Suppressing the spontaneous emission in quantum emitters ensembles (atoms) is one of the topical problems in quantum optics and quantum technology. While many approaches are based on utilizing the subradiance effect in ordered quantum emitters arrays, the ensemble configurations providing the minimal spontaneous emission rate are yet unknown. In this work, we employ the differential evolution algorithm to identify the optimal configurations of a few atomic ensembles that support quantum states with maximal radiative lifetime. We demonstrate that atoms tend to assemble mostly in quasi-regular structures with specific geometry, which strongly depends on the minimally allowed interatomic distance . While the discovered specific non-radiative realizations of small ensembles cannot be immediately predicted, there is particular correspondence to the non-radiative states in the atomic lattices. In particular, we have found that states inheriting their properties either from the bound states in the continuum or band edge states of infinite lattices dominate across a wide range of values. Additionally, we show that for small interatomic distances, the linear arrays with modulated spacing have the smallest radiative losses exponentially decreasing as the size of the ensemble increases.
REFERENCES
1.
A. S.
Sheremet
,
A. D.
Manukhova
,
N. V.
Larionov
, and
D. V.
Kupriyanov
, “
Cooperative light scattering on an atomic system with degenerate structure of the ground state
,” Phys. Rev. A
86
(4
), 043414
(2012
).2.
M. O.
Scully
, “
Single photon subradiance: Quantum control of spontaneous emission and ultrafast readout
,” Phys. Rev. Lett.
115
, 243602
(2015
).3.
H.
Cai
,
D.-W.
Wang
,
A. A.
Svidzinsky
,
S.-Y.
Zhu
, and
M. O.
Scully
, “
Symmetry-protected single-photon subradiance
,” Phys. Rev. A
93
, 053804
(2016
).4.
D. F.
Kornovan
,
A. S.
Sheremet
, and
M. I.
Petrov
, “
Collective polaritonic modes in an array of two-level quantum emitters coupled to an optical nanofiber
,” Phys. Rev. B
94
(24
), 245416
(2016
).5.
H. H.
Jen
,
M.-S.
Chang
, and
Y.-C.
Chen
, “
Cooperative light scattering from helical-phase-imprinted atomic rings
,” Sci. Rep.
8
(1
), 9570
(2018
).6.
D.
Plankensteiner
,
C.
Sommer
,
M.
Reitz
,
H.
Ritsch
, and
C.
Genes
, “
Enhanced collective Purcell effect of coupled quantum emitter systems
,” Phys. Rev. A
99
(4
), 043843
(2019
).7.
Y.-X.
Zhang
,
C.
Yu
, and
K.
Mølmer
, “
Subradiant bound dimer excited states of emitter chains coupled to a one dimensional waveguide
,” Phys. Rev. Res.
2
(1
), 013173
(2020
).8.
Y. A.
Fofanov
,
I. M.
Sokolov
,
R.
Kaiser
, and
W.
Guerin
, “
Subradiance in dilute atomic ensembles: Role of pairs and multiple scattering
,” Phys. Rev. A
104
(2
), 023705
(2021
).9.
D.
Pavolini
,
A.
Crubellier
,
P.
Pillet
,
L.
Cabaret
, and
S.
Liberman
, “
Experimental evidence for subradiance
,” Phys. Rev. Lett.
54
(17
), 1917
–1920
(1985
).10.
R. G.
DeVoe
and
R. G.
Brewer
, “
Observation of superradiant and subradiant spontaneous emission of two trapped ions
,” Phys. Rev. Lett.
76
(12
), 2049
–2052
(1996
).11.
W.
Guerin
,
M. O.
Araújo
, and
R.
Kaiser
, “
Subradiance in a large cloud of cold atoms
,” Phys. Rev. Lett.
116
, 083601
(2016
).12.
J.
Rui
,
D.
Wei
,
A.
Rubio-Abadal
,
S.
Hollerith
,
J.
Zeiher
,
D. M.
Stamper-Kurn
,
C.
Gross
, and
I.
Bloch
, “
A subradiant optical mirror formed by a single structured atomic layer
,” Nature
583
, 369
–374
(2020
).13.
G.
Ferioli
,
A.
Glicenstein
,
L.
Henriet
,
I.
Ferrier-Barbut
, and
A.
Browaeys
, “
Storage and release of subradiant excitations in a dense atomic cloud
,” Phys. Rev. X
11
, 021031
(2021
).14.
R. H.
Dicke
, “
Coherence in spontaneous radiation processes
,” Phys. Rev.
93
(1
), 99
–110
(1954
).15.
D.
Barredo
,
V.
Lienhard
,
S.
De Léséleuc
,
T.
Lahaye
, and
A.
Browaeys
, “
Synthetic three-dimensional atomic structures assembled atom by atom
,” Nature
561
, 79
–82
(2018
).16.
N. V.
Corzo
,
B.
Gouraud
,
A.
Chandra
,
A.
Goban
,
A. S.
Sheremet
,
D. V.
Kupriyanov
, and
J.
Laurat
, “
Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide
,” Phys. Rev. Lett.
117
(13
), 133603
(2016
).17.
A.
Asenjo-Garcia
,
M.
Moreno-Cardoner
,
A.
Albrecht
,
H. J.
Kimble
, and
D. E.
Chang
, “
Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays
,” Phys. Rev. X
7
(3
), 031024
(2017
).18.
Y.-X.
Zhang
and
K.
Mølmer
, “
Subradiant emission from regular atomic arrays: Universal scaling of decay rates from the generalized Bloch theorem
,” Phys. Rev. Lett.
125
(25
), 253601
(2020
).19.
D. F.
Kornovan
,
R. S.
Savelev
,
Y.
Kivshar
, and
M. I.
Petrov
, “
High-Q localized states in finite arrays of subwavelength resonators
,” ACS Photonics
8
(12
), 3627
–3632
(2021
).20.
N.
Fayard
,
I.
Ferrier-Barbut
,
A.
Browaeys
, and
J.-J.
Greffet
, “
Optical control of collective states in one-dimensional ordered atomic chains beyond the linear regime
,” Phys. Rev. A
108
(2
), 023116
(2023
).21.
R. T.
Sutherland
and
F.
Robicheaux
, “
Collective dipole-dipole interactions in an atomic array
,” Phys. Rev. A
94
(1
), 013847
(2016
).22.
A.
Asenjo-Garcia
,
J. D.
Hood
,
D. E.
Chang
, and
H. J.
Kimble
, “
Atom-light interactions in quasi-one-dimensional nanostructures: A Green's-function perspective
,” Phys. Rev. A
95
(3
), 033818
(2017
).23.
D. F.
Kornovan
,
N. V.
Corzo
,
J.
Laurat
, and
A. S.
Sheremet
, “
Extremely subradiant states in a periodic one-dimensional atomic array
,” Phys. Rev. A
100
(6
), 063832
(2019
).24.
Y.
Ke
,
A. V.
Poshakinskiy
,
C.
Lee
,
Y. S.
Kivshar
, and
A. N.
Poddubny
, “
Inelastic scattering of photon pairs in qubit arrays with subradiant states
,” Phys. Rev. Lett.
123
(25
), 253601
(2019
).25.
A. N.
Poddubny
, “
Quasiflat band enabling subradiant two-photon bound states
,” Phys. Rev. A
101
(4
), 043845
(2020
).26.
G.
Facchinetti
,
S. D.
Jenkins
, and
J.
Ruostekoski
, “
Storing light with subradiant correlations in arrays of atoms
,” Phys. Rev. Lett.
117
(24
), 243601
(2016
).27.
R. J.
Bettles
,
S. A.
Gardiner
, and
C. S.
Adams
, “
Cooperative ordering in lattices of interacting two-level dipoles
,” Phys. Rev. A
92
(6
), 063822
(2015
).28.
K. E.
Ballantine
and
J.
Ruostekoski
, “
Subradiance-protected excitation spreading in the generation of collimated photon emission from an atomic array
,” Phys. Rev. Res.
2
(2
), 023086
(2020
).29.
I.
Volkov
,
N.
Ustimenko
,
D.
Kornovan
,
R.
Savelev
,
A.
Sheremet
, and
M.
Petrov
, “
Strongly subradiant states in planar atomic arrays
,” arXiv: 2310.06791 (2023
).30.
M. B.
De Paz
and
P. A.
Huidobro
, “
Bound states in the continuum in subwavelength emitter arrays
,” Phys. Rev. Res.
5
, 033108
(2023
).31.
N.
Ustimenko
,
D.
Kornovan
,
I.
Volkov
,
A.
Sheremet
,
R.
Savelev
, and
M.
Petrov
, “
Non-radiant multiphoton states in quantum ring oligomers
,” arXiv: 2309.14461 (2023
).32.
H. S.
Freedhoff
, “
Cooperative single-quantum excitations of a closed-ring polymer chain
,” J. Chem. Phys
85
(10
), 6110
–6117
(1986
).33.
J.
Cremer
,
D.
Plankensteiner
,
M.
Moreno-Cardoner
,
L.
Ostermann
, and
H.
Ritsch
, “
Polarization control of radiation and energy flow in dipole-coupled nanorings
,” New J. Phys.
22
(8
), 083052
(2020
).34.
M.
Moreno-Cardoner
,
D.
Plankensteiner
,
L.
Ostermann
,
D. E.
Chang
, and
H.
Ritsch
, “
Subradiance-enhanced excitation transfer between dipole-coupled nanorings of quantum emitters
,” Phys. Rev. A
100
(2
), 023806
(2019
).35.
R.
Holzinger
,
D.
Plankensteiner
,
L.
Ostermann
, and
H.
Ritsch
, “
Nanoscale coherent light source
,” Phys. Rev. Lett.
124
(25
), 253603
(2020
).36.
M.
Moreno-Cardoner
,
R.
Holzinger
, and
H.
Ritsch
, “
Efficient nano-photonic antennas based on dark states in quantum emitter rings
,” Opt. Express
30
(7
), 10779
–10791
(2022
).37.
R.
Holzinger
,
J.
Peter
,
S.
Ostermann
,
H.
Ritsch
, and
S.
Yelin
, “
Harnessing quantum emitter rings for efficient energy transport and trapping
,” arXiv:2309.11376 (2023
).38.
S.
Krasikov
,
A.
Tranter
,
A.
Bogdanov
, and
Y.
Kivshar
, “
Intelligent metaphotonics empowered by machine learning
,” Opto-Electron. Adv.
5
(3
), 210147
(2022
).39.
T.
Pan
,
J.
Ye
,
Z.
Zhang
, and
Y.
Xu
, “
Inverse design of coupled subwavelength dielectric resonators with targeted eigenfrequency and Q factor utilizing deep learning
,” Opt. Lett.
47
, 3359
(2022
).40.
A.
Mikhailovskaya
,
K.
Grotov
,
D.
Vovchuk
,
A.
Machnev
,
D.
Dobrykh
,
R. E.
Noskov
,
K.
Ladutenko
,
P.
Belov
, and
P.
Ginzburg
, “
Superradiant scattering limit for arrays of subwavelength scatterers
,” Phys. Rev. Appl.
18
, 054063
(2022
).41.
S.
Gladyshev
,
T. D.
Karamanos
,
L.
Kuhn
,
D.
Beutel
,
T.
Weiss
,
C.
Rockstuhl
, and
A.
Bogdanov
, “
Inverse design of all-dielectric metasurfaces with accidental bound states in the continuum
,” Nanophotonics
12
, 3767
–3779
(2023
).42.
N.
Ustimenko
,
K. V.
Baryshnikova
,
R.
Melnikov
,
D.
Kornovan
,
V.
Ulyantsev
,
B. N.
Chichkov
, and
A. B.
Evlyukhin
, “
Multipole optimization of light focusing by silicon nanosphere structures
,” J. Opt. Soc. Am. B
38
(10
), 3009
(2021
).43.
A. D.
Tranter
,
H. J.
Slatyer
,
M. R.
Hush
,
A. C.
Leung
,
J. L.
Everett
,
K. V.
Paul
,
P.
Vernaz-Gris
,
P. K.
Lam
,
B. C.
Buchler
, and
G. T.
Campbell
, “
Multiparameter optimisation of a magneto-optical trap using deep learning
,” Nat. Commun.
9
, 4360
(2018
).44.
E.
Rozenberg
,
A.
Karnieli
,
O.
Yesharim
,
J.
Foley-Comer
,
S.
Trajtenberg-Mills
,
D.
Freedman
,
A. M.
Bronstein
, and
A.
Arie
, “
Inverse design of spontaneous parametric downconversion for generation of high-dimensional qudits
,” Optica
9
, 602
(2022
).45.
K.
Srakaew
,
P.
Weckesser
,
S.
Hollerith
,
D.
Wei
,
D.
Adler
,
I.
Bloch
, and
J.
Zeiher
, “
A subwavelength atomic array switched by a single Rydberg atom
,” Nat. Phys.
19
, 714
–719
(2023
).46.
L.
Novotny
and
B.
Hecht
, Principles of Nano-Optics
(
Cambridge University Press
,
Cambridge, England, UK
, 2012
).47.
V. A.
Markel
and
A. K.
Sarychev
, “
Propagation of surface plasmons in ordered and disordered chains of metal nanospheres
,” Phys. Rev. B
75
(8
), 085426
(2007
).48.
R.
Storn
and
K.
Price
, “
Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces
,” J. Global Optim.
11
(4
), 341
–359
(1997
).49.
W. H.
Weber
and
G. W.
Ford
, “
Propagation of optical excitations by dipolar interactions in metal nanoparticle chains
,” Phys. Rev. B
70
, 125429
(2004
).50.
A.
Figotin
and
I.
Vitebskiy
, “
Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers
,” Phys. Rev. E
72
, 036619
(2005
).51.
C. W.
Hsu
,
B.
Zhen
,
A. D.
Stone
,
J. D.
Joannopoulos
, and
M.
Soljačić
, “
Bound states in the continuum
,” Nat. Rev. Mater.
1
, 16048
(2016
).52.
Z.
Sadrieva
,
K.
Frizyuk
,
M.
Petrov
,
Y.
Kivshar
, and
A.
Bogdanov
, “
Multipolar origin of bound states in the continuum
,” Phys. Rev. B
100
(11
), 115303
(2019
).53.
A. C.
Overvig
,
S. C.
Malek
,
M. J.
Carter
,
S.
Shrestha
, and
N.
Yu
, “
Selection rules for quasibound states in the continuum
,” Phys. Rev. B
102
, 035434
(2020
).54.
A. S.
Sheremet
,
M. I.
Petrov
,
I. V.
Iorsh
,
A. V.
Poshakinskiy
, and
A. N.
Poddubny
, “
Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations
,” Rev. Mod. Phys.
95
(1
), 015002
(2023
).55.
Y.-X.
Zhang
and
K.
Mølmer
, “
Theory of subradiant states of a one-dimensional two-level atom chain
,” Phys. Rev. Lett.
122
, 203605
(2019
).56.
K.
Pichugin
,
A.
Sadreev
, and
E.
Bulgakov
, “
Ultrahigh-Q system of a few coaxial disks
,” Nanophotonics
10
(17
), 4341
–4346
(2021
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
