Emergent Magnetic Monopole in Artificial Polariton Spin Ice

Abstract

Artificial spin ice provides a versatile setting for emergent gauge fields and magnetic monopole excitations. Here we propose a driven-dissipative polariton realization of artificial spin ice, in which the circular polarization of each link mode plays the role of an Ising degree of freedom, while an auxiliary lossy vertex mode dynamically enforces a local ice-rule constraint. Adiabatic elimination of the vertex mode yields an effective spin-ice penalty, favoring the two-in two-out manifold in the steady state. We show that local polarization flips generate monopole-antimonopole defects, and that sequential flips transport these defects across the lattice while defining a Dirac string. In an extended spin-ice geometry, the vertex charges and their dynamics can be directly reconstructed from polarization-resolved real-space imaging. Our results establish polariton lattices as a controllable photonic platform for creating, manipulating, and observing emergent gauge charges in nonequilibrium spin-ice systems.

Figures (3)

• Figure 1: (a) Schematic figure of ground state of the artificial spin ice. Red and blue links represents the polariton condensates with pseudospin up and down, generated by spin-polarized pumps respectively. The vertex couples the two-in and two-out condensates. Arrows pointing towards and outwards the vertex indicate opposite lattice gauges. (b) Real part of wavefunction of the link eigenmode $\varphi_l$ and vertex eigenmode $\chi_v$. The width and length of each link are $0.6\rm\ \mu m$ and $5\rm\ \mu m$, the radius of vertex cavity is $0.8\rm\ \mu m$. Lattice gauge is designed as $(\eta_{L},\eta_{R},\eta_{D},\eta_{U})=(+1,-1,+1,-1)$. The spin-polarized pump at each link follows an elliptic Gaussian profile.
• Figure 2: (a) Ground state $Q_v=0$ and excitation $Q_v=2,4$ of the artificial polariton spin ice. The black arrows indicate the in/out configurations for the links. $Q_v=0$ has 2-in 2-out configuration, while for the first excitation $Q_v=2$ it becomes 3-in 1-out and for $Q_v=4$ all arrows point to the vertex. The real space Ising variables $\sigma_\ell$ for $Q_v=0,2,4$ states are shown at the stationary state. (b) The total link population $N(t)$ for the three configurations $Q_v=0$ (blue solid curve), $Q_v=2$ (red dashed curve) and $Q_v=4$ (yellow dash-dotted curve), without external pumping. Inserted: single link population $N_3(t)$ for the down link. (c) Evolution of $|\xi|^2$ for the three configurations. (d) The total link population $N(t)$ under spin-polarized pumps with the same intensity. Inserted: a zoom-in for the time window $0-10$ ps. Parameters: $m=3\times10^{-5}m_e$ is the effective mass of polariton ($m_e$ is the mass of an electron), $\gamma=0.132 \ \rm meV$, $\Gamma=2.63 \ \rm meV$, $g=\alpha=\beta=1.58 \ \rm meV$.
• Figure 3: (a) Schematic of the protocol. The system is initially prepared in the ice-rule state with $Q_1=Q_2=Q_3=0$. At $t=50~\mathrm{ps}$, the pump polarization on link 2 is flipped, creating a monopole-antimonopole pair, $(Q_1,Q_2,Q_3)=(2,-2,0)$. At $t=150~\mathrm{ps}$, the pump polarization on link 3 is flipped, transferring the defect to the right vertex and yielding $(Q_1,Q_2,Q_3)=(2,0,-2)$. Green arrows point to the links where the pump polarization is flipped. (b) Time evolution of the vertex charges $Q_1$ (blue solid curve), $Q_2$ (red dashed curve), and $Q_3$ (yellow dash-dotted curve). (c) Time evolution of the corresponding link Ising variables $\sigma_1$ (blue solid curve), $\sigma_2$ (red dashed curve), $\sigma_3$ (yellow dash-dotted curve), and $\sigma_4$ (purple dotted curve). (d) Final vertex charges versus vertex dissipation rate $\Gamma$. Larger $\Gamma$ drives the charges closer to the ideal values $Q_v=\pm2$, consistent with the adiabatic-elimination picture and the Ising limit. Parameters are the same as in Fig. \ref{['fig:excitation']} unless otherwise specified.