Interaction between Atoms and Slow Light: A Study in Waveguide Design

Xiaorun Zang, Jianji Yang, Rémi Faggiani, Christopher Gill, Plamen G. Petrov, Jean-Paul Hugonin, Kevin Vynck, Simon Bernon, Philippe Bouyer, Vincent Boyer, and Philippe Lalanne

Phys. Rev. Applied 5, 024003 – Published 5 February 2016

Abstract

The emerging field of on-chip integration of nanophotonic devices and cold atoms offers extremely strong and pure light-matter interaction schemes, which may have a profound impact on quantum information science. In this context, a long-standing obstacle is to achieve a strong interaction between single atoms and single photons and at the same time trap atoms in a vacuum at large separation distances from dielectric surfaces. In this work, we study waveguide geometries that challenge these conflicting objectives. The designed photonic-crystal waveguide is expected to offer a good compromise, which additionally allows for easy manipulation of atomic clouds around the structure, while being tolerant to fabrication imperfections.

Received 2 November 2015

DOI:https://doi.org/10.1103/PhysRevApplied.5.024003

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Quantum description of light-matter interaction Quantum information with atoms & light

Waveguides

Quantum Information, Science & Technology

Authors & Affiliations

Xiaorun Zang¹, Jianji Yang¹, Rémi Faggiani¹, Christopher Gill², Plamen G. Petrov², Jean-Paul Hugonin³, Kevin Vynck¹, Simon Bernon¹, Philippe Bouyer¹, Vincent Boyer², and Philippe Lalanne^1,*

¹Laboratoire Photonique Numérique et Nanosciences (LP2N), UMR 5298, CNRS-IOGS-Univ. Bordeaux, 33400 Talence, France
²University of Birmingham, School of Physics and Astronomy, Birmingham B15 2TT, West Midlands, England, United Kingdom
³Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau, France

^*Corresponding author. philippe.lalanne@institutoptique.fr

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Vol. 5, Iss. 2 — February 2016

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Images

Figure 1
Robustness to fabrication inaccuracies near the boundary of the first Brillouin zone. The green solid curve shows the ideal (no fabrication error) dispersion curve of a hybrid-clad waveguide with a channel width of $L = 240 nm$ . At the atom-line frequency $ω_{A}$ , the theoretical group velocity is $v_{0}$ . Because of slight inevitable fabrication errors, the targeted ideal dispersion curve is never implemented, and the actual dispersion curves correspond to slightly shifted versions of the ideal dispersion curve. The blue dash-dotted and red dashed curves are obtained by assuming that the channel widths are $L = 240 \mp 2 nm$ . Thus, the actual group velocity is no longer $v_{0}$ at $ω = ω_{A}$ , but $v_{0} + Δ v_{g}$ . Note that a blueshift (redshift) results in a Bloch state with a larger (smaller) group velocity. Note also that, if the targeted group velocity is not large enough, a redshift may result in a Bloch state with an evanescent character (as illustrated in the figure).
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Figure 2
TIR versus PhC guidance for controlling mode flatness. (a) Guidance is achieved with total-internal-reflection (TIR) in Bragg-type waveguides. The effective index modulation is very weak, especially for extended modes. This results in a very small effective mass. (b) With photonic-crystal (PhC) guidance, the zigzag propagation exhibits an additional phase $ϕ$ at the reflection on the PhC clads, and $d ϕ / d λ$ represents an additional degree of freedom to control the mode flatness. (c) Schematic dispersion curves of structures shown in (a) and (b). (d) Dispersion curves of alligator (solid blue, $m c = 0.6 μ m^{- 1}$ ) waveguide [11] and hybrid-clad waveguide for $L = 240 nm$ (dashed red, $m c = 36 μ m^{- 1}$ ). (e) Dispersion curves of the 1D-Bragg waveguide (green solid, $m c = 4 μ m^{- 1}$ ) and W1 waveguide (purple dashed, $m c = 40 μ m^{- 1}$ ) [26].
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Figure 3
Hybrid-clad waveguide geometry. (a) Sketch of the geometry (only four rows of air holes are shown on the left side of the waveguide). The atoms decay into the fundamental guided mode and the continuum of radiation modes with decay rates $γ_{M}$ and $γ_{rad}$ , respectively. (b) The red, green, and blue (from top to bottom) dispersion curves represent the guided TE-like Bloch mode for channel widths $L = 230$ , 240, and 250 nm and effective masses $m c = 22.6$ , 36.1, and $177.6 μ m^{- 1}$ , respectively. The band gap of the bulk photonic crystal opens in a frequency range of [345,400] THz. The vacuum light line is shown with the black line. (c),(d) Distributions of the dominant electric-field components ( $| E_{x} |$ , $| E_{z} |$ ) for $n_{g} = 50$ along the gray symmetry planes shown in (a). All results in (b) and (c) hold for $a = 340 nm$ , $r = 0.3 a$ , and $h = 300 nm$ .
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Figure 4
Reflectance of a single atom for $ω_{L} = ω_{A}$ as a function of the atom position in the main symmetry planes. $Δ x$ denotes the $x$ -separation distance from the vertical sidewall of the waveguide ( $Δ x = 0$ corresponds to the sidewall boundary). (a) The atom is placed in the $x − z$ horizontal plane [see Fig. 3], and $n_{g} = 50$ . (b) The atom is placed in the $x − y$ vertical plane [see Fig. 3], and $n_{g} = 50$ . (c) Reflectance for $y = 0$ and $z = a / 2$ and for $n_{g} = 2$ , 10, 50, and 100. The black contour line in (a) and (b) indicates a reflectance of 0.75.
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