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Lieb–Liniger interaction via self-interacting stationary light polaritons

U-Shin Kim, Yoon-Ho Kim

Published Jun 4, 2026• 0 citations
Publisher

Abstract

Abstract 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.

DOI
10.1038/s41534-026-01287-y

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Abstract 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.
We theoretically analyze the quasiparticle properties of stationary light polariton (SLP) modes in atoms via perturbative approaches of effective atom-light interaction Hamiltonian. First, we explicitly show the five SLP eigenmodes of the Hilbert space of the SLP system. Then, the quasiparticle properties, such as group velocities and effective masses of SLPs, are investigated under various parametric conditions, which include the emergence of negative effective mass and effective mass singularity. Finally, we derive the intrinsic lifetimes of each SLP mode, which features a complementary relation among the lifetimes of SLP modes. Our results offer quantitative analysis of the quasiparticle properties in Hilbert space spanned by the SLP modes, and it is expected to contribute to SLP-based atom-light interaction applications, such as photonic quantum gates, optical simulation of many-body physics, and exotic dispersion engineering.
In recent years, the development of various platforms for quantum simulation made it possible to study many-body systems under controlled conditions. Of particular interest are one-dimensional systems, known to exhibit some unique properties compared to their higher-dimensional counterparts. One of the current promising platforms for simulations of one-dimensional systems are Rydberg dark polaritons, quasiparticles of a photon-matter hybrid character emerging in the context of electromagnetically induced transparency (EIT) coupled with Rydberg atoms. These polaritons are long-lived (owing to the properties of EIT) and inherit interaction properties from the huge polarizability of Rydberg atoms, both attractive features in the context of simulations. We herein construct an experimental proposal for realizing one-dimensional physics through Rydberg dark polaritons. By using a stationary-light scheme, a sequence of steps allows a laser pulse incident on a transversally trapped gas of Rydberg atoms to yield a stationary pulse of weakly interacting polaritons. Within the stationarity regime, the lasers are further tuned to adjust the interaction effective one-dimensional scattering length through a Feshbach-like resonance to create a Tonks-Girardeau-type gas of polaritons. Signatures of non-trivial correlations can then experimentally probed by retrieving the photons through a subsequent adjustment of the laser strengths. Realizing this proposal would be a landmark achievement in the fields of many-body simulations and Rydberg physics.
Electromagnetically-induced transparency (EIT) with Rydberg atoms enables strong interactions between atoms to be controlled and measured by pulses of light. Consequently, Rydberg dark polaritons are a promising platform for quantum simulations. Of particular interest are simulations of one-dimensional systems, known to exhibit unique properties compared to their higher-dimensional counterparts. One limitation of standard EIT is that reducing the polariton group velocity to bring the dark polaritons to rest also implies activating strong Rydberg interactions. To achieve independent control of polariton speed and interaction strength, we propose a stationary light-scheme to bring Rydberg polaritons to a stand-still. This allows them to remain primarily photonic and, therefore, non-interacting, before Rydberg interactions are turned on. Once activated, in the dilute regime and in the presence of strong transverse confinement, the strong polarizabilities of Rydberg atoms give rise to an effective contact interaction between polaritons. By tuning the various parameters of the stationary-light scheme, the effective one-dimensional scattering length may be adjusted to yield various kinds of physics, including the regime of a Tonks-Girardeau gas, when polaritons exhibit fermionic behavior. We outline a protocol to observe the resulting spatial correlations between neighboring polaritons.
Dark-state polaritons (DSPs) based on the effect of electromagnetically induced transparency are bosonic quasiparticles, representing the superpositions of photons and atomic ground-state coherences. It has been proposed that stationary DSPs are governed by the equation of motion closely similar to the Schrödinger equation and can be employed to achieve Bose-Einstein condensation (BEC) with transition temperature orders of magnitude higher than that of the atomic BEC. The stationary-DSP BEC is a three-dimensional system and has a far longer lifetime than the exciton-polariton BEC. In this Letter, we experimentally demonstrated the stationary DSP dressed by the Rydberg-state dipole-dipole interaction (DDI). The DDI-induced phase shift of the stationary DSP was systematically studied. Notably, the experimental data are consistent with the theoretical predictions. The phase shift can be viewed as a consequence of elastic collisions. In terms of thermalization to achieve BEC, the μm^{2}-size interaction cross section of the DDI can produce a sufficient elastic collision rate for the stationary DSPs. This Letter makes a substantial advancement toward the realization of the stationary-DSP BEC.
The generation of stationary distributions of light with three-dimensional confinement is discussed and a novel scheme for Bose-Einstein condensation of the associated quasi-particles, dark-state polaritons (DSP), is proposed. DSPs are created in the Raman interaction of laser fields with atoms and are the basis of ultra-slow, stopped, and stationary light. Stationary DSPs have a quadratic dispersion profile with very small and variable effective mass and have a long intrinsic lifetime. Due to the small mass the corresponding condensation temperature can be many orders of magnitude higher than that of atoms. After introducing stationary dark-state polaritons their incoherent generation and thermalization is discussed and conditions for condensation analyzed. Finally potential methods for an experimental observation of the condensation will be put forward.