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arXiv:1906.09120 · Physical Review A

Light propagation in systems involving two-dimensional atomic lattices

Juha Javanainen, Renuka Rajapakse

Published Jul 15, 2019• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.100.013616

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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.
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 cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and super-radiant collective excitation eigenmodes, direct numerical solutions, and analytical transfer-matrix methods. We illustrate how the spectrum of transmitted light through the waveguide, including the emergence of narrow Fano resonances, can be understood by the resonance features of the eigenmodes. We describe a method based on super-radiant and subradiant modes to engineer the optical response of the waveguide and to store light. The stopping of light is obtained by transferring an atomic excitation to a subradiant collective mode with the zero radiative resonance linewidth by controlling the level shift of an atom in the waveguide. Moreover, we obtain an exact analytic solution for the transmitted light through the waveguide for the case of a regular lattice of atoms and provide a simple description of how the light transmission may present large resonance shifts when the lattice spacing is close, but not exactly equal, to half of the wavelength of the light. Experimental imperfections such as fluctuations of the positions of the atoms and loss of light from the waveguide are easily quantified in the numerical simulations, which produce the natural result that the optical response of the atomic array tends toward the response of a gas with random atomic positions.
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 study excitations of the local field (locsitons) in nanoscale two-dimensional (2D) lattices of strongly interacting resonant atoms and various unusual effects associated with them. Locsitons in low-dimensional systems and the resulting spatial strata and more complex patterns on a scale of just a few atoms were predicted by us earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133902 (2008)]. These effects present a radical departure from the classical Lorentz-Lorenz theory of the local field (LF), which assumes that the LF is virtually uniform on this scale. We demonstrate that the strata and patterns in the 2D lattices may be described as an interference of plane-wave locsitons, build an analytic model for such unbounded locsitons, and derive and analyze dispersion relations for the locsitons in an equilateral triangular lattice. We draw useful analogies between 1D and 2D locsitons but also show that the 2D case enables locsitons with the most diverse and unusual properties. Using the nearest-neighbor approximation, we find the locsiton frequency band for different mutual orientations of the lattice and the incident field. We demonstrate a formation of distinct vector locsiton patterns consisting of multiple vortices in the LF distribution and suggest a way to design finite 2D lattices that exhibit such patterns at certain frequencies. We illustrate the role of lattice defects in supporting localized locsitons and also demonstrate the existence of ``magic shapes,'' for which the LF suppression at the exact atomic resonance is canceled.
We report some investigations on the existence of matter-wave solitons when considering cross-combined optical lattices (OL) in three dimensions (3D), where we have a nonlinear OL in one of the directions, which is perpendicular to a two-dimensional (2D) plane with linear OLs in either one or both directions. This study can be useful to manage 3D solitons through spatial modulations of the scattering length in one of the OL directions. Another independent study is reported, by considering bright solitons manifested in a bosonic condensate gas carrying collinear dipole moments, which induces an external polarizing field with strength periodically modulated along one of the coordinates. This leads to an effective nonlocal nonlinear lattice, with solitonic solutions. Their dynamics and mobility can be investigated by an effective one-dimensional (1D) model. Interactions between solitons are also reported within this 1D model. In all the cases, we consider full numerical and variational approaches.