We propose the optical simulation of the Lieb–Liniger interaction using one-dimensional (1D) stationary light polaritons (SLPs) with nonlinear self-interaction. Our analysis reveals that the dark-state polariton (DSP) mode of the self-interacting SLP satisfies a Schrödinger-like equation exhibiting the Lieb–Liniger interaction, where both the effective mass and interaction strength can be tuned optically. We demonstrate the transition of the Lieb–Liniger interaction from a repulsion-dominant regime to a thermalization-dominant regime using experimentally achievable parameters. This results in the second-order correlation of the DSP mode spanning from anti-bunching to bunching statistics. By advancing the quantum simulation of the Lieb–Liniger model, our work opens new avenues for exploring complex Lieb–Liniger physics, such as interaction quenching and multi-particle bound states. Moreover, it lays the groundwork for developing novel single-photon sources operating in the anti-bunching regime, featuring narrow bandwidth, directional emission, and built-in quantum memory functionality.

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A theoretical proposal for optically simulating the Lieb–Liniger interaction using one-dimensional stationary light polaritons (SLPs) with nonlinear self-interaction. The dark-state polariton mode satisfies a Schrödinger-like equation exhibiting Lieb–Liniger physics, with both effective mass and interaction strength tunable optically. The work demonstrates a transition from repulsion-dominant to thermalization-dominant regimes, yielding second-order photon correlations ranging from anti-bunching to bunching statistics. Applications include exploring interaction quenching, multi-particle bound states, and developing narrow-bandwidth single-photon sources with built-in quantum memory.

Lieb–Liniger interaction via self-interacting stationary light polaritons