Jacqueline Bloch

Centre de Nanosciences et de NanotechnologiesC2N, CNRS/Universités Paris Sud/ Paris Saclay

Palaiseau, France

Quantum fluids of light

Jacqueline.bloch@c2n.upsaclay.frhttp://www.polaritonquantumfluid.fr

Jacqueline Bloch

Centre de Nanosciences et de NanotechnologiesC2N, CNRS/Universités Paris Sud/ Paris Saclay

Marcoussis, France

Jacqueline.bloch@c2n.upsaclay.frhttp://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)