In this paper we studied an one-dimensional array of atoms coupled to a single-mode waveguide. The formation of polaritonic states is considered in infinite system with and without account for chiral interactions. The effect of diagonal disorder was studied numerically in a finite atomic array. We showed that in the presence of disorder localized states were observed in a symmetrically coupled atoms along with delocalized states. With increase of the degree of directionality the delocalized states evolved into the end-of-array localized states, while the considered localized states survive till particular degree of directionality.

1.
M.
Scheucher
,
A.
Hilico
,
E.
Will
,
J.
Volz
, and
A.
Rauschenbeutel
, “
Quantum optical circulator controlled by a single chirally coupled atom
,”
Science
354
,
1577
1580
(
2016
), arXiv:1609.02492.
2.
J. D.
Hood
,
A.
Goban
,
A.
Asenjo-Garcia
,
M.
Lu
,
S. P.
Yu
,
D. E.
Chang
, and
H. J.
Kimble
, “
Atom-atom interactions around the band edge of a photonic crystal waveguide
,”
Proceedings of the National Academy of Sciences of the United States of America
113
,
10507
10512
(
2016
), arXiv:1603.02771.
3.
E.
Vetsch
,
D.
Reitz
,
G.
Sague
,
R.
Schmidt
,
S. T.
Dawkins
, and
A.
Rauschenbeutel
, “
Optical Interface Created by Laser-Cooled Atoms Trapped in the Evanescent Field Surrounding an Optical Nanofiber
,”
Physical Review Letters
104
,
203603
(
2010
).
4.
S. T.
Dawkins
,
R.
Mitsch
,
D.
Reitz
,
E.
Vetsch
, and
a.
Rauschenbeutel
, “
Dispersive Optical Interface Based on Nanofiber-Trapped Atoms
,”
Physical Review Letters
107
,
243601
(
2011
).
5.
P.
Solano
,
J. A.
Grover
,
J. E.
Hoffman
,
S.
Ravets
,
F. K.
Fatemi
,
L. A.
Orozco
, and
S. L.
Rolston
, “
Optical Nanofibers: A New Platform for Quantum Optics
,”
Advances in Atomic, Molecular and Optical Physics
66
,
439
505
(
2017
), arXiv:1703.10533.
6.
P.
Lodahl
,
S.
Mahmoodian
,
S.
Stobbe
,
A.
Rauschenbeutel
,
P.
Schneeweiss
,
J.
Volz
,
H.
Pichler
, and
P.
Zoller
, “
Chiral quantum optics
,”
Nature
541
,
473
480
(
2017
).
7.
A.
Aiello
,
P.
Banzer
,
M.
Neugebauer
, and
G.
Leuchs
, “
From transverse angular momentum to photonic wheels
,”
Nature Photonics
9
,
789
795
(
2015
).
8.
P. W.
Anderson
, “
Absence of diffusion in certain random lattices
,”
Physical Review
109
,
1492
1505
(
1958
).
9.
H. R.
Haakh
,
S.
Faez
, and
V.
Sandoghdar
, “
Polaritonic normal-mode splitting and light localization in a one-dimensional nanoguide
,”
Physical Review A
94
,
1
8
(
2016
).
10.
I. M.
Mirza
,
J. G.
Hoskins
, and
J. C.
Schotland
, “
Chirality, band structure, and localization in waveguide quantum electrodynamics
,”
Physical Review A
96
,
30
32
(
2017
), arXiv:1708.00902.
11.
I. M.
Mirza
and
J. C.
Schotland
, “
Influence of disorder on electromagnetically induced transparency in chiral waveguide quantum electrodynamics
,”
Journal of the Optical Society of America B
35
,
1149
(
2018
), arXiv:1709.04641.
12.
D.
Kornovan
,
M.
Petrov
, and
I.
Iorsh
, “
Transport and collective radiance in a basic quantum chiral optical model
,”
Physical Review B
96
,
115162
(
2017
), arXiv:1701.06311.
13.
N.
Hatano
and
D. R.
Nelson
, “
Localization transitions in non-hermitian quantum mechanics
,”
Physical Review Letters
77
,
570
573
(
1996
).
14.
M.
Petrov
, “
Disorder-induced Purcell enhancement in nanoparticle chains
,”
Physical Review A
91
,
023821
(
2015
).
15.
D. F.
Kornovan
,
A. S.
Sheremet
, and
M. I.
Petrov
, “
Collective polaritonic modes in an array of two-level quantum emitters coupled to optical nanofiber
,”
Physical Review B
94
,
245416
(
2016
), arXiv:arXiv:1608.03202v1.
16.
R.
Modak
,
S.
Mukerjee
,
E. A.
Yuzbashyan
, and
B. S.
Shastry
, “
Integrals of motion for one-dimensional Anderson localized systems
,”
New Journal of Physics
18
(
2016
), , arXiv:1503.07019.
17.
R.
Movassagh
and
L. P.
Kadanoff
,
Journal of Statistical Physics
, Vol.
167
(
Springer US
,
2017
) pp.
959
996
, arXiv:1604.08295.
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