quantum fluids of light in semiconductor lattices · photonic component confinement in...
TRANSCRIPT
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Jacqueline Bloch
Center for Nanoscience and NanotechnologyC2N, CNRS - Université Paris Saclay
Palaiseau, France
Quantum fluids of light in semiconductor lattices
[email protected]://www.polaritonquantumfluid.fr
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Inspiration: Emerging physics in the solid state
Fractional Quantum Hall effect
Graphene Topological insulators
Superfluidity
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Emulation with lightTopologicaledge 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)
2 photon Laughling state Arxiv 1907.05872
B.Bahari et al., Science10.1126/science.aao4551(2017)
M. A. Bandres et al. Science 10.1126/science.aar4005 (2018)
S. Klembt et al.,Nature 562, 552 (2018)
Non reciprocal lasing
Randon quantum walk
A. Crespi, Nature Photonics 7, 322 (2013)
Quasi crystal
Kraus et al., PRL 109, 106402 (2012)
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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
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Use nanotechnology to engineer photonic lattices
2 µm
Image from Würzburg
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Outline
Introduction to polariton lattices
Emergence of criticality in quasi-crystals
Discrete gap solitons in a flat band
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Upper polariton
Lower polariton
Exciton
Photon
Angle θ (º)
kin-plane (μm-1)
Em
issi
onen
ergy
(eV
)
Properties
Photonic component confinement in microstructuresreal space, k-space imaging
Excitonic component
Microcavity polaritons : mixed exciton-photon states
Microcavity polaritons
~ 15meV
-2 0 2
-20 -10 0 10 20
k kpol X exc C phot= +
Mirror
Cavity Quantum wells
Mirror
• Interactions - χ(3) (dominated by exchange)
• Gain (lasing)
• Sensitivity to magnetic field
Bragg mirrorGaAs/AlAs
T = 10K
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k// = ω/c sin(θ)
Imaging of k-space
Imaging of real space
Interferometry Coherenceg(1)
g(2)
0
1
Density
10 µm
- vortices- solitons
θ
Probing polariton states
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Kasprzak et al. Nature, 443, 409 (2006)
See also H. Deng et al. Science (2002), R. Balili et al., Science (2007)
kx
ky
Benoid Deveaud
Le Si Dang
Increase excitation power
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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
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Realizing the classical XY Hamiltonian inpolariton simulators, Natalia G. Berloff et al., Nature Materials 16, 1120 (2017)
Emulation of many body systems with lattices of polaritons
Phase locking of polariton condensates
Spin order and phase transitions in chainsof polariton condensates,
H. Ohadi, et al., Phys. Rev. Lett.. 119, 067401 (2017)
Polarization instability in coupledpolariton condensates
Southampton Cambridge
Cambridge
Pavlos Lagoudakis Natalia Berloff
Jeremy Baumberg
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Ene
rgy
(meV
)
x (µm)
2 µm
x (µm)
S
P
0 10-10 0 1-1
0
2
1
k (µm-1)
Band structure
x (µm)
Ene
rgy
(meV
)
P band
S band
Polariton lattices:Tight binding approach
Review: C. Schneider et al., Rep. Prog. Phys. 80, 16503 (2017)
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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
�
� ∗
flatband-??
+
F. Baboux et al. PRL116, 066402 (2016)See also Stanford, Sheffield, Würzburg
Emission of flat band in real space
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4 µm
Pillar diameter = 3 µm Interpillar distance a = 2.4 µm
Polariton honeycomb lattice
y
-20
2-4 -2 0 2 4
kx/(2π/3a)
ky/(
2π
/3√3
a)
Ene
rgy
(meV
–15
77)
Jacqmin et al., PRL 112, 116402 (2014)
Dirac cones
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Polaritonics at C2N
Quasi-periodic 1D latticeD. Tanese et al.,
PRL 112, 146404 (2014)
F. Baboux et al.,PRB 95, 161114(R) (2017)
V. Goblot et al., Arxiv1911.07809
Flat band physicsDirac physics
Spin orbit coupling
Sala et al., Phys. Rev. X 5, 011034 (2015)
T. Jacqmin et al., PRL 112, 116402 (2014)M. Milicevic et al, 2D Mater. 2, 034012 (2016)M. Milicevic et al. PRL. 118, 107403 ( 2017)M. Milicevic et al., Phys. Rev. X 9, 31010 (2019)
O. Jamadi et al., arXiv:2001.10395P. St-Jean et al., arXiv:2002.09528
Hawking physics H.S. Nguyen et al., PRL. 114, 036402 (2015)
F. Baboux et al. PRL116, 066402 (2016)
V. Goblot et al. Phys. Rev. Lett. 123, 113901
(2019)
SSH chain and topological lasing
P. Saint Jean et al., Nature Photonics 11, 651 (2017)
N Carlon Zambon et al., Nature Photonics 13, 283 (2019)
N. Carlon Zambon et al.,Opt. Lett. 44, 4531 (2019)
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Outline
Introduction to polariton lattices
Emergence of criticality in quasi-crystals
Discrete gap solitons in a flat band
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• Quasicrystal: aperiodic system with long-range order
• Penrose tilings • Diffraction peaks of AlMn alloys:
Shechtman et al., PRL, 1984
(2011)Levine, Steinhardt, PRL, 1984
Quasicrystals
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Cold atoms
Phonons
Coupled waveguides
Multilayer structures Microwave resonators
Gellermann et al., PRL 72, 633 (1994)Hattori et al., PRB 50, 4220 (1994)
Vignolo et al., PRB 93, 075141 (2016)
Levi et al., Science 332, 1541 (2011)Lahini et al., PRL 103, 013901 (2012)Kraus et al., PRL 109, 106402 (2012)
Roati et al., Nature 453, 895 (2008)
Steurer & Sutter-Widmer, J. of Phys. D: Applied Physics 40, R229 (2007)
Dareau et al., PRL 119, 215304 (2017)
Digital Mirror Device array
Synthetic Quasicrystals
Henrik P. Lüschen et al., Phys. Rev. Lett. 119, 260401
(2017)
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• Crystal perturbed by incommensurate on-site potential:
� �
-1
1
Aubry-André-Harper quasicrystal
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• Crystal perturbed by incommensurate on-site potential:
• Also in coupled waveguides arrays:• Cold atoms in optical lattices:
Lahini et al., Phys. Rev. Lett. 103, 013901 2009)
Roati et al., Nature 453, 895 (2008)
Aubry-André-Harper quasicrystal
� �
-1
1
• Localization properties:
Extended
Localized
Lahini et al., Phys. Rev. Lett. 103, 013901 (2009)
λ/t = 2λ/t
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For each site Vn = ±λ, according to:
Fibonacci quasicrystal
Y. E. Kraus et al., PRL 109, 106402 (2012)
• Fibonacci quasicrystal: ABAABABAABAABABAABABAABAABABAAλ
-λ
n
phasonsite 2/(1+√5)
• Localization properties:critical eigenstates
site
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• Interpolating Aubry-André-Fibonacci model:
Kraus, Zilberberg, PRL 109, 116404 (2012)
O. Zilberberg
Modulation frequency: b = 2/(1+√5)
Continuous deformation: IAAF model
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• Interpolating Aubry-André-Fibonacci model:
Kraus, Zilberberg, PRL 109, 116404 (2012)
O. Zilberberg
Modulation frequency: b = 2/(1+√5)
Continuous deformation: IAAF model
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Localization phase diagram: theory
• Tight-binding approach:
• Inverse participation ratio for a state:
• Extended state:
• State localized on Nstates:
O. ZilberbergA. Štrkalj
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Localization phase diagram: theory
• Tight-binding approach:
• Inverse participation ratio for a state:
• Extended state:
• State localized on Nstates:
O. ZilberbergA. Štrkalj
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D. Tanese et al., Nature Com. 4, 1749 (2013)
Polaritons in a 1D periodic potential
ExperimentTheory
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Polaritons Interpolating AA-Fibo structures
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Aubry André (Harper) quasi-periodic potential
On-site potential incommensuratewith the lattice period
a = 2 µm
Ene
rgy
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Localization in interpolating AAFibo structures
V. Goblot et al., Arxiv1911.07809
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Localization in interpolating AAFibo structures
V. Goblot et al., Arxiv1911.07809
Band curvature=
Extended states
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Experimental localization phase diagram
V. Goblot et al., Arxiv1911.07809
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Experimental localization phase diagram
V. Goblot et al., Arxiv1911.07809
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Outline
Introduction to polariton lattices
Emergence of criticality in quasi-crystals
Discrete gap solitons in a flat band
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What about interactions? Non-linear physics?
C. Ciuti & I. Carusotto, Rev. Mod. Phys. 85, 299 (2013)
�ℏ�Ψ
��= −
ℏ
2� + � � + � � − �
�
2� + �� � ���(������)
Weak on-site interaction :
�
�≪ 1
Mean field approximation :
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Nonlinear micropillar
2-4 µmsingle pillar gapped spectrum
Interaction energy Decay
• Repulsive interactions leadto resonance blue-shift
Bistability
Baas et al., PRB. 70, 161307(R) (2004)Baas et al., PRA 69, 023809 (2004)
cwpumping
�ℏ!"
!�= # + � " − �
γ
2" + �����
F≪ γ
-2 0 20
0.5
1
1.5
2
(ω - ω0)/γ
U|ψ
|2 /γ
F≪ γ F~γ
ω0
Optical bistabiiltyH.M. Gibbs et al., PRL 36, 1135 (1976)
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Nonlinear dimer
�ℏ!"&
!�= #& + � "&
− �γ1
2"& − '" + �����
�ℏ!"
!�= # + � "
− �γ2
2" − '"&
1/J
γ1 γ2
U U
tiFe
ω
S. Rodriguez et al., Nature Commun. 7, 11887 (2016).
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Weak driving: F ≪ γT – driven ("&)– undriven (")
γ= 26 µeV
2J = 263µeV
Transmission of the dimer
Bonding Anti-Bonding
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Phase diagram at strong driving
Optical Limiter Bistability Multistability
Very Strong driving: UNT ≫ γT , J
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Observation of tristability
1476.3 1476.5 1476.7 1476.9 1477.10
0.2
0.4
0.6
0.8
1
Energy (meV)
Tra
nsm
itte
d I
nte
nsi
ty (
no
rm.)
Undriven
Pump
S. Rodriguez et al., Nature Commun. 7, 11887 (2016).
Interaction induceddestructive interference
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Non-linearity in a flat band
Coupled waveguidesD. Guzman-Silva et al., New. J. Phys. 16, 063061 (2014)Rodrigo A. Vicencioet al., PRL 114, 245503 (2015)S. Mukherjee et al., PRL 114, 245504 (2015)
Cold atomsShintaro Taie et al., Sci. Adv. 1, e1500854 (2015)
PolaritonsNaoyuki Masumoto et al., NJP 14 065002 (2012)S. Klembt et al., Appl. Phys. Lett. 111, 231102 (2017)C. E. Whittaker et al., Phys. Rev. Lett. 120, 97401 (2018)
Coupled lasers: M. Nixon et al., Phys. Rev. Lett. 110, 184102 (2013).
�ℏ�Ψ
��= −
ℏ
2� + � � + � � − �
�
2� + �� � ���(������)
No kinetic energy => strong effect of disorder, of interactions
2D Lieb lattice
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Non-linearity in a flat band
A
B
C
5 µm
Excitation in the gap: laser detuning = interaction energy
Pump
V. Goblot et al, Phys. Rev. Lett. 123, 113901 (2019)
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P increasing
Linear regime
a
b
c
d
• Formation of nonlinear domains:
• Total intensity in the chain:
a
b cd
0 10.5• Spot profile:
Dom
ain
size
(u.
c.)
Power (a.u.)0 5 10 15 20 25
0
5
10
• Domain size:
Linear regime
a b
c d
Non-linearity in a flat band
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• Discretized GPE equation:
Excitation of gap solitons
• Truncated Bloch Waves in conservative systems:
? = @ ℏA
? = B ℏA
C. Bersch et al., Phys. Rev. Lett. 109, 093903 (2012)
F. Bennet et al., Phys. Rev. Lett. 106, 093901 (2011)Th. Anker et al., Phys. Rev. Lett. 94, 020403 (2005)
Here driven dissipative context
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- - - -- - -
--
y / a
0
1
0 2 4 6-2-4
-6
Multistability of the domains
- - - -- - -
--
y / a
0
1
0 2 4 6-2-4
-6- - - -- - -
--
y / a
0
1
0 2 4 6-2-4
-6
x / a
- - - -- - -
--
y / a
0
1
0 2 4 6-2-4-6
High degeneracy (no kinetic energy) => Complex multistability
Dynamical hysteresis? Chaotic instability?
V. Goblot et al, Phys. Rev. Lett. 123, 113901 (2019)
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Summary
Emulation of Hamiltonians with lattices of coupled cavities
Potential for Applications
Important developments for room temperature operation of polariton devicesZnO, 2D materials, Perovskite……
- What about going beyond mean field? Blockade regime
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How far from quantum regime ? Quantum correlations?
�
�C 1Photon blockade if :
Presently in the best samples : �
�D 0.1
G. Muñoz-Matutano et al, Nature Materials 18, 213 (2019) A. Delteil et al., Nature Materials 18, 219 (2019)
First evidence for « weak » polariton antibunching:
A. Verger et al., Phys. Rev. B 73, 193306 (2006)
See J. Simon’s group: Nature Physics 14, 550, (2018)
U
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How to increase interactions? Couple to different excitations
Dipolar polaritons:P. Cristofolini et al., Science 336, 704 (2012)E. Togan et al., Physical Review Letters 121, 227402 (2018)see also : I. Rosenberg et al., Sci. Adv. 4, eaat8880 (2018)
Polaron polaritons: S. Ravets et al., Phys. Rev. Lett. 120, 057401 (2018) Trion in 2D materials : R. P. A. Emmanuele et al., arXiv:1910.14636
Photons coupled to fractional quantum Hall states, P. Knüppel et al., Nature 572, 91 (2019)
Bose-Hubbard
Strongly correlatedphoton phaseswithin reach!!!
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Generation of multi-photon correlated states
I. Carusotto et al., Phys. Rev. Lett. 103, 033601 (2009)
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Acknowledgment to our theoretician collaborators
FranceGuillaume Malpuech
Cristiano Ciuti
IacopoCarusotto
DmitrySolnishkov
Wim Casteels Florent Storme
TomokiOzawa
Paris
Trento
Filippo Vincentini
OdedZilberberg
Antonio Štrkalj
Jose Lado
Alexandre Le Boité
MichielWouters
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Alberto AmoLilles University
Isabelle Sagnes Luc LegratietMartina MorassiAristide Lemaitre
Acknowledgements to experimentalists
SylvainRavets
Abdou Herouri
Valentin Goblot
Philippe St Jean
NicolaCarlon
Zambon
Nicolas Pernet
Said Rodrigueznow at Amolph
AteebToor
and to fundings
QuentinFontaine