Full Stark control of polariton states on a spin-orbit hypersphere

The orbital angular momentum and the polarization of light are physical quantities widely investigated for classical and quantum information processing. In this work we propose to take advantage of strong light-matter coupling, circular-symmetric confinement, and transverse-electric transverse-magnetic splitting to exploit states where these two degrees of freedom are combined. To this end we develop a model based on a spin-orbit Poincaré hypersphere. Then we consider the example of semiconductor polariton systems and demonstrate full ultrafast Stark control of spin-orbit states. Moreover, by controlling states on three different spin-orbit spheres and switching from one sphere to another we demonstrate the control of different logic bits within one single physical system.

Figure 1

Schematic of the polariton states. (a) Eigenenergies and eigenmodes in the presence of 2D harmonic confinement and TE-TM splitting. (b)–(d) SO-Poincaré spheres resulting from the states ${\mathbf{\psi }}_{\text{RA}}$ and ${\mathbf{\psi }}_{\text{AZ}}$ (b), ${\mathbf{\psi }}_{\text{RA}}$ and ${\mathbf{\psi }}_{\text{HY1}}$ (c), and ${\mathbf{\psi }}_{\text{RA}}$ and ${\mathbf{\psi }}_{\text{HY2}}$ (d) (a detailed mathematical description is in the Supplemental Material [38]). The angular coordinates are ${\phi }_1$ and ${\phi }_2$.

Figure 2

Manipulation of a SOV state on the SOPS in Fig. 1, starting from ${\mathbf{\psi }}_{\text{AZ}}$ to arrive to ${\mathbf{\psi }}_{\text{RA}}$ (animation in the Supplemental Material [38]). Top panel: Polariton population as a function of time: ${\sigma }^{+}$ (black squares), ${\sigma }^{-}$ (red triangles) in the main panel, $H$ (green squares), $V$ (blue triangles), $D_{+}$ (purple squares), and $D_{-}$ (gray triangles) in the insets. Bottom panel: Polariton distribution and polarization at different times, the color code indicates the local polariton density. Two ${\sigma }^{+}$ polarized Stark pulses are simulated by a shift of the ${\sigma }^{+}$ polariton with ${\sigma }_{\text{st}}=1$ ps and $\hslash \delta {\omega }^{{\sigma }^{+}}=0.4$ meV, and centered at $t_1^{\text{st}}=6.58$ and $t_2^{\text{st}}=18.15$ ps. The parameters here and in the rest of the paper are $m_{\text{LP}}=2.4\times {10}^{-5}{m}_e$ ($m_e$ being the electron mass), ${\omega }_{\text{HO}}=4.0{\text{ps}}^{-1},\beta =0.04\text{meV}\mu {\text{m}}^2,{\gamma }_{\text{LP}}=0.02$ meV [39, 40].

Figure 3

Polariton population as a function of time and polariton distribution and polarization during a SOV manipulation (animations in the Supplemental Material [38]). Top panels: Manipulation on the SOPS of Fig. 1 with the $H$ and $V$ polarizations in green squares and blue triangles. Bottom panels: Manipulation on the SOPS of Fig. 1 with the $D^{+}$ and $D^{-}$ polarizations in purple squares and gray triangles. The Stark pulses are simulated by two consecutive shifts of the $H$ ($D^{+}$) polarized polariton with ${\sigma }_{\text{st}}=1$ ps, $\delta {\omega }^H=\delta {\omega }^{D^{+}}=0.305$ meV, $t_1^{\text{st}}=6.58$, and $t_2^{\text{st}}=32.1$ ps.