This readme is for the data submitted in conjunction with the paper:
Title: " Cooperative eigenmodes and scattering in 1D atomic arrays"
Authors: Robert J. Bettles, Simon A. Gardiner, and Charles S. Adams

The data was produced using Matlab and the figures produced in Inkscape. The data in the files described below is the raw data used in the paper figures; the data included is sufficient to reproduce all figures in the paper. 




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Explanations of structure for data files
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Files included in /Fig1/:
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(1.1) Fig1_a_L.csv
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Nearest neighbor spacing a as a function of wavelength lambda

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(1.2) Fig1_gamma_N=51.csv
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Cooperative half-decay rate gamma_N+gamma_0 for the fully anti-phased eigenmode of a chain of N=51 atoms polarized perpendicular to the atomic axis as a function of nearest neighbor spacing a, in units of the natural half-decay rate gamma_0. Red solid line.

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(1.3) Fig1_gamma_N=inf.csv
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Cooperative half-decay rate for a single atom inside a cavity polarized parallel to the mirros as a function of mirror spacing a, taken from Eq. (21). Grey shaded region.



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Files included in /Fig2/:
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(2.1) Fig2_Detuning.csv
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Detuning, in units of the natural half-decay rate gamma_0. 

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(2.2) Fig2a_CS_tot.csv
(2.3) Fig2c_CS_tot.csv
(2.4) Fig2e_CS_tot.csv
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Total scattering cross section (red solid lines) in Figs (a,2.2), (c,2.3), and (e,2.4), as a function of detuning. In units of N times the resonant single atom cross section.

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(2.5) Fig2a_CS_l.csv
(2.6) Fig2c_CS_l.csv
(2.7) Fig2e_CS_l.csv
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Direct scattering cross sections (blue and green solid lines) due to individual modes in Figs (a,2.5), (c,2.6), and (e,2.7), as a function of detuning. The ith row corresponds to the ith eigenmode. In units of N times the resonant single atom cross section.

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(2.8) Fig2b_CS_int.csv
(2.9) Fig2d_CS_int.csv
(2.10) Fig2f_CS_int.csv
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Interference cross sections sigma{l,l'} as defined in Eq. (18) as a function of detuning. In units of N times the resonant single atom cross section.

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(2.11) Fig2_CS_single.csv
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Single atom scattering cross section as a function of detuning, in units of the resonant single atom cross section. Black solid lines in Figs. 2(b,d,f).



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Files included in /Fig3/:
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(3.1) Fig3_eigenvectors.csv
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Eigenvectors of a chain of N=25 atoms. Each column is a different eigenvector, with the column number corresponding to the eigenmode index. Each row is a different atom along the chain. Each element corresponds to the complex amplitude of the dipole vector polarized perpendicular to the atomic axis. 

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(3.2) Fig3_cos_correlation.csv
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Correlation function defined in Eq. (23) for a chain of N=25 atoms polarized perpendicularly to the atomic axis. The ith element in (3.2) corresponds to the ith eigenmode. 



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Files included in /Fig4/:
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(4.1) Fig4_cos_correlation.csv
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Same as (3.2). Red plus signs.

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(4.2) Fig4_Re_correlation.csv
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Real part of the correlation function defined in Eq. (24) for a chain of N=25 atoms polarized perpendicularly to the atomic axis. The ith element in (4.2) corresponds to the ith eigenmode.

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(4.3) Fig4_Im_correlation.csv
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Imaginary part of the correlation function used in (4.2). 



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Files included in /Fig5/:
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(5.1) Fig5_Delta.csv
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Eigenmode shifts in units of the natural half-decay rate gamma_0, for a chain of N=25 atoms polarized perpendicularly to the atomic axis separated by a=0.25lambda. The ith element in (5.1) corresponds to the ith eigenmode.

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(5.2) Fig5_gamma.csv
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Eigenmode half-decay rates in units of the natural half-decay rate gamma_0, for a chain of N=25 atoms polarized perpendicularly to the atomic axis separated by a=0.25lambda. The ith element in (5.2) corresponds to the ith eigenmode.



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Files included in /Fig6/:
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(6.1) Fig6a_Detuning.csv
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Fig. 6(a) - Detuning in units of the natural half-decay rate gamma_0.

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(6.2) Fig6a_N=25_CS_tot.csv
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Fig. 6(a) - Total scattering cross section of a chain of N=25 atoms polarized perpendicularly to the atomic axis as a function of detuning, in units of N times the resonant single atom cross section. Red solid line.

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(6.3) Fig6a_N=25_CS_l.csv
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Fig. 6(a) - Direct scattering cross sections due to individual modes for a chain of N=25 atoms polarized perpendicular to the atomic axis as a function of detuning. The ith row corresponds to the ith eigenmode. In units of N times the resonant single atom cross section.

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(6.4) Fig6a_N=3_CS_tot.csv
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Fig. 6(a) inset - Total scattering cross section of a chain of N=3 atoms polarized perpendicularly to the atomic axis as a function of detuning, in units of N times the resonant single atom cross section. Red solid line.

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(6.5) Fig6a_N=3_CS_l.csv
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Fig. 6(a) inset - Direct scattering cross sections due to individual modes for a chain of N=3 atoms polarized perpendicular to the atomic axis as a function of detuning. The ith row corresponds to the ith eigenmode. In units of N times the resonant single atom cross section.

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(6.6) Fig6b_Detuning.csv
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Fig. 6(b) - Detuning in units of the natural half-decay rate gamma_0.

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(6.7) Fig6b_N=25_CS_tot.csv
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Fig. 6(b) - Total scattering cross section of a chain of N=25 atoms polarized perpendicularly to the atomic axis as a function of detuning, in units of N times the resonant single atom cross section. Red solid line.

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(6.8) Fig6b_N=25_CS_l.csv
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Fig. 6(b) - Direct scattering cross sections due to individual modes for a chain of N=25 atoms polarized perpendicular to the atomic axis as a function of detuning. The ith row corresponds to the ith eigenmode. In units of N times the resonant single atom cross section.



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Files included in /Fig7/:
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(7.1) Fig7abcd_a_L.csv
(7.2) Fig7ef_a_L.csv
(7.3) Fig7aInset_a_L.csv
(7.4) Fig7bInset_a_L.csv
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Nearest neighbor atomic spacing in units of lambda for (7.1): Fig. 7(a-d), (7.2): Fig. 7(e-f), (7.3): Fig. 7(a) Inset, (7.4): Fig. 7(b) Inset

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(7.5) Fig7a_gamma.csv
(7.6) Fig7aInset_gamma.csv
(7.7) Fig7b_gamma.csv
(7.8) Fig7bInset_gamma.csv
(7.9) Fig7e_gamma.csv
(7.10) Fig7f_gamma.csv
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Cooperative half-decay rates of all the eigenmodes of a chain of N=25 atoms polarized perpendicular to the atomic axis [(7.5),(7.6),(7.9)] and parallel to the atomic axis [(7.7),(7.8),(7.10)]. In units of the natural half-decay rate gamma_0. The ith row corresponds to the ith eigenmode. (7.5): Fig. 7(a), (7.6): Fig. 7(a) Inset, (7.7): Fig. 7(b), (7.8): Fig. 7(b) Inset, (7.9): Fig. 7(e), (7.10): Fig. 7(f)

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(7.11) Fig7c_Delta.csv
(7.12) Fig7d_Delta.csv
(7.13) Fig7e_Delta.csv
(7.14) Fig7f_Delta.csv
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Cooperative shifts of all the eigenmodes of a chain of N=25 atoms polarized perpendicular to the atomic axis [(7.11),(7.13)] and parallel to the atomic axis [(7.12),(7.14)]. In units of the natural half-decay rate gamma_0. The ith row corresponds to the ith eigenmode. (7.11): Fig. 7(c), (7.12): Fig. 7(d) Inset, (7.13): Fig. 7(e), (7.14): Fig. 7(f) 



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Files included in /Fig8/:
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(8.1) Fig8_N=3_gamma.csv
(8.2) Fig8_N=11_gamma.csv
(8.3) Fig8_N=25_gamma.csv
(8.4) Fig8_N=51_gamma.csv
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Cooperative half-decay rate for N=3 (8.1), N=11 (8.2), N=25 (8.3), and N=51 (8.4) atoms in a chain polarized perpendicular to the atomic axis separated by a=0.25lambda, in units of the natural half-decay rate gamma_0. The ith element corresponds to the ith eigenmode.

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(8.5) Fig8_N=3_Delta.csv
(8.6) Fig8_N=11_Delta.csv
(8.7) Fig8_N=25_Delta.csv
(8.8) Fig8_N=51_Delta.csv
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Cooperative shifts for N=3 (8.5), N=11 (8.6), N=25 (8.7), and N=51 (8.8) atoms in a chain polarized perpendicular to the atomic axis separated by a=0.25lambda, in units of the natural half-decay rate gamma_0. The ith element corresponds to the ith eigenmode.

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(8.9) Fig8_ansatz_gamma.csv
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Cooperative half-decay rates for different numbers of atoms in a chain calculated using the ansatz in Eq. (26b). The atoms are polarized perendicular to the atomic axis and separated by a=0.25lambda. In units of the natural decay rate gamma_0.
 
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(8.10) Fig8_ansatz_Delta.csv
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Cooperative shifts for different numbers of atoms in a chain calculated using the ansatz in Eq. (26a). The atoms are polarized perendicular to the atomic axis and separated by a=0.25lambda. In units of the natural decay rate gamma_0.

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(8.11) Fig8_ansatz_N.csv
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Number of atoms in the chains in (8.9) and (8.10).



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Files included in /Fig9/:
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(9.1) Fig9_a_L.csv
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Nearest neighbor spacing a as a function of wavelength lambda.

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(9.2) Fig9a_gamma_N=3.csv
(9.3) Fig9a_gamma_N=11.csv
(9.4) Fig9a_gamma_N=51.csv
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Fig. 9(a) - Cooperative half-decay rate gamma_N+gamma_0 for the fully anti-phased eigenmode of a chain of N=3 (purple line), N=11 (blue line), and N=51 (red line) atoms polarized perpendicular to the atomic axis as a function of nearest neighbor spacing a, in units of the natural half-decay rate gamma_0. 

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(9.5) Fig9a_gamma_N=2.5e5.csv
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Fig. 9(a) - Cooperative half-decay rate using the eigenvector ansatz in Eq. (25), with nearest neighbor phase difference phi=pi. Black dashed line.

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(9.6) Fig9a_gamma_N=inf.csv
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Fig. 9(a) - Cooperative half-decay rate for a single atom inside a cavity polarized parallel to the mirros as a function of mirror spacing a, taken from Eq. (21). Grey shaded region.

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(9.7) Fig9b_gamma_N=3.csv
(9.8) Fig9b_gamma_N=11.csv
(9.9) Fig9b_gamma_N=51.csv
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Fig. 9(b) - Same as (9.2-9.4), but for dipoles polarized parallel to the atomic axis. 

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(9.10) Fig9b_gamma_N=2.5e5.csv
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Fig. 9(b) - Same as (9.5), but for dipoles polarized parallel to the atomic axis.

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(9.11) Fig9b_gamma_N=inf.csv
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Fig. 9(b) - Same as (9.6), but for dipoles polarized parallel to the atomic axis.

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(9.12) Fig9c_Delta_N=3.csv
(9.13) Fig9c_Delta_N=11.csv
(9.14) Fig9c_Delta_N=51.csv
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Fig. 9(c) - Same as (9.2-9.4), but plotting the cooperative shift rather than half-decay rate. 

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(9.15) Fig9c_Delta_N=2.5e5.csv
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Fig. 9(c) - Same as (9.5), but plotting the cooperative shift rather than half-decay rate.

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(9.16) Fig9d_Delta_N=3.csv
(9.17) Fig9d_Delta_N=11.csv
(9.18) Fig9d_Delta_N=51.csv
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Fig. 9(d) - Same as (9.7-9.9), but plotting the cooperative shift rather than half-decay rate. 

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(9.19) Fig9d_Delta_N=2.5e5.csv
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Fig. 9(d) - Same as (9.10), but plotting the cooperative shift rather than half-decay rate.






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For queries, contact Robert Bettles at rjbettles89@gmail.com

