Hydrodynamic solitons in polariton superfluids

Transcription

1 Hydrodynamic solitons in polariton superfluids Laboratoire Kastler Brossel (Paris) A. Amo * V.G. Sala,, R. Hivet, C. Adrados,, F. Pisanello, G. Lemenager,, J. Lefrère re, E. Giacobino, A. Bramati Laboratoire MPQ (Paris) S. Pigeon, C. Ciuti NNL, Instituto Nanoscienze (Lecce) D. Sanvitto INO-CNR BEC (Trento) I. Carusotto EPFL (Lausanne) R. Houdré * now at

2 Outline Polaritons in semiconductor microcavities Superfluidity in polaritons Observation of oblique dark solitons

3 Semiconductor microcavities GaAs Top DBR Quantum Wells Bottom DBR Polaritons θ k in-plane Emission energy (ev) Angleθ(º) -2-2 ~ 5meV Upper polariton k in-plane (µm - ) Photon Exciton Lower polariton -2 2

4 Semiconductor microcavities GaAs Top DBR Quantum Wells Bottom DBR θ k in-plane Emission energy (ev) Angleθ(º) -2-2 ~ 5meV Upper polariton Photon Exciton Lower polariton Polaritons Composite bosons Properties -2 2 k in-plane (µm - ) Excitonic component strong interactions (non-linearities χ 3 ) Photonic component low mass ( -5 m e ) Short lifetime (~ps) out of equilibrium

5 Polariton condensation Excitation -2-2 Atomic BEC Polariton condensate m/m e 4-5 T c < µk >3 K λ T at T c µm - µm Emission energy (ev) Lower polariton Polariton density -2 2 k in-plane (µm - ) T = 5 K CdTe k y k x Kasprzak et al. Nature, 443, 49 (26)

6 Polariton condensation Angleθ(º) -2-2 Atomic BEC Polariton condensate m/m e 4-5 T c < µk >3 K λ T at T c µm - µm Emission energy (ev) Propagating condensate Lower polariton Polariton density -2 2 k in-plane (µm - ) T = 5 K CdTe k y k x Kasprzak et al. Nature, 443, 49 (26)

7 Boson quantum fluids Coherent propagation t =28ps t =7ps Vortex and half vortex t =48ps Superfluidity 5 µm Amo et al., Nature 457, 295 (29) Lagoudakis et al., Nature Phys. 4, 76 (28), and Science 326, 974 (29) Nardin et al., arxiv:.846v3 Krizhanovskii et al., PRL 4, 2642 (2) Roumpos et al., Nature Phys. 7, 29 (2) This talk 2 µm Energy (ev) Persistent currents Hydrodynamics: solitons Wertz et al., Nature Phys. 6, 86 (2) Long-range order phases Sanvitto et al., Nature Phys. 6, 527 (2) This talk D BEC arrays Real space Momentum space Lai et al., Nature 45, 529 (27) Cerda-Méndez et al., PRL 5, 642 (2)

8 Superfluidity: Landau criterion Interacting Bosonic condensate linearised spectrum of excitations E c s k

9 Superfluidity: Landau criterion Interacting Bosonic condensate linearised spectrum of excitations SUPERFLUID E c s k Galilean boost v f < c s c s -v f E c s +v f k FLOW

10 Superfluidity: Landau criterion Interacting Bosonic condensate linearised spectrum of excitations SUPERFLUID E c s k Galilean boost v f < c s c s -v f E 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 242, 2224 (25)

11 Superfluidity in atomic condensates Linearised spectrum of excitations Steinhauer et al., PRL 88, 247 (22) c s g ψ = ħ m 2 Critical velocity Supersonic Cerenkov shockvawes expanding BEC potential v f =3c s v f =.5c s v f =.8c s FLOW v f =.3c s time Onofrio et al. PRL 85, 2228 (2) Raman et al., PRL 83, 252 (999) Carusotto et al. PRL 97, 2643 (26)

12 Superfluidity in polaritons Emission angle (degrees) -2-2 Resonant excitation of the polariton mode Control of velocity, density and frequency of the fluid Energy (ev) (d) Far field CCD -2-2 k y (µm - ) Near field CCD Transmission experiment in a InGaAs/GaAs/AlAs microcavity (2/24 pairs) k z k Excitation laser k θ Y X Microcavity sample

13 Superfluid regime low momentum Elastic scattering.5 v f < c s E - E p. Pump c s 2 REAL SPACE 3 µm - k y (µm - ) g ψ = ħ Linear regime m FLOW MOMENTUM Nature Physics 5, 85 (29) k x (µm - ) Polariton density

14 Superfluid regime Polariton-polariton interactions low momentum v f < c s c s g ψ = ħ m 2 REAL SPACE E - E p Elastic scattering.5. 3 µm Pump - k y (µm - ) Linear regime FLOW E - E p Collapse of the ring.5. Pump - k y (µm - ) Superfluid MOMENTUM Nature Physics 5, 85 (29) k x (µm - ) k x (µm - ) Polariton density k x (µm - ) k y (µm - )

15 low momentum v f < c s Superfluid regime Theory (non-equilibrium Gross-Pitaevskii) 2 P / P P P i tψ ( x, t) = D iγ / 2 + V ψ ( x, t) ψ ( x, t) + FPe e normal mode coupling decay pol-pol interaction ( x x ) 2 σ i( k x ω t) CW Pump (finite spot) c s 2 g ψ = ħ Linear regime Superfluid m REAL SPACE MOMENTUM 3 µm FLOW Nature Physics 5, 85 (29) k x (µm - ) k x (µm - ) Polariton density k x (µm - )

16 Nature Physics 5, 85 (29) Polariton density Čerenkov regime 2 P / P P P i tψ ( x, t) = D iγ / 2 + V ψ ( x, t) ψ ( x, t) + FPe e ( x x ) 2 σ i( k x ω t) high momentum v f > c s Landau condition c s g ψ = ħ m 2 EXPERIMENT E - E p.5. Elastic scattering 4 µm - k y (µm - ) FLOW.5. - THEORY Pump Linear regime E - E p Linear wavefronts available states k y (µm - ) Čerenkov 4 µm

17 Nature Physics 5, 85 (29) Polariton density Čerenkov regime 2 P / P P P i tψ ( x, t) = D iγ / 2 + V ψ ( x, t) ψ ( x, t) + FPe e ( x x ) 2 σ i( k x ω t) high momentum v f > c s Landau condition c s g ψ = ħ m 2 EXPERIMENT E - E p.5. Elastic scattering 4 µm Pump - k y (µm - ) Linear regime FLOW E - E p.5. θ c sin = 2 v s f 5 c = 8. m / s s Linear wavefronts available states - k y (µm - ) Čerenkov Supersonic atomic BEC THEORY Carusotto et al. PRL 97, 2643 (26) 4 µm

18 E c s +v f Local speed of sound large barriers c s -v f k

19 Local speed of sound c s -v f E c s +v f k v f = v large barriers Landau critical speed v <,c cs [Frisch et al., PRL 69, 644 (992): v. 4c ] =,c s Velocity gradient ħ v f,t,t m ( r ) = φ ( r ) v f = 2 v Hydrodynamic effects: Quantized vortices Solitons v f = v

20 Nucleation of topological excitations Atomic condensates (Gross-Pitaevskii theory) Total drag From vortex shedding Vortex emission induces a drag even at subsonic speed /c s High vortex shedding frequency Vortex street soliton Flow Flow Winiecki et al., J. Phys. B: At. Mol. Opt. Phys. 33, 469 (2) El et al., PRL 97, 845 (26)

21 Hydrodynamic solitons in polaritons Polaritons (theory) v c s vortex solitons Pigeon et al., PRB 83, 4453 (2)

22 Hydrodynamic solitons in polaritons Polaritons (theory) v c s vortex solitons 2π phase Phase jump, depth, width and speed are correlated s ξ vs 2 n w cs φ n cos = = = 2 The deeper, the slower (and bigger phase jump) Pigeon et al., PRB 83, 4453 (2)

23 Hydrodynamic solitons in polaritons Polaritons (theory) Phase must be free to evolve Resonant pump out of the nucleation region v c s vortex solitons Phase jump, depth, width and speed are correlated s ξ vs 2 n w cs φ n cos = = = 2 The deeper, the slower (and bigger phase jump) Pigeon et al., PRB 83, 4453 (2)

24 Excitation spot (d) Far field CCD Near field CCD k z k Excitation laser k θ Y X Microcavity sample

25 Excitation spot

26 Soliton nucleation v f =.79 µm/ps k=.34 µm - subsonic Superfluidity Excitation density supersonic Real space emission µm Flow Interference with a coherent reference beam - Visibility of fringes (degree of coherence at τ=) Science 332, 67 (2) µm

27 Soliton nucleation v f =.79 µm/ps k=.34 µm - subsonic Superfluidity Excitation density Vortex ejection supersonic Real space emission µm Flow Interference with a coherent reference beam - Visibility of fringes (degree of coherence at τ=) Science 332, 67 (2) µm Vortex streets

28 Soliton nucleation v f =.79 µm/ps k=.34 µm - subsonic Superfluidity Excitation density Vortex ejection Solitons supersonic Real space emission µm Flow Interference with a coherent reference beam - Visibility of fringes (degree of coherence at τ=) Science 332, 67 (2) µm

29 Soliton nucleation v f =.79 µm/ps k=.34 µm - subsonic Superfluidity Excitation density Vortex ejection Solitons supersonic Real space emission µm Flow Interference with a coherent reference beam - Visibility of fringes (degree of coherence at τ=) Science 332, 67 (2) µm

30 Soliton nucleation

31 Soliton nucleation v f =.7 µm/ps k=.73 µm High speed: no need of mask y (µm) Flow 4 y = 4 µm Polariton density (arb. units) n y = 26 µm y = 36 µm n s -2 2 x x (µm) (µm)

32 Soliton nucleation v f =.7 µm/ps k=.73 µm y (µm) 2 2 n s φ cos = 2 n 2 4 Flow 4 y = 4 µm Polariton density (arb. units) n y = 26 µm y = 36 µm n s Polariton density (arb. units) φ 2 Relative phase π x (µm) -2 2 x x (µm) (µm)

33 Soliton nucleation v f =.7 µm/ps k=.73 µm y (µm) 2 2 n s φ cos = 2 n 2 4 Flow 4 Polariton density (arb. units) y = 4 µm n y = 26 µm y = 36 µm n s soliton relative depth (n d /n) phase jump (rad)..5. π π x x (µm) (µm) y (distance from the defect; µm)

34 Soliton nucleation v f =.7 µm/ps k=.73 µm y (µm) 2 2 n s φ cos = 2 n 2 4 Flow 4 Polariton density (arb. units) y = 4 µm n y = 26 µm y = 36 µm n s soliton relative depth (n d /n) phase jump (rad)..5. π π 2 Science 332, 67 (2) -2 2 x x (µm) (µm) y (distance from the defect; µm)

35 Hydrodynamic soliton multiplets

36 Hydrodynamic soliton multiplets k =.2 µm - 2 µm Flow

37 Hydrodynamic soliton multiplets k =.2 µm - k =. µm - 2 µm Flow

38 Hydrodynamic soliton multiplets k =.2 µm - k =. µm - Atomic condensates (GPE theory) 2 µm Flow El et al., PRL 97, 845 (26)

39 Summary Observation of superfluidity of polaritons superfluid supersonic A.A., J. Lefrère et al., Nature Phys. 5, 85 (29) Transition from the superfluid to vortex ejection and solitons Superfluidity Vortex ejection Solitons Oblique dark soliton multiplets A.A., S. Pigeon et al., Science 332, 67 A.A., S. Pigeon et al., Science 332, 67 (2)