Controlled Polarization Switch in a Polariton Josephson Junction

Abstract

The interaction between a particle's spin and momentum -- known as spin-orbit (SO) coupling -- is the cornerstone of modern spintronics. In Bose-Einsten condensates of ultracold atoms, SO coupling can be implemented and precisely controlled experimentally; photonic systems, on the other hand, possess an intrinsic SO interaction due to the longitudinal-transverse splitting of the photon modes. In this work, we focus on such spinor, SO-coupled exciton-polariton condensates on a ring, where the strength of the synthetic magnetic field is controlled by the geometrical dimensions of the structure. Inspired by recent experiments, we investigate the dynamics of a weakly-nonlinear four-mode bosonic Josephson junction within this geometry. We discover a narrow parameter range in which the interplay of the tunneling dynamics with polariton-specific SO coupling leads to a new regime, with dynamical switching of the fluid's circular polarization degree to the opposite, along the entire ring or on just one of its halves. Our results demonstrate polariton condensates in ring configurations as excellent candidates for all-optical controllable spin-switch applications, with prospects for scalability and observing non-trivial polarization patterns.

Figures (11)

• Figure 1: Geometry of the system. (a) Solid lines: TE-TM splitting vs. the ring width for different ratios $m_{\rm TM}/m_{\rm TE}$ as marked, for $m = 10^{-5}m_0$ ($m_0$ is the free electron mass). Dashed lines: same for $m = 10^{-4}m_0$ and $m_{\rm TM}/m_{\rm TE}=0.99$ (green), 0.98 (yellow) and 0.96 (orange). Stars indicate the values used in this work. (b) Sketch of the polariton ring, $r_1=10~\mu$m, $r_2=12~\mu$m, with the two Josephson junctions dividing it effectively in two potential wells. Color (in arb. units) shows the intensity map of the symmetric initial state (no particle imbalance). (c) Right axis, dotted line: the azimuthal potential along the ring circumference shown in (b), of a height $V = 0.5$ meV and width $\alpha = 0.8$ rad. Left axis: the two lowest eigenstates $\psi_g$ (blue) and $\psi_e$ (yellow) of the GPE, for $g = 1~\mu$eV $\mu$m$^2$ and the average one-component density $\rho = 50~\mu$m$^{-2}$ (dark solid lines) and $200~\mu$m$^{-2}$ (light solid lines). Thin dashed lines show the linear limit $g=0$.
• Figure 2: The spatial Josephson effect in presence of SO coupling. Evolution of the particle imbalance obtained from the four-mode dynamical model \ref{['seteq']} for different initial values $z(0)$: (a,d,g) $0.2$, (b,e,h) $0.3$, (c,f,i) $0.4$ and various initial DCP of the fluid. (a--c) Linear-polarization case $\wp_c(0)\to 0$ resembles the scalar-case result. (d--f) As $\wp_c(0)$ approaches $\wp_c^{\rm crit}$, the spatial Josephson oscillations are destroyed. (g--i) When $\wp_c(0)>\wp_c^{\rm crit}$ and approaches 1 (circular polarization), the conventional regimes are recovered with the doubled particle number. Vertical dashed lines are guides to the eye for comparison of oscillation frequencies. Parameters: $m = 10^{-5}m_0$, $\Delta=0.02$ meV, $g = 1~\mu$eV $\mu$m$^2$, $\rho_{tot} = 100~\mu$m$^{-2}$, $V=0.5$ meV, $\alpha = 0.8$.
• Figure 3: Polarization oscillations and polarization switching. (a) Evolution of the DCP on the left (the blue lines) and right (the yellow lines) half-rings without switching (top) and in the switching regime (bottom). Parameters: $m=10^{-5}m_0$, $\Delta = 0.02$ meV; $\rho_{tot} = 100$ (a--e) and $200~\mu$m$^{-2}$ (f); $g=0.2$ (a,d) and $1~\mu$eV $\mu$m$^2$ (b,c,e,f). The following regimes are displayed: (a) conventional harmonic oscillations [$z(0) = 0.4$, $\wp_c(0) = 0.5$]; (b) anharmonic anti-phase oscillations of the DCP of the left and right half-rings [$z(0) = 0.25$, $\wp_c(0) = 0.55$]; (c) self-localization of $\wp_c^L$, accompanied by the regular oscillations of $\wp_c^R$ [$z(0) = 0.65$, $\wp_c(0) = 0.45$]; (d) polarization switching from anharmonic oscillations [$z(0) = 0.6$, $\wp_c(0) = 0.9$]; (e) polarization switching from self-trapped oscillations [$z(0) = 0.05$, $\wp_c(0) = 0.65$]; (f) the DCP of the left half-ring undergoes all regimes in sequence, harmonic--anharmonic--self-trapped and then switches sign [$z(0) = 0.45$, $\wp_c(0) = 0.1$]. The green lines show the critical value $\wp_{c\,L}^{\rm crit}(t)$.
• Figure 4: Diagram of polarization oscillations regimes. (a) Dependence of the critical value $\wp_c^{\rm crit}$ of the DCP defining the transition to the polarization self-trapping regime versus the TE-TM parameter $\Delta$, in the absence of the external Josephson effect [$z(0)=0$], for different nonlinearity values. (b) Diagram of dynamical regimes of the DCP oscillations depending on the initial values $\wp_c(0)$ and $z(0)$ for the left half-ring. White: oscillations with zero average, blue: self-localization of polarization, red: the switching regime. (c--e) Anharmonic oscillations (c), polarization switching (d), and the self-trapping regime (e) realized across the critical region [see panel (b)] for $\wp_c(0)=0.3$. In panels (b--e), $\Delta = 0.02$ meV, $g = 1~\mu$eV $\mu$m$^2$, $\rho_{tot} = 200~\mu$m$^{-2}$.
• Figure 5: Parameters governing the dynamics versus the barriers width $\alpha$. According to Eq. \ref{['UKJ']}, we plot the interaction parameter $U$ (a); the spin-flip rate $J$ (b); the parameters defining the effective tunneling rate $K_0$ (c) and $K_1N$ (d). In all panels, the full condensate density $\rho_{tot} = 100~\mu$m$^{-2}$ and $g=1~\mu$eV $\mu$m$^2$, $\Delta = 0.02$ meV. Different lines correspond to different barriers height $V$, as marked in (a--b): 0.3 meV (purple), 0.5 meV (red), 0.7 meV (pink), 1.0 meV (light blue), and 1.5 meV (dark blue). The gray-shaded region marks the widths smaller than the healing length. The dotted (dashed) parts of the lines mark the regions of widths where the barriers are too narrow (too wide) to work as Josephson junctions. Various markers (circles, diamonds, stars, triangles) mark the parameters used in simulations (see Fig. \ref{['fig6']} and Fig. \ref{['fig:notun']}).