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Optics Express

Light reflection and transmission in planar lattices of cold atoms

Sung-Mi Yoo, Juha Javanainen

Published Mar 9, 2020• 11 citations
Publisher

Abstract

Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Here we present a theoretical scheme that enables efficient computation of collective optical responses of mono- and bi-layer planar square lattices of dense, cold two-level atoms using classical electrodynamics of coupled dipoles in the limit of low laser intensity. The steady-state transmissivity and reflectivity are obtained at a field point far away from the atomic lattices in the regime with no Bragg reflection. While our earlier method was based on exact solution of the electrodynamics for a small-scale lattice, here we calculate the dipole moments assuming that they are the same at all lattice sites, as for an infinite lattice. Atomic lattices with effectively over one hundred times more sites than in our earlier exact computations can then be simulated numerically with fewer computational resources. We have implemented an automatic selection of the number of sites under the given convergence criteria. We compare the numerical results from both computational schemes. We also find similarities and differences of a stack of two atomic lattices from a two-atom sample. Such aspects may be exploited to engineer a stack for potential applications.

DOI
10.1364/oe.389570

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Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Here we present a theoretical scheme that enables efficient computation of collective optical responses of mono- and bi-layer planar square lattices of dense, cold two-level atoms using classical electrodynamics of coupled dipoles in the limit of low laser intensity. The steady-state transmissivity and reflectivity are obtained at a field point far away from the atomic lattices in the regime with no Bragg reflection. While our earlier method was based on exact solution of the electrodynamics for a small-scale lattice, here we calculate the dipole moments assuming that they are the same at all lattice sites, as for an infinite lattice. Atomic lattices with effectively over one hundred times more sites than in our earlier exact computations can then be simulated numerically with fewer computational resources. We have implemented an automatic selection of the number of sites under the given convergence criteria. We compare the numerical results from both computational schemes. We also find similarities and differences of a stack of two atomic lattices from a two-atom sample. Such aspects may be exploited to engineer a stack for potential applications.
We theoretically investigate the optical response of many cold atoms within a pair of identical planar lattices mostly in a dense regime using microscopic electrodynamics numerical simulations. We find cooperative optical properties of the double atomic lattices to a normal incidence of low-intensity radiation at particular ranges of sample parameters. The main findings are that resonance shifts, linewidths, and transmittance could be engineered by varying layer-to-layer distance, lattice constant, and parameters for incident light. We also propose a bilayer atomic lattice could be modeled as two effective superatoms. Simulation results qualitatively agree with the ones from an isotropic infinite lattice model in the ranges of external parameters for which a mean-field approximation is not valid. Hopefully, our bilayer lattice samples might be exploited for implementing an optical switch and a photonic device in quantum computing.
We study light propagation in dense low-temperature atoms on two-dimensional (2D) square and kagome lattices using a basically exact large-scale numerical computations. In the limit of weak laser intensity, shifts of the resonance line are shown in homogeneously broadened stationary samples with high atom densities, whereas the shifts are not shown in the samples with low densities. We obtain the dependence of shifts on interatomic spacing for square lattices with the various numbers of atoms, and our numerical results are in good agreement with shifts derived using a 2D isotropic infinite lattice model and experimental data for nanometric-thickness atomic ensembles in the literature.
We study strong, light-mediated, resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a ``superatom'' whose response is similar to electromagnetically induced transparency but which exhibits an ultranarrow collective size-dependent subradiant resonance linewidth. The superatom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions for the resonance linewidths of the collective eigenmodes. We propose a protocol to transfer almost the entire radiative excitation to a single correlated subradiant eigenmode in a lattice and show that the medium obtained by stacked lattice arrays can form a cooperative magnetometer. Such a magnetometer utilizes similar principles as magnetometers based on the electromagnetically induced transparency. The accuracy of the cooperative magnetometer, however, is not limited by the single-atom resonance linewidth but the much narrower collective linewidth that results from the strong dipole-dipole interactions.
We study the optical response of a two-dimensional (2D) square lattice of atoms using classical electrodynamics. Because of dipole-dipole interactions, the lattice atoms polarize as if the lattice were an atom with up to three resonance frequencies, with cooperatively shifted resonances and altered transition linewidths. We show that when the distance between two 2D lattices is large enough and Bragg reflections are absent, the lattices interact among themselves as if they radiated a plane wave whose amplitude is in accordance with the radiation from a dipole moment continuously distributed in the lattice plane. We employ these results to study light propagation in stacks of 2D lattices, drawing on simple qualitative pictures of the response of a 2D lattice and light propagation in one-dimensional (1D) waveguides. We show that a stack of 2D lattices may emulate regularly spaced atoms in a lossless 1D waveguide, and argue that in a suitable geometry the resonance shifts characteristic of 1D and 2D lattice structures may completely cancel to eliminate density-dependent resonance shifts of atoms bound to a three-dimensional (3D) lattice. A generalization to the case of anisotropic polarizability, such as in the presence of a magnetic field, reveals light frequencies induced by the magnetic field for which a 2D lattice is either completely transparent or completely opaque.
Light propagation in disordered media is a fundamental and important problem in optics and photonics. In particular, engineering light-matter interaction in disordered cold atomic ensembles is one of the central topics in modern quantum and atomic optics. The collective response of dense atomic gases under light excitation, which crucially depends on the spatial distribution of atoms and the geometry of the ensemble, has important impacts on quantum technologies like quantum sensors, atomic clocks and quantum information storage. Here we analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on the coupled-dipole simulations under different atom number densities and correlation lengths, we show that the collective effects are strongly influenced by those positional correlations, manifested as significant shifts and broadening or narrowing of transmission resonance lines. We also analyze the eigenstate distribution of different atomic ensembles. This work may provide profound implications on collective and cooperative effects in cold atomic ensembles as well as the study of mesoscopic physics concerning light transport in strongly scattering disorder media.
We determine the transmission of light through a planar atomic array beyond the limit of low light intensity that displays optical bistability in the mean-field regime. We develop a theory describing the intrinsic optical bistability, which is supported purely by resonant dipole-dipole interactions in free space, showing how bistable light amplitudes exhibit both strong cooperative and weak single-atom responses and how they depend on the underlying low light intensity collective excitation eigenmodes. Similarities of the theory with optical bistability in cavities are highlighted, while recurrent light scattering between atoms takes on the role of cavity mirrors. Our numerics and analytic estimates show a sharp variation in the extinction, reflectivity, and group delays of the array, with the incident light completely extinguished up to a critical intensity well beyond the low light intensity limit. Our analysis paves a way for collective nonlinear optics with cooperatively responding dense atomic ensembles.