Research ArticleQUANTUM PHYSICS

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid

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Science Advances  04 Dec 2015:
Vol. 1, no. 11, e1500807
DOI: 10.1126/sciadv.1500807
  • Fig. 1 Generation of optical and polariton FVs and HVs.

    (A and B) Experimental scheme for creation of optical FV (A) and HV (B) state via a q-plate. The disks and helices represent the isophase surfaces for Gaussian and vortex beams, respectively, in the radial regions of larger intensity. Red and yellow refer to the σ+) circular polarizations. (C and D) Emission density of the polariton fluid at the time of initial generation and the corresponding phase maps.

  • Fig. 2 Evolution of the main singularity upon HV injection.

    (A and B) Gaussian map together with the core trajectory in the opposite σ, both 15 ps into the evolution, at the power of P1 = 0.77 mW (A) and P2 = 1.8 mW (B) (see also movie S1 for power P1). (C and D) Complete xyt vortex trajectories (time range Δt = 5 to 40 ps, time step δt = 0.5 ps) are shown for P1 (C) and P2 (D), with the blue spheres representing the Gaussian centroid and the red ones representing the phase singularity. (E) Angle θ and distance d between the HV core and the opposite spin centroid represented for three different powers. (F) Phase-intensity plot along a vertical cut for P2 and t = 22 ps (arrows follow y), higlighting π-jumps in the phase between adjacent maxima (that is, when crossing the dark ring). norm. un., normalized units.

  • Fig. 3 Evolution of the twin singularities upon FV injection.

    (A to C) σ+ density at t = 20 ps with superimposed phase singularities for both polarizations, marked by symbols (circle for V, star for AV, and color for spin) (see movies S2 to S4). (D to F) Trajectories of the primary vortices plotted as 3D curves xyt (time range Δt = 5 to 26 ps, time step δt = 0.5 ps) (see movie S5 for P1). (G) Evolution in time of the intercore distance for the three cases of the previous panels. (H) Proliferation of secondary pairs (at t = 30 ps) upon increasing pump power. The used laser powers are P1–5 = 0.17, 0.77, 1.8, 3.1, and 4.4 mW, which correspond to an initial excitation of 0.2, 1.0, 1.8, 2.2, and 2.6 × 106 total polaritons, respectively.

  • Fig. 4 Theoretical trajectories of primary singularities for FV state.

    (A to C) Three-dimensional (x,y,t) curves simulated at three increasing powers, with time step δt = 0.4 ps in a time span Δt = 0 to 60 ps. (D) Evolution of the intercore distance for the three different cases.

  • Fig. 5 Branching dynamics of an HV polariton condensate.

    (A to D) Four rows show frames, taken at t = 8, 16, 24, and 32 ps, respectively, with densities and vortices in the first column and associated phase maps for σ in the second column. The initial condensate (orange due to overlap of red and yellow σ+ intensity scales) (A) undergoes the formation of concentric ripples (B to D; see also movie S6). (E) Spontaneous full V-AV formation with quadrupole symmetry for the initially Gaussian population tracked and represented as (x,y,t) vortex strings with a time step of 0.5 ps in a time span of 5 to 35 ps (see movie S7). An intermediate power (1.8 mW) was used.

  • Fig. 6 Branching dynamics of an FV polariton condensate.

    (A to C) Density frames and vortices taken at t = 8, 12, and 24 ps, respectively. (D to F) Corresponding phase maps for just one polarization (σ). The initial condensate [(A), orange due to overlap of red and yellow σ] develops concentric ripples (B to D); see also movie S4. (G) Spontaneous full V-AV formation tracked as (x,y,t) vortex branches with time step δt = 0.5 ps and time range Δt = 6 to 24 ps (see movie S8), for both the populations. Each secondary HV stays close to its spin counterpart until quite late into the dynamics.

  • Fig. 7 Theoretical FV case without the disorder potential.

    (A to C) Each row corresponds to a different time: t = 8 (A), 24 (B), and 40 ps (C). Left and right columns represent the σ+ and σ densities, respectively, with their phase singularities superimposed, marked by symbols (circle for V, star for AV, and color for spin; see also movie S9).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/11/e1500807/DC1

    Movie S1. HV density map and vortex evolution (corresponding to Fig. 2A).

    Movies S2 to S4. FV density maps (on a 50 × 50–μm2 area) and twin-cores evolution at three powers (corresponding to Fig. 3, A to C).

    Movie S5. FV density plus 3D xyt trajectory (corresponding to Fig. 3, A and D).

    Movie S6. HV density and phase maps (corresponding to Fig. 5, A to D).

    Movie S7. HV branching dynamics as 3D xyt trajectory (corresponding to Fig. 5E).

    Movie S8. FV branching dynamics as 3D xyt trajectory (corresponding to Fig. 6G).

    Movie S9. FV theoretical density and phase singularities (corresponding to Fig. 7).

  • Supplementary Materials

    This PDF file includes:

    • Legends for movies S1 to S9

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). HV density map and vortex evolution (corresponding to Fig. 2A).
    • Movie S2, Movie S3, and Movie S4 (.avi format). FV density maps (on a 50 × 50–μm2 area) and twin-cores evolution at three powers (corresponding to Fig. 3, A to C).
    • Movie S5 (.avi format). FV density plus 3D xyt trajectory (corresponding to Fig. 3, A and D).
    • Movie S6 (.avi format). HV density and phase maps (corresponding to Fig. 5, A to D).
    • Movie S7 (.avi format). HV branching dynamics as 3D xyt trajectory (corresponding to Fig. 5E).
    • Movie S8 (.avi format). FV branching dynamics as 3D xyt trajectory (corresponding to Fig. 6G).
    • Movie S9 (.avi format). FV theoretical density and phase singularities (corresponding to Fig. 7).

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