Dynamically Stable Vortices in Exciton-Polariton Condensates Engineered by Repulsive Interactions

Abstract

We present an analytical and numerical study of the dynamics and stability of exciton-polariton condensates described by the open-dissipative Gross-Pitaevskii equation, incorporating both binary and short-range three-body interactions. Using an asymptotic description, we identify the parameter regime and derive equations for the instability amplitude, providing insights into vortex formation via the snake instability of dark solitons. We find that a repulsive three-body interaction, when combined with a binary interaction, supports stable vortex-antivortex pair formation. On the other hand, the reinforcement of attractive three-body interactions with binary interaction triggers the emergence of snake instability, leading to boundary-driven vortex disintegration. The time evolution of the instability under the influence of reservoir effects indicates that the boundary effects are more pronounced, to the extent of destabilizing the vortices with attractive three-body interactions compared to repulsive three-body interactions, thereby underscoring the stable nature of vortices in the repulsive domain.

Figures (10)

• Figure 1: The velocity fields from Eq. \ref{['del-s']} for an instability amplitude $A(0) = 0.25$ for different $k$.
• Figure 2: Evolution of a dark soliton subject to snake instability, leading to the formation of a vortex necklace. The dynamics are driven by repulsive three-body interactions ($\chi = 1$) and an initial modulation amplitude $A = 0.25$, without a reservoir ($m_R = 0$). The top row (a--c) tracks the development of the instability in the density profile, while the bottom row (d--f) shows the associated phase, where the discrete $2\pi$ phase jumps and the clear signature of a vortex-antivortex pair in (f) confirm the nature of the topological defects. The dynamics for the attractive three-body interaction ($\chi = -0.2$) and an initial modulation amplitude $A = 0.25$, without reservoir effects (g)-(i) represent the density evolution and (j)-(l) the associated phase profiles.
• Figure 3: Comparative evolution of dark solitons undergoing snake instability for two different instability amplitudes in the presence of repulsive three-body interactions ($\chi = 1$) and reservoir coupling. For amplitude $A = 0.25$, (a)--(c) show the density evolution, and (d)--(f) the corresponding phase evolution. For amplitude $A = 0.5$, (g)--(i) present the density evolution, and (j)--(l) the associated phase profiles. In both cases, the wavenumber is $k = 1.0$, and the chemical potential is $\mu = 1$. The density plots illustrate the breakup of the dark soliton into vortex–antivortex pairs, whose lifetimes depend strongly on the initial amplitude. The phase plots reveal characteristic phase windings that confirm vortex formation and show the damping effects induced by reservoir coupling. Other parameters are the same as in Fig. \ref{['fig:den-3body']}.
• Figure 4: Comparative evolution of dark solitons undergoing snake instability for different initial amplitudes in the presence of repulsive three-body interactions ($\chi = 1$) and reservoir coupling. The top two rows correspond to an initial amplitude $A = 0.25$: panels (a)–(c) show the density evolution, while (d)–(f) display the corresponding phase profiles. The bottom two rows present the results for $A = 0.5$: panels (g)–(i) depict the density evolution, and (j)–(l) show the associated phase profiles. In both cases, the wavenumber is $k = 1.0$, and the chemical potential is $\mu = 1$. The remaining parameters are fixed as $g_{R} = 2$, $\gamma_{C} = 3$, $\gamma_{R} = 15$, and $R = 0.5$.
• Figure 5: Time evolution of density profiles illustrating the snake instability of a dark soliton with repulsive three-body interactions, shown for an initial perturbation amplitude $A = 0.5$ and weak pumping conditions. Panels (a)–(i) illustrate vortex formation influenced by the reservoir at different stimulated scattering rates: (a)–(c) $R = 1$, (d)–(f) $R = 5$, and (g)–(i) $R = 10$. Other parameters are fixed at $g_{R} = 2$, $\gamma_{R} = 3$, and $\gamma_{C} = 15$.