburgh Q. Glorieux, A. Bramati (LKB)PRL 120, 055301 (2018)
M. Bellec, C. Michel (INPHYNI)
Outline
Lecture 1 : Introduction to cavity polaritons
Lecture 2: Polariton non-linearities : Superfluidity, BEC December 10th
Lecture 3: Polariton lattices December 12th
Lecture 4: Quantum fluids of light in propagating geometry December 17th
Quentin Glorieux, LKB
Lecture 1: Introduction to cavity polaritons
Microcavity polaritons
Excitonic polaritons : Mixed light-matter particles
Photons confined in an optical cavity Excitons confined in a quantum well
• Very light (m=0 in vacuum)
• Very fast
• No interactions
• Very heavy
• Very slow
• Interactions
Photon confinement
0.75 0.80 0.85 0.900.0
0.2
0.4
0.6
0.8
1.0
λ (µm)
Refl
ect
ivit
y 715
25λλλλΒΒΒΒ
λλλλΒΒΒΒ/4/4/4/4
λλλλΒΒΒΒ
Distributed Bragg reflector Very high reflectivities
n1n2n1n2
n1
Photon confinement
0.750 0.775 0.800 0.825 0.8500.0
0.2
0.4
0.6
0.8
1.0
Refle
ctivity
λ (µ m)
Optical mode
0.75 0.80 0.85 0.900.0
0.2
0.4
0.6
0.8
1.0
λ (µm)
Refl
ect
ivit
y 715
25
λλλλc~ λλλλB
λλλλc
λλλλΒΒΒΒ
λλλλΒΒΒΒ/4/4/4/4
λλλλΒΒΒΒ
Distributed Bragg reflector Very high reflectivities
Fabry-Perot resonator (microcavity)
normal incidence
n1n2n1n2
n1
-2 0 2
-20 -10 0 10 20
Top DBR
Bottom DBR
θGaAs/AlGaAsbased structures
Optical cavity
Bragg mirrorGaAs/AlAs
Cavity
Bragg mirrorGaAs/AlAs
TEM, G. Patriarche, LPN
Photon
Angle θ (º)
kin-plane (μm-1)
Em
issio
n e
nerg
y (
eV
)
Microcavity polaritons
5 K
Top DBR
Bottom DBR
Quantum Wells
θGaAs/AlGaAs based structures
Exciton
QW
e-
h+
AlGaAsGaAsAlGaAs
Quantum well exciton
5 K
Microcavity polaritons
Excitonic resonance
Top DBR
Bottom DBR
Quantum Wells
θGaAs/AlGaAs based structures
-2 0 2
-20 -10 0 10 20
Exciton
Photon
Angle θ (º)
kin-plane (μm-1)
Em
issio
n e
nerg
y (
eV
)
Exciton
QW
e-
h+
AlGaAsGaAsAlGaAs
Quantum well exciton
Microcavity polaritons
5 K
0
ℏ
2
with
Typically
10
Claude WeisbuchPRL 69, 3314 (1992)
Upper polariton
Lower polariton
~ 5meV
-2 0 2
-20 -10 0 10 20
Top DBR
Bottom DBR
Quantum Wells
θGaAs/AlGaAs based structures
Exciton
Photon
Angle θ (º)
kin-plane (μm-1)
Em
issio
n e
nerg
y (
eV
)
QW
e-
h+
AlGaAsGaAsAlGaAs
polaritonCavity
Microcavity polaritons : mixed exciton-photon states
Microcavity polaritons
5 K
with
-10 -5 0 5 10E
ne
rgie
k// (µm
-1)
Photon
ExcitonRabi splitting 2g
( ) ( ) ( )( ) 22
////// 4gkEkEk XC +−=∆
=
)(
)(
//
//
// kEg
gkEH
C
X
k
Microcavity polaritons
| polariton > = αααα |photon> + ββββ |exciton>
Microcavity polaritons
αααα2222
αααα2222
αααα2222
ββββ2222
ββββ2222
ββββ2222
Exciton photon detuning:+ , 0 - . 0/
+ 0 0
+ 0
+ 1 0
s-shaped dispersion : inflexion point
z θθθθ
θθθθ k//
0 1 2 3
E
k ( 104 cm
-1 )
k// (104 cm-1)
émission(θθθθ)
k// = ω/c sin(θ)
Selective excitation and
probe of polariton states
Probing polariton states: Angle resolved experiments
Resonant excitation
How to generate microcavity polaritons?
Control of :- Energy- k//
- Phase
Non resonant excitation
- Population of many low energy modes
- Creation of an excitonic reservoir
- Possibility to enter a stimulated regime:lasing, Bose Einstein Condensation
Phys. Rev. Lett. 73, 2043 (1994)
Romuald Houdré
EPFL
Probing polariton states: Angle resolved experiments
Fourrier plane
SampleSpectrometer
slit
Energy
Typical experimental scheme
(d)Far fieldInterference witha reference beam
Coherence mapg(1)
Emission statisticsg(2)
0
1
Density
Phase dislocations- vortices- solitons
-0.5 0.0 0.5
kx (µm-1)k
y(µ
m-1
)
kx (µm-1)
Energ
y
Far field imaging: k space Real space imaging
Cavity polaritons : an exciton-photon mixed state
| polariton > = αααα |photon> + ββββ |exciton>
ββββ2 exciton partαααα2 photon part
Properties
Photonic component low mass (10-5 me)
| polariton > = αααα |photon> + ββββ |exciton>
Microcavity polaritons
αααα2222
αααα2222
αααα2222
ββββ2222
ββββ2222
ββββ22221
234
5
236
7
8At k = 0:
s-shaped dispersion : inflexion point
+ 0 0
+ 0
+ 1 0
Exciton photon detuning:+ , 0 - . 0/
Beyond inflexion point: negative effective mass
Effective mass: 1
234
1
ℏ
Resonant pulsed
excitation
Probing polariton states: Real space propagation
Group velocity
Resonant
excitation
+ 0 0
+ 0
+ 1 0
9: 1
ℏ
9:.;/ 59236 79 X
Probing polariton states: Real space propagation
Cavity polaritons : an exciton-photon mixed state
| polariton > = αααα |photon> + ββββ |exciton>
ββββ2 exciton partαααα2 photon part
Properties
Photonic component low mass (10-5 me)
Short lifetime (1-100 ps) dissipative system
Polariton lifetime
Emission
Scattering
Resonantexcitation
1
<234
5
<236
7
<8
Polariton have a finite (short) lifetime : 1-100 ps
Cavity polaritons : an exciton-photon mixed state
| polariton > = αααα |photon> + ββββ |exciton>
ββββ2 exciton partαααα2 photon part
Properties
Photonic component low mass (10-5 me)
Short lifetime (1-100 ps) dissipative system
Pseudo spin
Polariton spin
Photon have an angular momentum : +- 1
Only J=1 excitons are coupled to light
Polaritons have two spin projections:
jz = +1jz = -1
σ +σ −
pseudospin12
One-to-one relationship between pseudospin state and polarisation degree
Exciton : Jz = +- 1
Jz =+- 2
e h e h
e h e h
Spin : electron : +- ½heavy hole : +- 3/2
Cavity modes linearly polarized: TE-TM splitting
-2 0 2
1.482
1.484
1.486
Energ
y (
eV
)
kII (µm
-1)
TE pola.
TM pola.
Kavokin et al. PRL 95, 136601 (2005)
Effective magnetic field
Polariton spin: Intrinsic magnetic field
boundary conditions for the electromagnetic field at the interface of the different dielectric layers
Optical spin Hall effect
xk
InitialPseudospin
Linear polarisation along x
ττθ
SSS
t
Srr
rrr
−+Ω∧=∂
∂
1
0)(
yk
σ +
σ −σ +
σ −
θ
Kavokin et al. PRL 95, 136601 (2005)Leyder et al. Nature Phys. 3, 628 (2007).
Optical spin Hall effect
kx
-0.5 +0.5
ky
Kavokin et al. PRL 95, 136601 (2005)
Leyder et al. Nature Phys. 3, 628 (2007).
cρ
Real Space
Spin currents
cρ
τpol= 10ps
Reciprocal Space
Cavity polaritons : an exciton-photon mixed state
| polariton > = αααα |photon> + ββββ |exciton>
ββββ2 exciton partαααα2 photon part
Properties
Photonic component low mass (10-5 me)
Short lifetime (1-100 ps) dissipative system
Pseudo spin
Sensitivity to magnetic field
Momentum (k)E
nerg
y(e
V)
∆>?@A
~ 1.2 DE
B = 7T
Energy (eV)
PL inte
nsity
B = 7T
∆>?@A
~ 1.7 DE
CavityQuantum well
Magneto-luminescence
Cavity polaritons : an exciton-photon mixed state
| polariton > = αααα |photon> + ββββ |exciton>
ββββ2 exciton partαααα2 photon part
Properties
Photonic component low mass (10-5 me)
Short lifetime (1-100 ps) dissipative system
Pseudo spin
Sensitivity to magnetic field
Polariton Interaction Highly non linear system (Kerr like)
Polariton lattices
Surface acoustic waves
Cerda-Méndez et al., PRL 105, 116402 (2010)de Lima et al., PRL 97, 045501 (2006)
Cerda-Méndez et al. PRB 86, 100301(R) (2012)
Berlin
Polariton lattices
Gold depositionon top mirror
Lai et al., Nature 450, 529 (2007) Kim et al., Nature Phys 7, 681 (2011)
d-wave condensation kx
ky
Low power
2 µµµµm
Stanford
Deveaud’s group at EPFL
El Daïf et al., APL 88, 061105 (2006)
Idrissi Kaitouni et al., PRB 74, 155311 (2006)
Cerna et al., PRB 80, 121309 (2009)
During-growth photonic trap
Würzburg
Coupled mesas
Winkler et al., New J. Phys. 17, 23001 (2015)
Hybrid cavities
Fiber-closed cavity
Imamoglu, Reichel,
Besga et al., Light: S&A 3, e135 (2014)S. Dufferwiel et al. Appl. Phys. Lett. 104, 192107 (2014)
See also T. Fink et al., Nature Physics 14, 365 (2018)G. Muñoz-Matutano et al, Nature Materials 18, 213 (2019) A. Delteil et al., Nature Materials 18, 219 (2019)
Polariton in 1D cavities
1D polariton sub-bands
Polariton lateral
confinement
kx= nπ/w
n=1,2,3,…
Quantization of kx:
A G H ℏ
2
IJ
K G
20 µm
Electron beam lithography+ ion dry etching
ky (µm-1)
1D periodic potential: free particle approach
D. Tanese et al., Nature Com. 4, 1749 (2013)
Experiment Theory
Energ
y (
meV
)
E ℏ
2
IJ
K./
Aubry André (Harper) quasi-periodic potential
On-site potential incommensurate with the lattice period
Lahini et al., Phys. Rev. Lett. 103, 013901 (2009)
Roati et al., Nature 453, 895 (2008)
V. Goblot et al., Arxiv1911.07809
a = 2 µm
Polariton lattices:Tight binding approach
Review: C. Schneider et al., Rep. Prog. Phys. 80, 16503 (2017)
En
erg
y (
me
V)
x (µm)
2 µm
x (µm)
S
P
0 10-10 0 1-1
0
2
1
k (µm-1)
Band structure
x (µm)
En
erg
y (
me
V)
P band
S band
Polariton lattices:Tight binding approach
CB
ACB
A
Pillar diameter = 3 µm
Interpillar distance= 2,4 µm
Engineering of a 1D flatband : “comb” lattice
-1 0 1
-2t
-t
0
t
2t
k / (π/a)
En
ergy
J
J ∗
flatband
-??
+
F. Baboux et al. PRL116, 066402 (2016)
Emission of flat band in real space
Thomas Ebbesen2019 CNRS Gold medal
Summary
Hybrid exciton-photon quasi-particles
Tunable properties : effective mass, group velocity
Lateral confinement : engineering of band structure
Spin dependent interactions
Optical access to all physical properties
2013
Reviews
20142017
C. Ciuti & I. Carusotto, Quantum fluids of light: Rev. Mod. Phys. 85, 299 (2013)
A. Amo and J. Bloch, “Exciton-polaritons in lattices: A non-linear photonicsimulator”, Comptes Rendus de l’Académie des Sciences 8, 805 (2016)