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.
Highlights
Atomic arrays with subwavelength lattice structures are found to be an ideal platform where electric dipole-dipole interactions between atoms are mediated by photons [9–18]
We study the effect of the discrepancy of optical lattices for the ground state and excited state atoms, where the transition of the internal state can be accompanied by transitions in the motional degree of freedom
We study quantum atomic arrays using a microscopic model with atoms in optical lattices
Summary
The ability to coherently storing photons and controlling their interaction with quantum matters is of vital importance for quantum science. There are proposals for realizing non-trivial topology in atomic arrays [19–21], controlling atom-photon interaction using atomic arrays [22–26], and efforts in understanding their subradiant behaviors and ability of photon storage [26–32]. In most of these works, atoms are treated as point-like with no motional degree of freedom. Atoms are trapped near the potential minimum, the wave function for the motional degree of freedom may still play a role. We study the effect of the discrepancy of optical lattices for the ground state and excited state atoms, where the transition of the internal state can be accompanied by transitions in the motional degree of freedom.
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