Trapping Effects in Quantum Atomic Arrays

TL;DR

This paper presents a microscopic quantum approach to study trapping effects in atomic arrays, revealing how mismatched trapping potentials and recoil influence optical responses, aligning with recent experimental findings.

Contribution

It introduces a novel microscopic quantum method using creation and annihilation operators to analyze trapping effects beyond previous spin-based models.

Findings

Mismatched trapping potentials cause multiple resonances in optical response.

The method aligns with previous results for magic wavelength lattices.

Recoil effects are significant for finite trapping frequencies.

Abstract

Quantum emitters, particularly atomic arrays with subwavelength lattice constant, have been proposed to be an ideal platform for studying the interplay between photons and electric dipoles. In this work, motivated by the recent experiment [1], we develop a microscopic quantum treatment using annihilation and creation operator of atoms in deep optical lattices. Using a diagrammatic approach on the Keldysh contour, we derive the cooperative scattering of the light and obtain the general formula for the $S$ matrix. We apply our method to study the trapping effect, which is beyond previous treatment with spin operators. If the optical lattices are formed by light fields with magical wavelength, the result matches previous results using spin operators. When there is a mismatch between the trapping potentials for atoms in the ground state and the excited state, atomic mirrors become imperfect, with multiple resonances in the optical response. We further study the effect of recoil for large but finite trapping frequency. Our results are consistent with existing experiments.