Cooperative eigenmodes and scattering in one-dimensional atomic arrays

Abstract

Publisher's copyright statement:Reprinted with permission from the American Physical Society: Bettles, Robert J. and Gardiner, Simon A. and Adams, Charles S. (2016) 'Cooperative eigenmodes and scattering in one-dimensional atomic arrays.', Physical review A., 94 (4). 043844 c 2016 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 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.

Subradiance-protected excitation transport

“…An ensemble of emitters couples collectively to a common electromagnetic bath, as was already investigated theoretically in the seminal papers of Dicke, Lehmberg and Agarwal in the 1950s and 70s [1][2][3]. Here, the exchange of virtual photons results in induced dipole-dipole interactions [4][5][6] and collective Lamb and Lorentz-Lorenz shifts [7][8][9][10][11][12][13]. Moreover, the emission of photons into the bath takes place at a rate much faster or slower (so-called super-and subradiance, respectively) than the single atom decay rate [14][15][16][17][18][19][20][21].…”

Exact electrodynamics versus standard optics for a slab of cold dense gas

“…The growing throughput of computers available to researchers is making such a plan practical. These methods, whether called classicalelectrodynamics simulations or coupled-dipole simulations, are now a routine theoretical tool [2,4,7,8,[14][15][16][17][18][19][20][21][22][23][24][25][26]. Closely related numerical techniques based on the analysis of the eigenstates of the coupled system of the light and the atoms [15,[27][28][29][30][31][32] or density matrices and quantum trajectories [33][34][35] are also widely used today.…”

Optimization of photon storage fidelity in ordered atomic arrays

“…Techniques to reversibly map between photonic and atomic excitations in arrays should find a variety of exciting applications. For example, it would allow for photonic quantum gates, given some form of spin interactions in the array (such as between Rydberg levels [64]), or would allow for exotic spin states (like subradiant [24][25][26][27][28][29] or topological excitations [31,32]) to be detected optically. It would also be interesting to investigate whether the spin state itself could be engineered to produce a useful non-classical state of outgoing light.…”

“…Intuitively, one expects that strong interference in light emission can emerge, which renders inoperable the typical theoretical approaches to modeling light-atom interfaces. Theoretically there has been growing interest in novel quantum optical effects in arrays, such as subradiance [24][25][26][27][28][29][30], topological effects [31,32], and complete reflection of light [33][34][35]. Indeed, it has already been shown numerically that an ordered one-dimensional array of atoms coupled to a nanofiber allows for a storage error exponentially smaller than the previously known bound [29].…”