Jacqueline Bloch...Jacqueline Bloch Centre de Nanosciences et de Nanotechnologies C2N,...
Transcript of Jacqueline Bloch...Jacqueline Bloch Centre de Nanosciences et de Nanotechnologies C2N,...
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)