We theoretically and numerically demonstrate enhanced extended superradiance using a diamond epsilon near-zero metamaterial design. Due to the large spatial coherence in this metamaterial, we experience an ultra-high superradiant decay rate enhancement over distances greater than 13 times the free-space wavelength for both two emitters and many-body configurations of emitters. We observe a power enhancement three orders of magnitude higher than an incoherent array of emitters in bulk diamond, corresponding to an N2 scaling with the number of emitters characteristic of superradiance.

1.
M. O.
Scully
and
M. S.
Zubairy
,
Quantum Optics
(
Cambridge University
,
1997
).
2.
H. J.
Kimble
, “
The quantum internet
,”
Nature
453
(
7198
),
1023
1030
(
2008
).
3.
H. J.
Kimble
,
Q. A.
Turchette
,
N. P.
Georgiades
,
C. J.
Hood
,
W.
Lange
,
H.
Mabuchi
,
E. S.
Polzik
, and
D. W.
Vernooy
,
Cavity Quantum Electrodynamics With a Capital Q
(
Springer
,
1996
), pp.
203
210
.
4.
S.
Nie
, “
Probing single molecules and single nanoparticles by surface-enhanced Raman scattering
,”
Science
275
(
5303
),
1102
1106
(
1997
).
5.
A.
Sipahigil
,
R. E.
Evans
,
D. D.
Sukachev
,
M. J.
Burek
,
J.
Borregaard
,
M. K.
Bhaskar
,
C. T.
Nguyen
,
J. L.
Pacheco
,
H. A.
Atikian
,
C.
Meuwly
,
R. M.
Camacho
,
F.
Jelezko
,
E.
Bielejec
,
H.
Park
,
M.
Lončar
, and
M. D.
Lukin
, “
An integrated diamond nanophotonics platform for quantum-optical networks
,”
Science
354
(
6314
),
847
850
(
2016
).
6.
T.
Zhong
,
J. M.
Kindem
,
J.
Rochman
, and
A.
Faraon
, “
Interfacing broadband photonic qubits to on-chip cavity-protected rare-earth ensembles
,”
Nat. Commun.
8
(
1
),
14107
(
2017
).
7.
R. H.
Dicke
, “
Coherence in spontaneous radiation processes
,”
Phys. Rev.
93
(
1
),
99
110
(
1954
).
8.
M.
Gross
and
S.
Haroche
, “
Superradiance: An essay on the theory of collective spontaneous emission
,”
Phys. Rep.
93
(
5
),
301
396
(
1982
).
9.
M. O.
Scully
and
A. A.
Svidzinsky
, “
The super of superradiance
,”
Science
325
(
5947
),
1510
1511
(
2009
).
10.
I.
Liberal
and
N.
Engheta
, “
Near-zero refractive index photonics
,”
Nat. Photonics
11
(
3
),
149
158
(
2017
).
11.
K. J.
Russell
,
T.-L.
Liu
,
S.
Cui
, and
E. L.
Hu
, “
Large spontaneous emission enhancement in plasmonic nanocavities
,”
Nat. Photonics
6
(
7
),
459
462
(
2012
).
12.
D.
Englund
,
D.
Fattal
,
E.
Waks
,
G.
Solomon
,
B.
Zhang
,
T.
Nakaoka
,
Y.
Arakawa
,
Y.
Yamamoto
, and
J.
Vučković
, “
Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal
,”
Phys. Rev. Lett.
95
(
1
),
013904
(
2005
).
13.
P.
Moitra
,
Y.
Yang
,
Z.
Anderson
,
I. I.
Kravchenko
,
D. P.
Briggs
, and
J.
Valentine
, “
Realization of an all-dielectric zero-index optical metamaterial
,”
Nat. Photonics
7
(
10
),
791
795
(
2013
).
14.
R.
Maas
,
J.
Parsons
,
N.
Engheta
, and
A.
Polman
, “
Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths
,”
Nat. Photonics
7
(
11
),
907
912
(
2013
).
15.
Y.
Li
,
S.
Kita
,
P.
Muñoz
,
O.
Reshef
,
D. I.
Vulis
,
M.
Yin
,
M.
Lončar
, and
E.
Mazur
, “
On-chip zero-index metamaterials
,”
Nat. Photonics
9
(
11
),
738
742
(
2015
).
16.
D. I.
Vulis
,
Y.
Li
,
O.
Reshef
,
P.
Camayd-Muñoz
,
M.
Yin
,
S.
Kita
,
M.
Lončar
, and
E.
Mazur
, “
Monolithic CMOS-compatible zero-index metamaterials
,”
Opt. Express
25
(
11
),
12381
(
2017
).
17.
O.
Reshef
,
I.
De Leon
,
M. Z.
Alam
, and
R. W.
Boyd
, “
Nonlinear optical effects in epsilon-near-zero media
,”
Nat. Rev. Mater.
4
(
8
),
535
551
(
2019
).
18.
I.
Liberal
and
N.
Engheta
, “
Zero-index structures as an alternative platform for quantum optics
,”
Proc. Natl. Acad. Sci.
114
(
5
),
822
827
(
2017
).
19.
I.
Liberal
and
N.
Engheta
, “
Nonradiating and radiating modes excited by quantum emitters in open epsilon-near-zero cavities
,”
Sci. Adv.
2
(
10
),
e1600987
(
2016
).
20.
M.
Lobet
,
I.
Liberal
,
E. N.
Knall
,
M. Z.
Alam
,
O.
Reshef
,
R. W.
Boyd
,
N.
Engheta
, and
E.
Mazur
, “
Fundamental radiative processes in near-zero-index media of various dimensionalities
,”
ACS Photonics
7
(
8
),
1965
1970
(
2020
).
21.
R.
Fleury
and
A.
Alù
, “
Enhanced superradiance in epsilon-near-zero plasmonic channels
,”
Phys. Rev. B
87
(
20
),
201101
(
2013
).
22.
A.
Alù
and
N.
Engheta
, “
Emission enhancement in a plasmonic waveguide at cut-off
,”
Materials
4
(
1
),
141
152
(
2011
).
23.
R.
Sokhoyan
and
H. A.
Atwater
, “
Quantum optical properties of a dipole emitter coupled to an ɛ-near-zero nanoscale waveguide
,”
Opt. Express
21
(
26
),
32279
(
2013
).
24.
Y.
Li
and
C.
Argyropoulos
, “
Controlling collective spontaneous emission with plasmonic waveguides
,”
Opt. Express
24
(
23
),
26696
(
2016
).
25.
E.
Özgün
,
E.
Ozbay
, and
H.
Caglayan
, “
Tunable zero-index photonic crystal waveguide for two-qubit entanglement detection
,”
ACS Photonics
3
(
11
),
2129
2133
(
2016
).
26.
M. J.
Burek
,
Y.
Chu
,
M. S. Z.
Liddy
,
P.
Patel
,
J.
Rochman
,
S.
Meesala
,
W.
Hong
,
Q.
Quan
,
M. D.
Lukin
, and
M.
Lončar
,
Nat. Commun.
5
(
1
),
5718
(
2014
).
27.
C.
Hepp
,
T.
Müller
,
V.
Waselowski
,
J. N.
Becker
,
B.
Pingault
,
H.
Sternschulte
,
D.
Steinmüller-Nethl
,
A.
Gali
,
J. R.
Maze
,
M.
Atatüre
 et al., “
Electronic structure of the silicon vacancy color center in diamond
,”
Phys. Rev. Lett.
112
(
3
),
036405
(
2014
).
28.
A.
Gruber
, “
Scanning confocal optical microscopy and magnetic resonance on single defect centers
,”
Science
276
(
5321
),
2012
2014
(
1997
).
29.
E.
Gibney
, “
Quantum physics: Flawed to perfection
,”
Nature
505
,
472
474
(
2014
).
30.
J. G.
Bohnet
,
Z.
Chen
,
J. M.
Weiner
,
D.
Meiser
,
M. J.
Holland
, and
J. K.
Thompson
, “
A steady-state superradiant laser with less than one intracavity photon
,”
Nature
484
(
7392
),
78
81
(
2012
).
31.
F.
Jahnke
,
C.
Gies
,
M.
Aßmann
,
M.
Bayer
,
H. A. M.
Leymann
,
A.
Foerster
,
J.
Wiersig
,
C.
Schneider
,
M.
Kamp
, and
S.
Höfling
, “
Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers
,”
Nat. Commun.
7
(
1
),
11540
(
2016
).
32.
V.
Paulisch
,
M.
Perarnau-Llobet
,
A.
González-Tudela
, and
J. I.
Cirac
, “
Quantum metrology with one-dimensional superradiant photonic states
,”
Phys. Rev. A
99
(
4
),
043807
(
2019
).
33.
A.
Kalachev
, “
Quantum storage on subradiant states in an extended atomic ensemble
,”
Phys. Rev. A
76
(
4
),
043812
(
2007
).
34.
A.
Kalachev
and
S.
Kröll
, “
Coherent control of collective spontaneous emission in an extended atomic ensemble and quantum storage
,”
Phys. Rev. A
74
(
2
),
023814
(
2006
).
35.
P. A. M.
Dirac
, “
The quantum theory of the emission and absorption of radiation
,”
Proc. R. Soc. London, Ser. A
114
(
767
),
243
265
(
1927
).
36.
E. M.
Purcell
, “
Spontaneous emission probabilities at radio frequencies
,”
Phys. Rev
69
,
681
(
1946
).
37.
A.
Svidzinsky
and
J.-T.
Chang
, “
Cooperative spontaneous emission as a many-body eigenvalue problem
,”
Phys. Rev. A
77
,
043833
(
2008
).
38.
E.
Shahmoon
and
G.
Kurizki
, “
Nonradiative interaction and entanglement between distant atoms
,”
Phys. Rev. A
87
(
3
),
033831
(
2013
).
39.
A.
Alù
,
M. G.
Silveirinha
, and
N.
Engheta
, “
Transmission-line analysis of ε-near-zero–filled narrow channels
,”
Phys. Rev. E
78
(
1
),
016604
(
2008
).
40.
X.
Huang
,
Y.
Lai
,
Z. H.
Hang
,
H.
Zheng
, and
C. T.
Chan
, “
Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials
,”
Nat. Mater.
10
(
8
),
582
586
(
2011
).
41.
J. D.
Jackson
,
Classical Electrodynamics
, 2nd ed. (
Wiley
,
1975
).
42.
D. R.
Smith
,
S.
Schultz
,
P.
Markoš
, and
C. M.
Soukoulis
, “
Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients
,”
Phys. Rev. B
65
(
19
),
195104
(
2002
).
43.
J. B.
Pendry
and
A.
Mackinnon
, “
Calculation of photon dispersion relations
,”
Phys. Rev. Lett.
69
(
19
),
2772
2775
(
1992
).
44.
P.
Markoš
and
C. M.
Soukoulis
, “
Numerical studies of left-handed materials and arrays of split ring resonators
,”
Phys. Rev. E
65
(
3
),
036622
(
2002
).
45.
D. R.
Smith
,
D. C.
Vier
,
T.
Koschny
, and
C. M.
Soukoulis
, “
Electromagnetic parameter retrieval from inhomogeneous metamaterials
,”
Phys. Rev. E
71
(
3
),
036617
(
2005
).
46.
Y.
Wu
,
J.
Li
,
Z.-Q.
Zhang
, and
C. T.
Chan
, “
Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit
,”
Phys. Rev. B
74
(
8
),
085111
(
2006
).
47.
See www.comsol.com for “
COMSOL Multiphysics® v. 5.6 (COMSOL AB, Stockholm, Sweden)
48.
C.
Argyropoulos
,
P.-Y.
Chen
,
G.
D'Aguanno
,
N.
Engheta
, and
A.
Alù
, “
Boosting optical nonlinearities in ε near-zero plasmonic channels
,”
Phys. Rev. B
85
(
4
),
045129
(
2012
).
49.
H. T.
Dung
,
L.
Knöll
, and
D.-G.
Welsch
, “
Resonant dipole–dipole interaction in the presence of dispersing and absorbing surroundings
,”
Phys. Rev. A
66
(
6
),
063810
(
2002
).
50.
E.
Shahmoon
,
D. S.
Wild
,
M. D.
Lukin
, and
S. F.
Yelin
, “
Cooperative resonances in light scattering from two-dimensional atomic arrays
,”
Phys. Rev. Lett.
118
(
11
),
113601
(
2017
).
51.
H.
Tang
,
C.
Devault
,
S. A.
Camayd-Muñoz
,
Y.
Liu
,
D.
Jia
,
F.
Du
,
O.
Mello
,
D. I.
Vulis
,
Y.
Li
, and
E.
Mazur
, “
Low-loss zero-index materials
,”
Nano Lett.
21
(
2
),
914
920
(
2021
).
52.
D. A.
Lidar
,
I. L.
Chuang
, and
K. B.
Whaley
, “
Decoherence-free subspaces for quantum computation
,”
Phys. Rev. Lett.
81
(
12
),
2594
2597
(
1998
).
53.
A.
Walther
,
A.
Amari
,
S.
Kröll
, and
A.
Kalachev
, “
Experimental superradiance and slow-light effects for quantum memories
,”
Phys. Rev. A
80
(
1
),
012317
(
2009
).
54.
R. A.
Shore
and
A. D.
Yaghjian
, “
Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers
,”
Radio Sci.
42
(
6
),
RS6S21
, (
2007
).
55.
C. R.
Simovski
and
S. A.
Tretyakov
, “
Local constitutive parameters of metamaterials from an effective-medium perspective
,”
Phys. Rev. B
75
(
19
),
195111
(
2007
).
56.
A.
Alù
,
A. D.
Yaghjian
,
R. A.
Shore
, and
M. G.
Silveirinha
, “
Causality relations in the homogenization of metamaterials
,”
Phys. Rev. B
84
(
5
),
054305
(
2011
).

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