All-Optical Linear-Polarization Engineering in Single and Coupled Exciton-Polariton Condensates

We demonstrate all-optical linear-polarization control in semiconductor microcavities using an exciton-polariton condensate in an elliptically shaped optical trap. The microcavity inherent TE-TM splitting lifts the pseudospin degeneracy of the anisotropic trap ground state. The emerging fine-structure modes are shown to be polarized linearly parallel and perpendicular to the trap major axis. We demonstrate polariton condensation into the excited pseudospin mode with a high degree of linear polarization, which rotates as we rotate the trap. We then extend our study to a system of two coupled linearly polarized condensates and demonstrate rich spin dynamics reflecting spontaneous synchronization and high correlation between the condensate pseudospins as a function of the pump parameters. Our findings open up exciting perspectives in both spinoptronics and studies on extended systems of interacting nonlinear optical elements with anisotropic coupling strength and adjustable fine structure.

Figure 1

The spatial intensity profiles of the (a),(b) excitation laser and (c),(d) condensate PL. The excitation laser induces a trapping potential with horizontal and vertical radii denoted a,b respectively. (e) The momentum distribution of the condensate PL. Panels (c)–(e) correspond to a condensate pumped twice above its condensation threshold (i.e., $P=2P_{\mathrm{th}}$).

Figure 2

(a) The power dependence of the condensate $S_{1,2,3}$ Stokes parameters (black, red, and blue markers) for the annular pump with a resultant cylindrically symmetric condensate profile (see the right and left insets, respectively). (b)–(d) The same, but now for a trap or condensate with a major axis orientated at (b) ${90}^{\circ }$, (c) ${45}^{\circ }$, and (d) $0^{\circ }$. The insets in (b)–(d) depict the real-space condensate PL, with black lines showing the orientation of the trap major axis.

Figure 3

(a) Condensate Stokes parameters for different orientations of the condensate major axis in real space (insets) at $P=1.94P_{\mathrm{th}}$. The black lines depict the major axis of the trap. The colored regions show the error of the measurement. (b) $S_1$ and (c) $S_2$ color maps for varying pump power and major-axis orientation, showing counterclockwise rotation of the pseudospin with increasing power.

Figure 4

(a) The distribution of the in-plane effective magnetic field $\mathbf{\Omega }(\mathbf{k})$ (red arrows) in momentum space due to TE-TM splitting given by Eq. (3). (b) The horizontal (black) and vertical (red) polarization resolved normalized spectra of the condensate emission at $k=0$ for a vertically elongated trap (${\theta }_{\min }=0$). The splitting between levels is approximately $20\mu \mathrm{eV}$. (c) The linear-polarization components and the DOP for different real-space ellipticities of the condensate. The data are taken at $P\approx 1.8P_{\mathrm{th}}$.

Figure 5

The spatially resolved $S_1$ of coupled condensates oriented horizontally and separated by $27.5\mu \mathrm{m}$ for (a),(b) two different quasi-cw 50-$\mu \mathrm{s}$ excitation shots, showing the formation of either (a) horizontal or (b) vertical polarization in both condensates. (c) The spatially resolved $S_1$ from one realization of the two coupled condensates orientated vertically at $26.5\mu \mathrm{m}$. The insets in (a) and (c) depict the corresponding $k$-space PL. (d),(e) One hundred time-integrated realizations (shots) of the $S_1$ for the left (blue) and right (red) condensate in the horizontal-horizontal major-axis configuration and (f),(g) in the vertical-vertical configuration. The experimental data are taken at approximately $1.8P_{\mathrm{th}}$. The distance dependence of the $S_1$ from simulations corresponding to (h) horizontal-horizontal and (i) vertical-vertical major-axis configurations. Each data point represents one shot (time-averaged). The green and purple backgrounds in (d)–(i) illustrate regions of similar behavior between experiment and theory.

Figure 6

The simulated time evolution of $S_1(t)$ and $S_2(t)$ for a single realization of the condensate at (a),(b) the black square and (c),(d) the black circle in Fig. 6, corresponding to the unstable and stable regimes, respectively. The red and blue colors correspond to the left and right condensates, respectively. (e),(f) Heat maps of the numerically obtained time-averaged Stokes parameters $S_{1,2}$ of one condensate from random initial conditions and varying pump power and distance.