Vortices and superfluidity

Vortices and superfluidity

Vortices in Polariton quantum fluids We should observe a phase change by π and a density minimum at the core Michelson interferometry Forklike dislocation in interference pattern Phase may be retrieved through off axis FT

Observation of vortices from interferogram Dynamics of vortex pinning Pulsed non resonant excitation Time integrated data: Clearly pinned vortex

Dynamics of vortex pinning Pulsed non resonant excitation Temporally resolved real space data Please note the time scale Background removed Phase map Half vortices in spinor quantum fluids Linear polarization Polaritons carry a spin New vortical entities Phase change by π Polarization rotation by π Circular polarization Vortex in one circular polarization, not in the other one

Simultaneous measurement in σ + and σ Full vortices in circular polarization Interferogram

Half vortices in circular polarization Interferograms (raw data) Now the phase trough Fourrier transformation

σ + - σ coherence through Polarization mixing Half vortex with polarisation mixing interference 0 x real space (μm) 4 8 1 16 0 0 x real space (μm) 5 10 15 0-40 -0 0 0 40 Amplitude (arb.units) 0.0 0.5 1.0 1.5 Phase (π).0

Half vortices are building blocks... 15 Observation of a spin vortex

Intensity 17

Dissociation of a full vortex into half vortices Time resolved interferogram Time resolved Phase profile Dissociation of a full vortex into half vortices

Theory : GP with Helium superfluidity By Alfred Leitner

Linearization of the dispersion Appearance of a Ghost branch Superfluid fountain : BBC Four Suppression of instabilities Stirring of quantized vortices Dark solitons Quantized vortex streets Bogoliubov transformation Excitations of a Bose condensate Pair of counter propagating particle-antiparticle Parabolic free particle dispersion gets linear 4

5 Heterodyne Four Wave Mixing 6

Polariton Ghost Branch Slava Grebenev et al., Science, 79, 083 (1998)

Resonant excitation Polariton flow LPB CW Pump -3 - -1 0 1 3 k (μm -1 ) v<vs v>vs Superfluidity: Landau criterion in a conservative system Interacting Bosonic condensate Gross-Pitaevskii equation i tψ xt = + V() x + gψ xt ψ xt m particle interactions (, ) (, ) (, ) E c s k Galilean boost E Elastic scattering k No-Interactions FLOW

Superfluidity: Landau criterion in a conservative system Interacting Bosonic condensate Gross-Pitaevskii equation E c s g ψ = h m i tψ( xt, ) = + V() x + gψ( xt, ) ψ( xt, ) m particle interactions SUPERFLUID c s k Superfluidity: Landau criterion in a conservative system Interacting Bosonic condensate Gross-Pitaevskii equation E c s k c s g ψ = h m Galilean boost v f < c s i tψ( xt, ) = + V() x + gψ( xt, ) ψ( xt, ) m particle interactions SUPERFLUID E c s +v f c s -v f k FLOW

Superfluidity: Landau criterion in a conservative system Interacting Bosonic condensate Gross-Pitaevskii equation E c s k c s g ψ = h m Galilean boost v f < c s i tψ( xt, ) = + V() x + gψ( xt, ) ψ( xt, ) m particle interactions SUPERFLUID E c s +v f c s -v f k FLOW ČERENKOV REGIME E c s Galilean boost Elastic scattering E c s +v f FLOW k v f > c s c s -v f k C. Ciuti and I. Carusotto PRL 93, 166401 (004) Resonantly driven polariton gas normal mode coupling Non-linear Schrödinger equation decay () ikpx P i tψ( xt, ) = D iγ / + V x + gψ( xt, ) ψ( xt, ) + Fe P potential pol-pol interaction ( ω t) CW Pump Resonant excitation LPB CW Pump -3 - -1 0 1 3 k (μm -1 ) i tψ xt = + V() x + gψ xt ψ xt m (, ) (, ) (, ) Transmission experiment Resonant excitation of the polariton mode Control of velocity, density and frequency of the fluid We need an obstacle to probe superfluidity (d) Far field CCD k z k Excitation laser k θ Y X Real space CCD Microcavity sample T=10 K

Photonic defect InGaAs/GaAs/AlGaAs Sample from R. Houdré Field of view: 3.x0.9 mm wedge 00 μm resonance at 837.1 nm resonance at 837.05 nm wedge Photonic defect InGaAs/GaAs/AlGaAs Sample from R. Houdré Field of view: φ 100 μm wedge Single defect 00 μm resonance at 837.1 nm resonance at 837.05 nm wedge

Superfluid regime () P / P P P i tψ( xt, ) = D iγ / + V x + gψ( xt, ) ψ( xt, ) + Fe P e ( x x ) σ i( k x ω t) low momentum Elastic scattering 0.5 v f < c s Landau condition c s g ψ = h m REAL SPACE E - E p Pump 0.0-1 0 1 k y (μm -1 ) 30 µm Linear regime FLOW MOMENTUM -1.0-0.5 0.0 0.5 k x (μm -1 ) Amo et al., Nature Physics 5, 805 (009) Polariton density Superfluid regime low momentum v f < c s Landau condition c s g ψ = h m REAL SPACE E - E p P / σp P ωp i tψ( xt, ) = D iγ / + V x + gψ( xt, ) ψ( xt, ) + Fe P e Polariton-polariton interactions Elastic scattering 0.5 0.0 30 µm Pump -1 0 1 k y (μm -1 ) Linear regime FLOW () 0.5 0.0 Linearisation c s +v f c s -v f Pump -1 0 1 k y (μm -1 ) Superfluid ( x x ) i( k x t) Carusotto & Ciuti, PRL (004); phys. stat. sol. (b). 4, 4 (005) 1 0 MOMENTUM -1.0-0.5 0.0 0.5 k x (μm -1 ) Amo et al., Nature Physics 5, 805 (009) -1.0-0.5 0.0 0.5 k x (μm -1 ) Polariton density Collapse of the ring 0.5 0.0-0.5-1.0-0.5 0.0 0.5 1.0 k x (μm -1 ) k y (μm -1 )

Superfluid regime: theory Theory (non-equilibrium Gross-Pitaevskii) () P / P P P i tψ( xt, ) = D iγ / + V x + gψ( xt, ) ψ( xt, ) + Fe P e low momentum v f < c s Landau condition ( x x ) σ i( k x ω t) c s g ψ = h Linear regime Superfluid m REAL SPACE MOMENTUM 30 µm FLOW 1 0 1.0 0.5 0.0-0.5-1.0-0.5 0.0 0.5 k x (μm -1 ) Amo et al., Nature Physics 5, 805 (009) -1.0-0.5 0.0 0.5 k x (μm -1 ) Polariton density -1.0-0.5 0.0 0.5 1.0 k x (μm -1 ) Cerenkov regime high momentum v f > c s Landau condition c s g ψ = h m EXPERIMENT P / P P P i tψ( x, t) = D iγ / + gψ( x, t) ψ( x, t) + FPe e E - E p 0.5 0.0 Elastic scattering 40 µm -1 0 1 k y (μm -1 ) FLOW 0.5 0.0-1 0 1 k y (μm -1 ) THEORY Pump Linear regime E - E p Linear wavefronts available states c s +v f Čerenkov ( x x ) σ i( k x ω t) 40 µm Amo et al., Nature Physics 5, 805 (009) Polariton density

Quantum fluid properties ik () () ( x ω t x ) P P i tψ( x, t) = D iγ /+ V x + gψ( x, t) ψ(, t) + FP x e superfluid vortex solitons Non-equilibrium Gross-Pitaevskii equation Density Transition from superfluid to vortex emission and soliton nucleation interaction vc s kinetic Topological excitations Phase Vortices Solitons phase dislocation phase slip Pigeon et al., PRB 83, 144513 (011)

Polariton Flow Polariton flow

Superfluidity and solitons Excitation spot (d) Theoretical proposal by Pigeon et al., PRB 83, 144513 (011) k z k Excitation laser k θ Y X Microcavity sample Phase free to evolve in the masked region

Soliton and vortex streets v f = 0.79 μm/ps k=0.34 μm -1 Real space emission Interaction energy Superfluidity 100 10 Excitation density Kinetic energy c s g ψ = h m 1 10 μm Flow 1 Interference with a coherent reference beam 0-1 Visibility of fringes (degree of coherence at τ=0) 1 10 μm 0 Amo et al., Science 33, 1167 (011) Soliton and vortex streets Interaction Excitation density Kinetic energy energy v f = 0.79 μm/ps Superfluidity Vortex ejection k=0.34 μm -1 100 Real space emission 10 c s g ψ = h m 1 10 μm Flow 1 Interference with a coherent reference beam 0-1 Visibility of fringes (degree of coherence at τ=0) 1 0 10 μm Amo et al., Science 33, 1167 (011) Vortex streets

Soliton and vortex streets v f = 0.79 μm/ps k=0.34 μm -1 Real space emission Interaction energy Superfluidity 100 10 Excitation density Vortex ejection Solitons Kinetic energy c s g ψ = h m 1 10 μm Flow 1 Interference with a coherent reference beam 0-1 Visibility of fringes (degree of coherence at τ=0) 1 0 10 μm Amo et al., Science 33, 1167 (011) Vortex streets Soliton and vortex streets v f = 0.79 μm/ps k=0.34 μm -1 Interaction energy Superfluidity 100 Excitation density Vortex ejection Solitons Kinetic energy Real space emission 10 1 10 μm Flow 1 Interference with a coherent reference beam 0-1 Visibility of fringes (degree of coherence at τ=0) 1 See also Grosso et al., PRL 107, 45301 (011) 0 10 μm Amo et al., Science 33, 1167 (011) Vortex streets

Soliton nucleation -0 0 0-0 0 0 v f = 1.7 μm/ps k= 0.73 μm -1 0 0 High speed Δy (μm) 0 0 40 40 Flow Amo et al., Science 33, 1167 (011) Soliton nucleation -0 0 0-0 0 0 v f = 1.7 μm/ps k= 0.73 μm -1 0 0 High speed Δy (μm) 0 0 40 40 Flow 1D soliton in the x-direction y-direction: time coordinate movement of the soliton El et al., PRL 97, 180405 (006) Density Δφ π Phase 0 10 0 Δx (μm) 0 Amo et al., Science 33, 1167 (011) Characteristic phase jump

Time Idea, Josephson Nobel 73 Supraconductors separated by a thin insulating layer Oscillations with cw V Q-Bits at 4 K.

Two spatially separated wells with BEC on each side Phase and density differences govern the oscillations To probe ΔΝ we performed temporally resolved real space imaging To probe Δφ we temporally resolved the interference pattern of the two wells Time averaged image

From interferogram reconstruction By fitting the sinusoidal behaviour in each pixel we get initial phase Phase and density Note phase profile shows oscillation smaller than π

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Polariton bistability Baas et al, PRA, 69 (004) Bajoni et al, PRL, 101 (008) Sarkar et al, PRL, 101 (010) How to prepare traps for polaritons? 8 nm QW } } } Top DBR 1 pairs λ cavity Bottom DBR pairs GaAs AlAs In 0.04 Ga 0.96 As

Lateral confinement of photons 6 nm high mesa Ø: 3, 9, 19 μm 8 nm QW } } } Top DBR 1 pairs λ cavity Bottom DBR pairs GaAs AlAs In 0.04 Ga 0.96 As Real space spectroscopy of confined polaritons 3 μm 9 μm 19 μm Upper D Confined Upper Polaritons Lower D Confined Lower Polaritons

Momentum space spectrum of confined polaritons 3 μm 9 μm 19 μm Upper D Confined Upper Polaritons Lower D Confined Lower Polaritons Momentum space (negative detuning -6 mev) 3 μm 9 μm Upper D Lower D Confined Lower Polaritons 19 μm

Direct image in standard optics of the wavefunction of a quantum object! Low noise, frequency stabilized cw excitation nonlinearity: α 1 n > 0 (blueshift) Energy (ev) 1.485 1.484 1.483 1.48 D 0D E1 GS - 1 0 1 Position ( ) σ Energy cw laser polariton state Transmission intensity σ Excitation intensity

Polaritons have spin ±1 Blueshift : α 1 n co + α n contra Anisotropy : α 1 >> α Elliptical excitation Sigma + Sigma - Energy Ell. laser 75-5 Transmission Excitation intensity Predicted by Gippius (PRL 07) Spinor Bistability : Elliptical excitation

Spinor Bistability : Elliptical excitation Spin-up / spin down intensity Output Polarization degree 100 σ 1.0 0.5 10 ρ c 0.0 1 0.1 0.5 1.0 1.5.0-0.5 σ Linearly polarized excitation -1.0 0.5 1.0 1.5.0 Input power (mw)

Changing power Changing polarization At given polarization At given power 1.0 0.8 Linear pump ρ p =0 1.0 0.5 ρ c 0.6 0.4 ρ C 0.0 0. -0.5 0.0 0.5 1.0 1.5.0 Input Power(mW).5-1.0-0.4-0. 0.0 0. 0.4 ρ pump 1.0 0.5 Sigma + ρ C 0.0-0.5-1.0 Sigma - -0.4 0.0 0.4 Excitation polar degree

Streak camera screen Intesity (arb.) 6 x 104 5 4 3 1 Sigma Plus Sigma Minus X Y σ 0 500 1000 1500 0 0 500 1000 1500 time (ps) σ 1 0 00 400 600 800 1000 100 1400 time (ps) Polarization degree 0.5 0-0.5-1 0 500 1000 150 time (ps) ( ) ( ) γ + β ψ i α ψ + α ψ + ψ δ 1 linψ 1 = F + 1 ψ Feshbach resonance in polaritons?