Abstract
We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. The method allows us to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments.
Highlights
Weak interactions of photons with each other are the basis for many applications of light signals in areas such as optical communication
We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states
Many other applications in classical and quantum communication, computation, and metrology would greatly benefit from tunable photon-photon interactions
Summary
Weak interactions of photons with each other are the basis for many applications of light signals in areas such as optical communication. In the Rydberg-EIT system, a photon entering the atomic gas is converted into a slow-light polariton with a substantial admixture of the Rydberg state. It is the latter admixture that maps the Rydberg-Rydberg interaction onto an effective interaction between slow Rydberg polaritons. Within this approach, a single-photon source [11] and switch [29,30,31] were realized, the photon blockade [13] and the formation of bound states of Rydberg polaritons [14] have been demonstrated, and atom-photon entanglement was observed [32]. A full description of the system, including the short-range and finite-energy effects relevant to ongoing experiments [13,14], is limited to extended numerical simulations [10,34]
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