Nonresonant optical control of a spinor polariton condensate

We investigate the spin dynamics of polariton condensates spatially separated from and effectively confined by the pumping exciton reservoir. We obtain a strong correlation between the ellipticity of the nonresonant optical pump and the degree of circular polarization (DCP) of the condensate at the onset of condensation. With increasing excitation density we observe a reversal of the DCP. The spin dynamics of the trapped condensate are described within the framework of the spinor complex Ginzburg-Landau equations in the Josephson regime, where the dynamics of the system are reduced to a current-driven Josephson junction. We show that the observed spin reversal is due to the interplay between an internal Josephson coupling effect and the detuning of the two projections of the spinor condensate via transition from a synchronized to a desynchronized regime. These results suggest that spinor polariton condensates can be controlled by tuning the nonresonant excitation density offering applications in electrically pumped polariton spin switches.

Figure 1

(a) Schematic representation of reservoir and condensate in the microcavity. Real space map of the degree of circular polarization (b) below ($P=0.95P_{\mathrm{th}}$), and (c) above ($P=1.08P_{\mathrm{th}}$) condensation threshold. (d) Normalized intensity of the polariton emission above threshold (red line, right axis), below threshold (blue line, right axis) and DCP (black line, left axis) across the white dotted line profile of (c).

Figure 2

Variation of the condensate's DCP with the linear polarization angle of the excitation beam. Circular polarization maps of the confined polariton condensate just above threshold for linear polarization angle: (a) $\theta =0^{\circ }$, (b) ${150}^{\circ }$, and (c) ${270}^{\circ }$. (d) The average DCP is plotted vs external polarization angle featuring a $2\theta$ dependence (red dots mark the data at the above angles). (Inset) Schematic representation of the induced ellipticity to the excitation beam vs the linear polarization angle.

Figure 3

(a) DCP as a function of excitation power vs threshold power. (b) Power dependence vs a spatial cross-section of the DCP across the trap. Note the change in scale at 2.15. The figure shows the region where $\text{SNR}\ge 1\text{dB}$. The black line outlines the emission below threshold defining the trap. The inset in (a) shows the two normalized spin components of the 1D real-space profile of the condensate with respect to power above threshold.

Figure 4

The degree of circular polarization, $\xi$, as a function of the pumping strength $P/P_{\mathrm{th}}$ obtained by numerical integration of Eq. (7). The blue dots correspond to the desynchronized state where the polarization degree and condensate density are oscillating in time (the values of these functions are averaged over the period of their oscillation), the red dots corresponds to fixed points. Even for a small discrepancy in the pumping intensity, the degree of the circular polarization can vary from elliptical polarization to linear polarization to polarization reversal. The parameters used are $\gamma =10,g=0.7,b=15,R=1.0,U_{\alpha }=1.1,J=0.045,\text{and}\eta =1.1.$

Figure 5

(a) Simulated pump (dotted black line, right axis) and condensate (solid red line, right axis) real space profile plotted together with the condensate DCP profile (solid blue line, left axis) for ${\mathrm{P}}_{\mathrm{th}}=1.1$ that has been multiplied by an appropriate hyperbolic tangent function to avoid the irrelevant DCP behavior for the points where the condensate density is too small (less than ${10}^{-2}$). (b) DCP, $\xi$, as a function of $P/P_{\mathrm{th}}$ for a trapped condensate pumped in a ring. The red points correspond to the fixed points, while the blue points to the averaged values of the desynchronized solutions. The blue circle in (b) denotes the point from where the profiles presented in (a) are extracted. Parameters are $\gamma =10,g=0.7,b=15,R=1.0,U_{\alpha }=1.1,J_{\max }=0.07,\eta =1.05,\alpha =0.06,\text{and}{r}_0=5.$