Superfluidity of Polaritons in Engineered Potentials in Semiconductor Microcavities Alberto Amo, C. Adrados, J. Lefrère, E. Giacobino, A. Bramati Laboratoire Kastler Brossel, UPMC, ENS, CNRS, Paris, FR S. Pigeon, C. Ciuti Laboratoire MPQ, Université Denis Diderot, CNRS, Paris, FR I. Carusotto BEC-CNR-INFM and Dipartimento di Fisica, Universita di Trento, Povo, IT R. Houdré Institut de Physique de la Matière Condensée, EPFL, Lausanne CH

Outline Polaritons in semiconductor microcavities Observation of superfluidity of polaritons Engineering the polariton landscape

Semiconductor microcavities Angle θ (º) θ GaAs Upper polariton kin-plane Photon Emission energy (eV) Exciton ~ 5meV Top DBR Quantum Wells Lower polariton Bottom DBR kin-plane (μm-1) Polaritons The partial photonic character renders a very low mass The partial excitonic character provides the system with strong non-linearities

Semiconductor microcavities Angle θ (º) θ GaAs Upper polariton kin-plane Photon Emission energy (eV) Exciton ~ 5meV Top DBR Quantum Wells Lower polariton Bottom DBR kin-plane (μm-1) Polaritons The partial photonic character renders a very low mass The partial excitonic character provides the system with strong non-linearities Properties Composite bosons Excitonic component strong interactions (non-linearities 3) Photonic component low mass (10-5 me) Short lifetime (~ps) out of equilibrium

Polariton condensation Excitation m/me Tc lT at Tc Atomic BEC 104 <1 mK 1 mm Polariton condensate 10-5 20-300 K 1-10 mm Emission energy (eV) Lower polariton kin-plane (μm-1) Polariton density T = 5 K CdTe ky kx Kasprzak et al. Nature, 443, 409 (2006)

Polariton quantum fluid effects Quantized vortices (m=1) Interferogram Phase map Lagoudakis et al., Nature Phys. 4, 706 (2008) Imprinted vortices (m=1,2) and persistent currents Sanvitto et al., Nature Phys. DOI: 10.1038/NPHYS1668 (2010)

Polariton quantum fluid effects Quantized vortices (m=1) Fluid dynamics Interferogram Phase map Real space Lagoudakis et al., Nature Phys. 4, 706 (2008) Momentum space Imprinted vortices (m=1,2) and persistent currents Amo et al., Nature 457, 291 (2009) Sanvitto et al., Nature Phys. DOI: 10.1038/NPHYS1668 (2010)

Landau criteriom for superfluidity Interacting Boson condensate linearized spectrum of excitations E cs k

Landau criteriom for superfluidity Interacting Boson condensate linearized spectrum of excitations SUPERFLUID E E Galilean boost cs+vf cs FLOW cs-vf vf < cs k k

Landau criteriom for superfluidity Interacting Boson condensate linearized spectrum of excitations SUPERFLUID E E Galilean boost cs+vf cs FLOW cs-vf vf < cs k k ČERENKOV REGIME E E Galilean boost cs+vf cs cs-vf FLOW vf > cs k k I. Carusotto and C. Ciuti, phys. stat. sol. (b) 242, 2224 (2005)

Polariton superfluidity Resonantly excited condensate with low momentum Elastic scattering E - Ep Pump ky (mm-1) Linear regime Real space FLOW 30 µm Momentum space Polariton density

Polariton superfluidity Resonantly excited condensate with low momentum Elastic scattering Collapse of the ring E - Ep E - Ep Pump vf < cs Pump ky (mm-1) ky (mm-1) Linear regime Superfluid 1 Real space FLOW 30 µm Momentum space Polariton density Amo et al., Nature Phys. 5, 805 (2009)

Polariton superfluidity Gross-Pitaevskii simulations Resonantly excited condensate with low momentum Elastic scattering Collapse of the ring E - Ep E - Ep Pump vf < cs Pump ky (mm-1) ky (mm-1) Linear regime Superfluid 1 Real space FLOW 30 µm Gross-Pitaevskii simulations FLOW 30 µm Polariton density Amo et al., Nature Phys. 5, 805 (2009)

Superfluid regime

Čerenkov regime (supersonic) Gross-Pitaevskii simulations High momentum Elastic scattering Linear wavefronts vf > cs E - Ep E - Ep Pump supersonic ky (mm-1) ky (mm-1) Linear regime Čerenkov 1 Real space FLOW 40 µm Gross-Pitaevskii simulations FLOW 40 µm Polariton density Amo et al., Nature Phys. 5, 805 (2009)

Čerenkov regime (supersonic) Gross-Pitaevskii simulations High momentum Elastic scattering Linear wavefronts vf > cs E - Ep E - Ep Pump supersonic ky (mm-1) ky (mm-1) Linear regime Čerenkov 1 Supersonic atomic BEC Carusotto et al. PRL 97, 260403 (2006) Real space q FLOW 40 µm Gross-Pitaevskii simulations FLOW 40 µm Polariton density Amo et al., Nature Phys. 5, 805 (2009)

Polariton landscape engineering probe σ + FLOW 20 μm Defect-free area h_bar k = mv

Polariton landscape engineering polariton-polariton interaction probe σ + control σ - + FLOW 20 μm 20 μm Defect-free area Strong field: renormalization of the polariton energy h_bar k = mv control Polariton energy y

Polariton landscape engineering polariton-polariton interaction probe σ + control σ - probe σ + + control σ - detection σ + + = FLOW FLOW 20 μm 20 μm Defect-free area Strong field: renormalization of the polariton energy h_bar k = mv control Polariton energy y Amo et al., arXiv:1003.0131v1

Polariton landscape engineering Probe + Probe + Probe only horizontal control diagonal control No control injected injected scattered injected 30 μm scattered h_bar k = mv Amo et al., arXiv:1003.0131v1

Polariton landscape engineering Probe + Probe + Probe only horizontal control diagonal control No control injected injected scattered injected 30 μm scattered h_bar k = mv Amo et al., arXiv:1003.0131v1

Polariton landscape engineering SUPERFLUID REGIME (high probe power) Probe only horizontal control diagonal control No control injected injected scattered injected injected 30 μm scattered no scattering h_bar k = mv Amo et al., arXiv:1003.0131v1

Josephson oscillations Summary Observation of superfluidity of polaritons Supersonic regime access to the sound speed h_bar k = mv Polariton-polariton interactions landscape engineering localization effects polariton circuits Josephson oscillations

Single polariton fluid: set-up X Y Near field CCD Far field CCD q k kz k║ Microcavity sample Excitation laser Single laser excitation (CW, single mode) resonant excitation of one polariton mode Excitation close to the bottom of the lower polariton branch UPB LPB Transmission experiment CW Pump

SUPERFLUID AROUND SEVERAL DEFECTS SHADOW EFFECT AROUND BIG DEFECT Other situations SUPERFLUID AROUND SEVERAL DEFECTS FLOW 40 µm SHADOW EFFECT AROUND BIG DEFECT h_bar k = mv FLOW 40 µm Polariton density

Superfluidity checklist Nature 457, 273 (2009) h_bar k = mv Resonantly pumped polariton condensates Amo, Lefrère, et al., Nature Physics, (in press). I Carusotto talk at ICSCE 4 conference (Cambridge, UK, 2008), available at http://www.tcm.phy.cam.ac.uk/BIG/icsce4/talks/carusotto.pdf

Polariton fluid dynamics: set up sample Lens F X Y Fourier plane 2ps pulsed fA Microcavity sample (grown at LPN) IDLER CW Lens A real space imaging PUMP Energy selection imaging spectrometer Lens B momentum space imaging l/2 cavity 20 nm GaAs QW Streak Camera CCD ħΩRabi = 4.4 meV ky kx

Polariton landscape engineering polariton-polariton interaction probe σ + control σ - probe σ + + control σ - detection σ + + = FLOW FLOW 20 μm 20 μm Defect-free area Strong field: renormalization of the polariton energy Simulation GP h_bar k = mv control FLOW Polariton energy y Amo et al., arXiv:1003.0131v1

Polariton landscape engineering polariton-polariton interaction probe σ + control σ - probe σ + + control σ - detection σ + + = FLOW FLOW 20 μm 20 μm Defect-free area Strong field: renormalization of the polariton energy h_bar k = mv Real defect control FLOW Polariton energy 30 µm y Amo et al., arXiv:1003.0131v1

Polariton fluid dynamics Original streak camera set-up Study of the dynamics of polariton wavepackets v = 1.2 mm/ps (~1% light speed) t = 7 ps t = 28 ps t = 48 ps 20 μm Division in two in the presence of a big defect t = 8 ps t = 25 ps t = 45 ps 20 μm Amo et al., Nature 457, 291 (2009)

TOPO Coexistence of three fluids Steady state CW (pump) 100 mm spot Triggered OPO (signal) 16 mm spot fed by pump Idler Pulse CW Pump TOPO Signal TOPO Idler LPB UPB Pump polaritons Energy Signal polaritons Amo et al., Nature 457, 291 (2009)

Linear dispersion 1 DE Amo et al., Nature 457, 291 (2009) pol-pol interaction normal mode coupling decay CW Pump Pulsed probe 1 DE Amo et al., Nature 457, 291 (2009)

Coherent propagation t= 7ps t= 28ps t= 48ps a b Amo et al., Nature 457, 291 (2009)

Flow through a defect Amo et al., Nature 457, 291 (2009) I t= 8ps b 2.5 0.0 Amo et al., Nature 457, 291 (2009)

compatible with superfluid behaviour Frictionless flow E=ħpump Pump polaritons Pump fluid: scattering waves Signal fluid no scattering with the defect Peaked momentum E=ħsignal Signal polaritons compatible with superfluid behaviour kX kY K-space real space Amo et al., Nature 457, 291 (2009)

Noise studies in the superfluid regime Intensity noise polariton density statistics Noise decreases in the superfluid regime Superfluid threshold h_bar k = mv

Splitting in two II t = 8 ps t = 25 ps t = 45 ps a b Amo et al., Nature 457, 291 (2009)

Polariton superfluidity High density (quantum fluid regime) T = 5 K High density (quantum fluid regime) Low density Linear regime Superfluid Čerenkov vf<cs vf >cs 30 µm FLOW 30 µm FLOW 40 µm FLOW Scattering with defects Fluid without friction Linear wavefronts Amo et al., Nature Physics 5, 805 (2009)

Polariton superfluidity High density (quantum fluid regime) Low density T = 5 K Linear regime Superfluid Čerenkov vf<cs vf >cs 30 µm FLOW 30 µm FLOW 40 µm FLOW Scattering with defects Fluid without friction Linear wavefronts Amo et al., Nature Physics 5, 805 (2009)

Čerenkov regime (supersonic) Gross-Pitaevskii simulations High momentum Elastic scattering Linear wavefronts vf > cs E - Ep E - Ep Pump supersonic ky (mm-1) ky (mm-1) Linear regime Čerenkov 1 Real space FLOW 40 µm Gross-Pitaevskii simulations FLOW 40 µm Polariton density Amo et al., Nature Phys. 5, 805 (2009)