Simulating One Dimensional Physics With Stationary Dark Polaritons

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.