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arXiv:1712.08013 · Physical Review A

Interaction of light with planar lattices of atoms: Reflection, transmission, and cooperative magnetometry

G. Facchinetti, Janne Ruostekoski

Published Feb 22, 2018• 46 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.023833

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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.
Collective coupling between dipoles can dramatically modify the optical response of a medium. Such effects depend strongly on the geometry of the medium and the polarization of the light. Using a classical coupled dipole model, here we investigate the simplest case of one-dimensional arrays of interacting atomic dipoles driven by a weak laser field. Changing the polarization and direction of the driving field allows us to separately address superradiant, subradiant, redshifted, and blueshifted eigenmodes, as well as observe strong Fano-like interferences between different modes. The cooperative eigenvectors can be characterized by the phase difference between nearest-neighbor dipoles, ranging from all oscillating in phase to all oscillating out of phase with their nearest neighbors. Investigating the eigenvalue behavior as a function of atom number and lattice spacing, we find that certain eigenmodes of an infinite atomic chain have the same decay rate as a single atom between two mirrors. The effects we observe provide a framework for collective control of the optical response of a medium, giving insight into the behavior of more complicated geometries, as well as providing further evidence for the dipolar analog of cavity QED.
By analyzing the parameters of electronic transitions, we show how bosonic Sr atoms in planar optical lattices can be engineered to exhibit optical magnetism and other higher-order electromagnetic multipoles that can be harnessed for wavefront control of incident light. Resonant $\ensuremath{\lambda}\ensuremath{\simeq}2.6\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ light for the $^{3}D_{1}\ensuremath{\rightarrow}{}^{3}{P}_{0}$ transition mediates cooperative interactions between the atoms while the atoms are trapped in a deeply subwavelength optical lattice. The atoms then exhibit collective excitation eigenmodes, e.g., with a strong cooperative magnetic response at optical frequencies, despite individual atoms having negligible coupling to the magnetic component of light. We provide a detailed scheme to utilize excitations of such cooperative modes consisting of arrays of electromagnetic multipoles to form an atomic Huygens' surface, with complete $2\ensuremath{\pi}$ phase control of transmitted light and almost no reflection, allowing nearly arbitrary wavefront shaping. In the numerical examples, this is achieved by controlling the atomic level shifts of Sr with off-resonant ${^{3}P}_{J}\ensuremath{\rightarrow}{^{3}D}_{1}$ transitions, which results in a simultaneous excitation of arrays of electric dipoles and electric quadrupoles or magnetic dipoles. We demonstrate the wavefront engineering for a Sr array by realizing the steering of an incident beam and generation of a baby-Skyrmion texture in the transmitted light via a topologically nontrivial transition of a Gaussian beam to a Poincar\'e beam, which contains all possible polarizations in a single cross-section.
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.