Photon statistics in chiral waveguide QED: I Mean field and perturbative expansions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910041580240896 |
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| author | Eltohfa, M. Robicheaux, F. |
| author_facet | Eltohfa, M. Robicheaux, F. |
| contents | Waveguide Quantum Electrodynamics (WQED) offers a suitable stage for controlling the interaction of light with atoms, allowing for collective phenomena such as super- and subradiance. In a chiral waveguide setup, the quantum state evolves through all the Hilbert space, rendering an exact theoretical treatment exponentially hard and unobtained to date for more than $\sim 20$ atoms. In this work, we use a computationally efficient higher order mean-field approximation to model the radiation dynamics in a chirally coupled array of atoms, showing good agreement with recent experimental results. Further, based on a perturbative approximation of the full dynamics, we develop an analytical solution that captures photon statistics for a moderate atom number, $N$, and a homogeneous atom-waveguide coupling, $β$. Finally, we show that capturing the onset of second-order coherence from a fully inverted state requires a fourth-order mean-field approximation, as lower-order treatments fail to account for the necessary four-body correlations. These results illustrate the complex behavior of a symmetry-lacking system, and the methods discussed here provide systematic analytical solutions to which semi-classical methods such as the cumulant expansion or the truncated Wigner approximation can be benchmarked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04591 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Photon statistics in chiral waveguide QED: I Mean field and perturbative expansions Eltohfa, M. Robicheaux, F. Quantum Physics Atomic Physics Waveguide Quantum Electrodynamics (WQED) offers a suitable stage for controlling the interaction of light with atoms, allowing for collective phenomena such as super- and subradiance. In a chiral waveguide setup, the quantum state evolves through all the Hilbert space, rendering an exact theoretical treatment exponentially hard and unobtained to date for more than $\sim 20$ atoms. In this work, we use a computationally efficient higher order mean-field approximation to model the radiation dynamics in a chirally coupled array of atoms, showing good agreement with recent experimental results. Further, based on a perturbative approximation of the full dynamics, we develop an analytical solution that captures photon statistics for a moderate atom number, $N$, and a homogeneous atom-waveguide coupling, $β$. Finally, we show that capturing the onset of second-order coherence from a fully inverted state requires a fourth-order mean-field approximation, as lower-order treatments fail to account for the necessary four-body correlations. These results illustrate the complex behavior of a symmetry-lacking system, and the methods discussed here provide systematic analytical solutions to which semi-classical methods such as the cumulant expansion or the truncated Wigner approximation can be benchmarked. |
| title | Photon statistics in chiral waveguide QED: I Mean field and perturbative expansions |
| topic | Quantum Physics Atomic Physics |
| url | https://arxiv.org/abs/2603.04591 |