Theory of Three-Photon Transport Through a Weakly Coupled Atomic Ensemble
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908860795584512 |
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| author | Wang, Yangming Demazure, Noe Mahmoodian, Sahand |
| author_facet | Wang, Yangming Demazure, Noe Mahmoodian, Sahand |
| contents | Understanding multi-photon interactions in non-equilibrium quantum systems is an outstanding challenge in quantum optics. In this work, we develop an analytical and diagrammatic framework to explore three-photon interactions in atomic ensembles weakly coupled to a one-dimensional waveguide. Taking advantage of the weak coupling, we use our diagrammatic framework to perform perturbation theory and calculate the leading-order contributions to the three-photon wavefunction, which would otherwise be intractable. We then compute the outgoing photon wavefunction of a resonantly driven atomic ensemble, with photon-photon interactions truncated up to three photons. Our formulation not only captures the individual transmission of photons but also isolates the connected S-matrix elements that embody genuine photon-photon correlations. Through detailed analysis, we obtain the analytic expressions of the connected third-order correlation function and the third-order electric-field-quadrature cumulant, which reveal non-Gaussian signatures emerging from the interplay of two- and three-photon processes. We also calculate the optical depth where non-Gaussian photon states can be observed. Numerical simulations based on a cascaded master equation validate our analytical predictions on a small-scale system. These results provide a formalism to further explore non-equilibrium quantum optics in atomic ensembles and extend this to the regime of non-Gaussian photon transport. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theory of Three-Photon Transport Through a Weakly Coupled Atomic Ensemble Wang, Yangming Demazure, Noe Mahmoodian, Sahand Quantum Physics Optics Understanding multi-photon interactions in non-equilibrium quantum systems is an outstanding challenge in quantum optics. In this work, we develop an analytical and diagrammatic framework to explore three-photon interactions in atomic ensembles weakly coupled to a one-dimensional waveguide. Taking advantage of the weak coupling, we use our diagrammatic framework to perform perturbation theory and calculate the leading-order contributions to the three-photon wavefunction, which would otherwise be intractable. We then compute the outgoing photon wavefunction of a resonantly driven atomic ensemble, with photon-photon interactions truncated up to three photons. Our formulation not only captures the individual transmission of photons but also isolates the connected S-matrix elements that embody genuine photon-photon correlations. Through detailed analysis, we obtain the analytic expressions of the connected third-order correlation function and the third-order electric-field-quadrature cumulant, which reveal non-Gaussian signatures emerging from the interplay of two- and three-photon processes. We also calculate the optical depth where non-Gaussian photon states can be observed. Numerical simulations based on a cascaded master equation validate our analytical predictions on a small-scale system. These results provide a formalism to further explore non-equilibrium quantum optics in atomic ensembles and extend this to the regime of non-Gaussian photon transport. |
| title | Theory of Three-Photon Transport Through a Weakly Coupled Atomic Ensemble |
| topic | Quantum Physics Optics |
| url | https://arxiv.org/abs/2507.03428 |