Based on the narrow linewidth ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition of the bosonic ${}^{88}$ Sr atom, we investigate the dispersion relation for light propagating in a three-dimensional (3D) atomic dipolar lattice. Two factors determine the presence of the photonic band gap (PBG): lattice geometry and the atomic polarization. For a two-level atomic system, the former factor plays a major role. An omnidirectional PBG is predicted in the non-Bravais diamond lattice while no PBG exists in the Bravais lattices. However, since a PBG happens around the resonant ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ line, the probe beam suffers a significant atomic absorption, which is the major drawback in Bragg scattering. We propose applying an external field to couple the atomic ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ transition so as to modify the atomic polarization of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition. In the three level ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ atomic system, the atomic polarization strongly affects the band structure besides the lattice geometry. Dual PBGs can exist in simple cubic and face-centered cubic lattices, but the original PBG, in the diamond lattice composed of the two-level atoms, vanishes. Meanwhile, since two PBGs can be pushed far away from the atomic resonant ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ line, the atomic absorption is significantly suppressed, which enhances the reflection efficiency in Bragg scattering.Based on the narrow linewidth ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition of the bosonic ${}^{88}$Sr atom, we investigate the dispersion relation for light propagating in a three-dimensional (3D) atomic dipolar lattice. Two factors determine the presence of the photonic band gap (PBG): lattice geometry and the atomic polarization. For a two-level atomic system, the former factor plays a major role. An omnidirectional PBG is predicted in the non-Bravais diamond lattice while no PBG exists in the Bravais lattices. However, since a PBG happens around the resonant ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ line, the probe beam suffers a significant atomic absorption, which is the major drawback in Bragg scattering. We propose applying an external field to couple the atomic ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ transition so as to modify the atomic polarization of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition. In the three level ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ atomic system, the atomic polarization strongly affects the band structure besides the lattice geometry. Dual PBGs can exist in simple cubic and face-centered cubic lattices, but the original PBG, in the diamond lattice composed of the two-level atoms, vanishes. Meanwhile, since two PBGs can be pushed far away from the atomic resonant ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ line, the atomic absorption is significantly suppressed, which enhances the reflection efficiency in Bragg scattering.

Physical Review AOct 20, 201110 citations

Photonic Band Structure of Atomic Lattices

D. V. van Coevorden, Rudolf Sprik, A. Tip +1 more

A calculation of the optical band structure of a three dimensional lattice of resonant two-level atoms in the dipole approximation is presented. The formation of band gaps is exhibited and confirmed by a calculation of the density of states. The band structure can be characterized by two dimensionless parameters. We find a longitudinal polarization mode as well as a class of vacuum modes that are unaltered by the interaction with matter. Numerical calculations are performed for a face centered cubic lattice; other lattices can be evaluated as easily.A calculation of the optical band structure of a three dimensional lattice of resonant two-level atoms in the dipole approximation is presented. The formation of band gaps is exhibited and confirmed by a calculation of the density of states. The band structure can be characterized by two dimensionless parameters. We find a longitudinal polarization mode as well as a class of vacuum modes that are unaltered by the interaction with matter. Numerical calculations are performed for a face centered cubic lattice; other lattices can be evaluated as easily.

Physical Review LettersSep 16, 199677 citations

Band Structure and Dynamics of Single Photons in Atomic Lattices

Wenxuan Xie, John C. Schotland

We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.

quant-pharXiv:2512.24596Physical Review AJan 1, 20260 citations

Microscopic theory of photonic band gaps in optical lattices

Marina Samoylova, N. Piovella, Romain Bachelard +1 more

arXiv:1302.5030Optics CommunicationsSep 20, 201313 citations

Based on the narrow linewidth ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition of the bosonic

{}^{88}

Sr atom, we investigate the dispersion relation for light propagating in a three-dimensional (3D) atomic dipolar lattice. Two factors determine the presence of the photonic band gap (PBG): lattice geometry and the atomic polarization. For a two-level atomic system, the former factor plays a major role. An omnidirectional PBG is predicted in the non-Bravais diamond lattice while no PBG exists in the Bravais lattices. However, since a PBG happens around the resonant ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ line, the probe beam suffers a significant atomic absorption, which is the major drawback in Bragg scattering. We propose applying an external field to couple the atomic ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ transition so as to modify the atomic polarization of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition. In the three level ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ atomic system, the atomic polarization strongly affects the band structure besides the lattice geometry. Dual PBGs can exist in simple cubic and face-centered cubic lattices, but the original PBG, in the diamond lattice composed of the two-level atoms, vanishes. Meanwhile, since two PBGs can be pushed far away from the atomic resonant ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ line, the atomic absorption is significantly suppressed, which enhances the reflection efficiency in Bragg scattering.