From few to many strongly interacting Rydberg polaritons

本计画旨在实验上实现并详细研究高非线性介质中强相互作用的里德伯极化激元系统。因此，它福尔斯本计划的“里德伯量子光学”类别，致力于实验实现新的多体状态。我们将从两个方面来实现多体里德伯极化激元系统的挑战。一方面，我们将在一个高度拉长的超冷原子云中实现2到10个同时相互作用的极化激元的系统。这使得从强关联（准）粒子的两体物理到多体物理的受控跃迁成为可能，其中所有的相互作用参数都是高度可控和可调的，并且可以通过时间分辨光子计数来测量完整的量子统计和关联。利用这个系统，我们将详细研究里德伯极化激元之间的两体相互作用，目的是观察极化子散射共振和尺寸增加的光子的新束缚态。我们还将研究排斥相互作用的情况，在足够的强度下，排斥相互作用导致玻色子极化激元的费米子化，从而导致多体光子态的结晶。作为有效的一维强相互作用系统的补充，我们将实现更大的三维极化激元液体与较弱的相互作用。我们将扩展我们的调查，传播极化激元的横模的相互作用的影响，我们将直接图像与高灵敏度的相机后，光子通过介质传播。在这个更大的系统中，我们将研究由里德伯相互作用介导的空间孤子的形成。我们希望解决的主要问题之一是在多大程度上对里德伯极化激元系统进行平均场处理是合理的，以及在什么条件下超越平均场效应变得相关。最终，我们计划将这两种方法联合收割机结合起来，实现中等尺寸（>10）的强关联极化激元系统，从中我们仍然可以提取完整的光子统计和关联。这为深入了解强关联系统的微观细节提供了前所未有的途径。

This project aims to experimentally realize and study in detail systems of strongly interacting Rydberg polaritons inside a highly nonlinear medium. It thus falls into the "Rydberg Quantum Optics" category of this programme, addressing the experimental implementation of novel many-body states.We will approach the challenge of realizing many-body Rydberg polariton systems from two sides. On the one hand we will realize systems on the scale of two to ten concurrently interacting polaritons inside a highly elongated ultra-cold atomic cloud. This enables a controlled transition from two- to many-body physics of strongly correlated (quasi-)particles, where all interaction parameters are highly controlled and tunable and measurement of the full quantum statistics and correlations through time-resolved photon counting is possible.With this system we will study in detail the two-body interaction between Rydberg polaritons, with the goal of observing polariton scattering resonances and novel bound states of photons of increasing size. We will also investigate the case of repulsive interactions, which, at sufficient strength, leads to the fermionization of the bosonic polaritons, resulting in the crystallization of the many-body photon state.Complementary to the effectively one-dimensional strongly interacting system, we will realize larger three-dimensional polariton liquids with weaker interaction. We will extend our investigation to the effect of interactions on the transverse mode of propagating polaritons, which we will directly image with a high-sensitivity camera after the photons have propagated through the medium. In this larger system, we will investigate the formation of spatial solitons mediated by Rydberg interaction. One of the main questions we hope to address is to what extend mean-field treatments of the Rydberg polariton system is justified and under which condition beyond mean-field effect become relevant.Ultimately, we plan to combine the two approaches and to realize strongly correlated polariton systems of moderate size (>10), from which we can still extract the full photon statistics and correlations. This gives unprecedented access to the microscopic details of a strongly correlated system.