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Quantum Fluids of Light Quantum fluids of light Jacqueline Bloch Centre de Nanosciences et de Nanotechnologies C2N, CNRS/Universités Paris Sud/ Paris Saclay Palaiseau, France [email protected] http://www.polaritonquantumfluid.fr Quantum fluids of light? General motivations Jacqueline Bloch Why cavity polaritons ? Centre de Nanosciences et de Nanotechnologies C2N, CNRS/Universités Paris Sud/ Paris Saclay Marcoussis, France Band structure? How do we perform experiments? Why non-linearities? [email protected] Where do we go?? http://www.polaritonquantumfluid.fr Fractional Quantum Hall effect Superfluidity Graphene Topological insulators Quantum fluids of light as an analogous system Same Hamiltonian => Same physical properties ℏ Why use synthetic quantum material? 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 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 !) Quantum fluids of light as an analogous system 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! Bose-Hubbard J U Driven-dissipative photonic Bose-Hubbard model Out of equilibrium quantum physics 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) Emulation with light Topological Chiral edge states Randon quantum walk edge states Si A. Crespi, Nature Photonics 7, 322 (2013) Zheng Wang et al., M. Hafezi, Nature 461 772 (2009) Nat. Phot. 7 1001 (2013) Quasicrystal Synthetic Landau levels Non reciprocal lasing N. Shine et al. B.Bahari et al., Science P. Vignolo et al., New J. Phys. 16 (2014) 043013 Nature 354, 671 (2016) 10.1126/science.aao4551(2017) M. A. Bandres et al. Science 10.1126/science.aar4005 (2018) Semiconductor microcavities : cavity polaritons 2 µµµm Nature 443, 409 (2006) T = 10 K Polariton density T = 5 K CdTe Benoid Deveaud ky kx Kasprzak et al. Nature , 443 , 409 (2006) Le Si Dang Polariton superfluidity Iacopo Carusotto Cristiano Ciuti Alberto Amo Alberto Bramati Elisabeth Giacobino C. Ciuti and I. Carusotto PRL 242, 2224 (2005) A. Amo et al. Nature Physics 5, 805 (2009) C. Ciuti & I. Carusotto, Rev. Mod. Phys. 85 , 299 (2013) Emulating Dirac Physics y -4 -2 0 2 4 -2 3a) k √ /(2 0 /3 ππ /3a) π /(2 y k 2 π Pillar diameter = 3 µm kx/(2 /3a) Interpillar distance a = 2.4 µm 4 µµµm Dirac cones Energy (meV – 1577) Jacqmin et al., PRL 112, 116402 (2014) See also Yamamot (Stanford), Krizhanovskii (Sheffield) Propagation of light in a non-linear medium Propagation of light in a non-linear medium Quentin Glorieux M. Bellec, C. Michel (INPHYNI) D. Faccio Edimburgh Q. Glorieux, A. Bramati (LKB) C. Michel et al. Nature Com 2018 PRL 120, 055301 (2018) 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 heavy • Very fast • Very slow • No interactions • Interactions Photon confinement Distributed Bragg reflector Very high reflectivities 1.0 n n n 0.8 15 1n2 1n2 1 7 0.6 0.4 λλλΒΒΒ Reflectivity 0.2 λλλΒΒΒ 25 0.0 0.75 0.80 0.85 0.90 λλλΒΒΒ/4/4/4 λ ( µm) Photon confinement Distributed Bragg reflector Very high reflectivities 1.0 n n n 0.8 15 1n2 1n2 1 7 0.6 0.4 λλλΒΒΒ Reflectivity 0.2 λλλΒΒΒ 25 0.0 0.75 0.80 0.85 0.90 λλλΒΒΒ/4/4/4 λ ( µm) Fabry-Perot resonator (microcavity) Optical mode 1.0 0.8 0.6 0.4 λλλc Reflectivity 0.2 0.0 0.750 0.775 0.800 0.825 0.850 λλλc~ λλλB λ ( µ m) normal incidence Microcavity polaritons GaAs/AlGaAs Angle θ (º) based structures θ -20 -10 0 10 20 5 K Photon Top DBR Bottom DBR Emission energy (eV) energy Emission -2 0 2 Optical cavity -1 kin-plane (μm ) Bragg mirror GaAs/AlAs Cavity Bragg mirror GaAs/AlAs TEM, G. Patriarche, LPN Microcavity polaritons GaAs/AlGaAs Excitonic resonance based structures θ 5 K Top DBR Quantum Wells Bottom DBR Quantum well exciton AlGaAs GaAs AlGaAs e- Exciton h+ QW Microcavity polaritons GaAs/AlGaAs Angle θ (º) based structures θ -20 -10 0 10 20 5 K Photon Exciton Top DBR Quantum Wells ℏ 0 Bottom DBR 2 Emission energy (eV) energy Emission -2 0 2 Quantum well exciton -1 kin-plane (μm ) AlGaAs GaAs AlGaAs with - e Typically 10 Exciton h+ QW Microcavity polaritons GaAs/AlGaAs Angle θ (º) based structures θ -20 -10 0 10 20 Upper 5 K polariton Photon Exciton Top DBR ~ 5meV Quantum Wells Lower Bottom DBR polariton Emission energy (eV) energy Emission -2 0 2 Microcavity polaritons : mixed exciton-photon states -1 kin-plane (μm ) AlGaAs GaAs AlGaAs e- Cavity polariton h+ Claude Weisbuch QW PRL 69 , 3314 (1992) Microcavity polaritons EX (k// ) g H = k// g EC (k// ) Photon Rabi splitting 2g Exciton Energie -10 -5 0 5 10 -1 k (µm ) with // 2 2 ∆()()()k// = ()EC k// − EX k// +4g Microcavity polaritons | polariton > = ααα |photon> βββ222 + βββ |exciton> ααα222 + 0 0 Exciton photon detuning: + , 0 - .0/ βββ222 s-shaped dispersion : inflexion point ααα222 + 0 βββ222 ααα222 + 1 0 Probing polariton states: Angle resolved experiments θθθ E z θθθ k// k = ω/c sin( θ) // émission( θθθ) 4 -1 0 1 2 3 k// (10 cm ) k ( 10 4 cm -1 ) Selective excitation and probe of polariton states How to generate microcavity polaritons? Resonant excitation Non resonant excitation - Population of many low energy modes Control of : - Energy - Creation of an excitonic reservoir - k// - Phase - 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 Spectrometer plane Sample slit Energy Typical experimental scheme Far field (d) Cavity polaritons : an exciton-photon mixed state | polariton > = ααα |photon> + βββ |exciton> ααα2 photon part βββ2 exciton part Properties -5 Photonic component low mass (10 me) Microcavity polaritons | polariton > = ααα |photon> βββ222 + βββ |exciton> ααα222 + 0 0 Exciton photon detuning: + , 0 - .0/ βββ222 s-shaped dispersion : inflexion point ααα222 1 1 + 0 Effective mass: 234 ℏ 1 5 7 222 At k = 0: βββ 234 236 8 ααα222 Beyond inflexion point: negative effective mass + 1 0 Probing polariton states: Real space propagation Resonant pulsed excitation Group velocity Probing polariton states: Real space propagation + 0 0 Resonant excitation 1 9 9:.;/ 5 9236 7 9 : ℏ X + 0 + 1 0 Cavity polaritons : an exciton-photon mixed state | polariton > = ααα |photon> + βββ |exciton> ααα2 photon part βββ2 exciton part Properties -5 Photonic component low mass (10 me) Short lifetime (1-100 ps) dissipative system Polariton lifetime Scattering Resonant excitation Emission 1 5 7 <234 <236 <8 Polariton have a finite (short) lifetime : 1-100 ps Cavity polaritons : an exciton-photon mixed state | polariton > = ααα |photon> + βββ |exciton> ααα2 photon part βββ2 exciton part Properties -5 Photonic component low mass (10 me) Short lifetime (1-100 ps) dissipative system Pseudo spin Polariton spin e e Spin : electron : +- ½ Exciton : J z = +- 1 h h heavy hole : +- 3/2 e h e h Jz =+- 2 Photon have an angular momentum : +- 1 Only J=1 excitons are coupled to light Polaritons have two spin projections: jz = +1 σ + 1 σ − 2 pseudospin jz = -1 One-to-one relationship between pseudospin state and polarisation degree Polariton spin: Intrinsic magnetic field Cavity modes linearly polarized: TE-TM splitting 1.486 1.484 TM pola. boundary conditions for the electromagnetic field at the interface of the different dielectric layers Energy (eV) Energy 1.482 TE pola. -2 0 2 Effective magnetic field -1 k ( µm ) II Kavokin et al. PRL 95 , 136601 (2005) Optical spin Hall effect Initial Linear polarisation along x Pseudospin r r r ∂S r r S S = S ∧ Ω(θ ) + 0 − ∂t τ1 τ σ − σ + kx θ σ + σ − ky Kavokin et al. PRL 95 , 136601 (2005) Leyder et al. Nature Phys. 3, 628 (2007). Optical spin Hall effect Reciprocal Space Real Space τpol = 10ps kx ρc ky -0.5ρc +0.5 Spin currents Kavokin et al. PRL 95 , 136601 (2005) Leyder et al. Nature Phys. 3, 628 (2007). Cavity polaritons : an exciton-photon mixed state | polariton > = ααα |photon> + βββ |exciton> ααα2 photon part βββ2 exciton part Properties -5 Photonic component low mass (10 me) Short lifetime (1-100 ps) dissipative system Pseudo spin Sensitivity to magnetic field Magneto-luminescence B = 7T Quantum well Cavity ∆>?@A ~ 1.7 DE B = 7T ∆>?@A ~ 1.2 DE Energy (eV) PL intensity PL Momentum (k) Energy (eV) Cavity polaritons : an exciton-photon mixed state | polariton > = ααα |photon> + βββ |exciton> ααα2 photon part βββ2 exciton part Properties -5 Photonic component low mass (10 me) Short lifetime (1-100 ps) dissipative system Pseudo spin Sensitivity to magnetic field Polariton Interaction Highly non linear system (Kerr like) Polariton lattices Polariton lattices Gold deposition Surface acoustic waves on top mirror Low power 2 µµµm ky d-wave condensation kx Cerda-Méndez et al., PRL 105 , 116402 (2010) de Lima et al., PRL 97 , 045501 (2006) Lai et al., Nature 450 , 529 (2007) Kim et al., Nature Phys 7, 681 (2011) Cerda-Méndez et al.
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