Polariton spin whirls

We report on the observation of spin whirls in a radially expanding polariton condensate formed under nonresonant optical excitation. Real space imaging of polarization- and time-resolved photoluminescence reveals a spiralling polarization pattern in the plane of the microcavity. Simulations of the spatiotemporal dynamics of a spinor condensate reveal the crucial role of polariton interactions with a spinor exciton reservoir. Harnessing spin-dependent interactions between the exciton reservoir and polariton condensates allows for the manipulation of spin currents and the realization of dynamic collective spin effects in solid-state systems.

Figure 1

Snapshots of the spatiotemporal dynamics of the degree of circular polarization $S_z$ under nonresonant linearly polarized excitation at (a) $38\mathrm{ps}$, (b) $41\mathrm{ps}$, and (c) $46\mathrm{ps}$ showing the clockwise rotation of the spin texture within the microcavity plane (zero time is defined at the PL onset; see the full dynamics in supplementary video S1 [29]). Panels (d)–(f): Theoretical simulations showing the circular Stokes vector of the spin whirls at (d) $30\mathrm{ps}$, (e) $45\mathrm{ps}$, and (f) $60\mathrm{ps}$. The parameters used in the simulations are reported in Ref. [34].

Figure 2

Panels (a)–(c): Spin textures showing the evolution of the degree of circular polarization $S_z$ after 50 ps in a system excited with (a) nearly circular (${\sigma }_{+}=1;{\sigma }_{-}=0.1$), (b) linear (${\sigma }_{+}={\sigma }_{-}=1$), and (c) elliptical (${\sigma }_{+}=1;{\sigma }_{-}=0.9$) pump polarization. Panels (d) and (e): Dynamics of the condensate and reservoir at the pump position under elliptical pumping. (d) Energy splitting vs time of the polariton condensate (blue [dark gray] line) and exciton reservoir (red [light gray] line). (e) Density vs time of the ${\mathrm{\Psi }}_{\pm }$ polariton condensate and ${\mathcal{N}}_{\pm }$ exciton reservoir at the pump position. The dashed line indicates the position where the energy splitting in panel (d) reverses.

Figure 3

The pseudospin vector $\mathbf{S}\left(t\right)$ (blue [dark gray] arrows) in the Poincaré sphere at (a) the pump spot and (b) outside the pump. At the pump spot position, (a), $\mathbf{S}\left(t\right)$ precesses around the $z$ direction since $\left|{\mathrm{\Omega }}_z\right|>\left|{\mathrm{\Omega }}_{\mathrm{LT}}\right|$. Outside the pump spot, (b), $\mathbf{S}\left(t\right)$ precesses around ${\mathrm{\Omega }}_{\mathrm{LT}}$ since $\left|{\mathrm{\Omega }}_{\mathrm{LT}}\right|>\left|{\mathrm{\Omega }}_z\right|$. (c) Time-resolved, spatially integrated measurements of the two circular polarization components (${\mathrm{\Psi }}_{+}$, red [light gray] and ${\mathrm{\Psi }}_{-}$, blue [dark gray]) PL intensity, normalized and integrated over the area imaged in Figs. 1–1, i.e., $(460\times 340){\mu \text{m}}^2$. In green (very light gray) we show the time-resolved degree of circular polarization $S_z$ averaged over an area ($1.78\times 1.78)\mu {\text{m}}^2$, centered at $(0,0)\mu \text{m}$ in Figs. 1–1, comparable with the $2-\mu \text{m}$ FWHM excitation spot. The blue (dark gray) solid circles annotated with (A), (B), and (C) refer to the three snapshots of Figs. 1–1.

Figure 4

Snapshots of real space, spectral tomography of the degree of circular polarization $S_z$ at (a) $1.541\mathrm{eV}$ and (b) $1.540\mathrm{eV}$ showing the clockwise rotation of the spin whirls within the microcavity plane under nonresonant linearly polarized excitation.