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The European Physical Journal Special Topics

The refractive index of a single three-level atom: quantum state separator

Jacob Emerick, Trever Harborth, Anil K. Patnaik, Yuri V. Rostovtsev

Published Oct 21, 2025• 2 citations
Publisher
DOI
10.1140/epjs/s11734-025-02018-8

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We study the propagation of a quantum field composed of a few photons interacting with a three-level Λ -atom driven by a coherent classical field. The quantum field acquires a phase shift, which can be interpreted as a dispersion effect on the photon wave packet and described by the refractive index for quantum fields down to the single-photon level. In this paper, we demonstrate that the phases acquired by quantum fields depend on the number of photons in the quantum states. Notably, the phases differ between single- and two-photon states, enabling the separation of multiphoton states. This finding highlights new applications related to the dispersion of three-level atoms, which are important in advancing quantum information processing and enhancing quantum communication technologies. The results are crucial for long-distance quantum communication and hold potential for developing quantum field-based linear devices such as beam splitters, lenses, and quantum prisms capable of separating different components of quantum fields. The findings can have interesting applications for manipulating and assembling of multiphoton entanglement states.
Atomic coherence phenomena are usually investigated using single beam techniques without spatial resolution. Here we demonstrate state-selective imaging of cold 85Rb^{85}\text{R}\text{b}85Rb atoms in a three-level ladder system, where the atomic refractive index is sensitive to the quantum coherence state of the atoms. We use a phase-sensitive diffraction contrast imaging (DCI) technique which depends on the complex refractive index of the atom cloud. A semiclassical model allows us to analytically calculate the detuning-dependent refractive index of the system. The predicted Autler-Townes splitting and our experimental measurements are in excellent agreement. DCI provided a quantitative image of the distribution of the excited-state fraction, and compared with on-resonance absorption and blue cascade fluorescence techniques, was found to be experimentally simple and robust.