Nonequilibrium polariton condensate in a magnetic field

We investigate exciton-polariton condensation in a magnetic field in a single high-quality semiconductor micropillar cavity. We observe successive polariton condensation of each spin component for two distinct threshold powers. Pronounced and nonmonotonous variations of both the Zeeman splitting and the circular polarization of the emission are measured across these two condensation thresholds. This unexpected behavior deeply deviates from the so-called spin-Meissner effect predicted for a fully thermalized system. Our measurements can be understood in a kinetic approach taking into account spin-anisotropic interactions within the entire system: the polariton condensate and the cloud of uncondensed excitons.

Figure 1

(a) Emission spectra measured under circular polarization for three different excitation powers $\left(P_{\text{th}}^{+}=0.44\mathrm{mW}\right)$. (Inset) Scanning electron microscopy image of a micropillar cavity with an edge length of $6\mu \mathrm{m}$; (b) (top) Integrated intensity for both circular polarizations and (bottom) energy of the ${\sigma }^{+}$ polariton mode as a function of excitation power. (c) Emission spectra measured under circular polarization for several excitation powers shown in smaller energy scale. For each power, the zero energy corresponds to the ${\sigma }^{+}$ polariton energy. $B=9\mathrm{T}$

Figure 2

(a)–(c) Integrated intensity for both circular polarizations, (d)–(f) Zeeman splitting and (g)–(i) circulation polarization ratio measured as a function of power for three values of the magnetic field. The vertical dashed lines indicate condensation threshold for both circular polarizations.

Figure 3

Simulations of the polariton emission intensity for both circular polarizations (a)–(c), Zeeman splitting (d)–(f) and degree of circular polarization (g)–(h) as a function of excitation power for three values of the magnetic field. The vertical dashed lines indicate condensation threshold for both circular polarizations. The dotted lines in (c), (f), (i) show numerical simulations taking into account constant scattering rates. The following parameters are used: ${\tau }_{\mathrm{ph}}=10\mathrm{ps},{\tau }_{\mathrm{r}}=300\mathrm{ps},{\alpha }_1=0.6\mu \mathrm{eV},{\alpha }_2=-0.06\mu \mathrm{eV},W_{\mathrm{XX}}={10}^5{\mathrm{s}}^{-1},W_{\mathrm{s}}=4\times {10}^{10}{\mathrm{s}}^{-1},\beta =2.2\times {10}^{-3}{\mathrm{cm}}^2$, and $\delta =2.2\times {10}^{-2}{\mathrm{cm}}^2$.

Figure 4

(Solid lines) Total normalized scattering rate into the $+$ and $-$ polariton states as a function of excitation power including mechanism 1; (dotted and dashed lines) Correction to the scattering rate, $\Delta W_{\mathrm{XX}}^{i,j}=\frac{W_{\mathrm{XX}}^{i,j}-W_{\mathrm{XX}}^0}{W_{\mathrm{XX}}^0}$, for the two interspin and intraspin components including mechanism 1. i (j) refers to the spin of the polariton state (reservoir). The vertical black (red) dashed line indicates condensation threshold for ${\sigma }^{+}$ $\left({\sigma }^{-}\right)$ polarization $B=9\mathrm{T}$.