Enhanced Optical Cross Section via Collective Coupling of Atomic Dipoles in a 2D Array

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Enhanced Optical Cross Section via Collective Coupling of Atomic Dipoles in a 2D Array

Robert J. Bettles, Simon A. Gardiner, and Charles S. Adams

Phys. Rev. Lett. 116, 103602 – Published 9 March 2016

Abstract

Enhancing the optical cross section is an enticing goal in light-matter interactions, due to its fundamental role in quantum and nonlinear optics. Here, we show how dipolar interactions can suppress off-axis scattering in a two-dimensional atomic array, leading to a subradiant collective mode where the optical cross section is enhanced by almost an order of magnitude. As a consequence, it is possible to attain an optical depth which implies high-fidelity extinction, from a monolayer. Using realistic experimental parameters, we also model how lattice vacancies and the atomic trapping depth affect the transmission, concluding that such high extinction should be possible, using current experimental techniques.

Received 27 October 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.103602

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cold gases in optical lattices Effects of atomic coherence on light propagation

Atomic, Molecular & Optical

Authors & Affiliations

Robert J. Bettles^*, Simon A. Gardiner^†, and Charles S. Adams^‡

Department of Physics, Joint Quantum Center (JQC) Durham-Newcastle, Durham University, South Road, Durham DH1 3LE, United Kingdom

^*r.j.bettles@durham.ac.uk
^†s.a.gardiner@durham.ac.uk
^‡c.s.adams@durham.ac.uk

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Issue

Vol. 116, Iss. 10 — 11 March 2016

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Images

Figure 1
Resonant optical transmission of a Gaussian beam through a random 2D monolayer of $N = 100$ interacting dipoles. As the 2D number density $N_{2 D}$ increases, the interacting monolayer (blue solid line) deviates from $T_{ind}$ (black dotted line), which assumes each dipole is a noninteracting opaque disk of cross sectional area $σ_{0}$ . Each data point is averaged over 100 realizations. The beam waist is $w_{0} ≃ 2.5 λ$ , and the collection lens has radius $R_{L} = 90 λ_{0}$ and position $z_{L} = 150 λ_{0}$ . (Inset) Weak cancellation of the total electric field magnitude $| E |$ in the $x z$ plane downstream of the monolayer ( $N_{2 D} ≃ 1.5 λ_{0}^{- 2}$ ). $x$ and $z$ vary between $\pm 6 λ_{0}$ and $\pm 30 λ_{0}$ , respectively. The Gaussian beam propagates with vector ${\hat{k}}_{L} = \hat{z}$ . The black dashed line shows the $1 / e$ beamwidth and the white circles the atom positions.
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Figure 2
Resonant optical transmission of a Gaussian beam through a triangular 2D array of $N = 102$ interacting dipoles (blue solid line). Unlike the random monolayer in Fig. 1, the transmission goes below and above $T_{ind}$ (black dotted line). $A$ , $B$ , and $C$ correspond to the lattice spacings used in Fig. 3. (Inset) At $a = 0.87 λ_{0}$ ( $N_{2 D} ≃ 1.5 λ_{0}^{- 2}$ ), the dipole and driving fields almost perfectly cancel downstream of the lattice, resulting in less than 1% transmission over the collection lens. The same parameters for the beam, lens, and inset are used as in Fig. 1.
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Figure 3
Transmission as a function of detuning through an $N = 102$ triangular lattice of interacting dipoles. The lattice spacings in (a)–(c) correspond to those labeled $A$ , $B$ , and $C$ in Fig. 2 (inset: $a / λ_{0} = 0.67, 0.92$ ). The solid lines plot the full interacting transmission for the same beam and lenses as Fig. 1. The dotted lines show $T_{ind}$ (i.e., assuming no interactions). The vertical dashed lines at $Δ = 0$ have dash lengths $Δ T = 0.05$ .
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Figure 4
The effect of finite trap depth (a) and finite filling factors (b) on resonant optical transmission through a $10 \times 10$ square lattice. (a) The trap depths are $V_{0} = \infty$ (grey dashed), $V_{0} = 5000 E_{R}$ (purple), $V_{0} = 500 E_{R}$ (blue), $V_{0} = 50 E_{R}$ (red), and $V_{0} = 5 E_{R}$ (green), where $E_{R}$ is the recoil energy and the filling is 100%. (b) The lattice sites are randomly occupied with filling factors of 100% (grey dashed), 90% (purple), 80% (blue), 70% (red), 60% (green), and 50% (pink), with $V_{0} = \infty$ . The purple line in the inset is a combination of finite trap depth ( $V_{0} = 50 E_{R}$ ) and 90% filling. Each line is an average of several hundred realizations. The same lens and beam parameters as in Fig. 1 are used.
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