We demonstrate the existence of two types of dark gap solitary waves—the dark gap solitons and the dark gap soliton clusters—in Bose–Einstein condensates trapped in a bichromatic optical superlattice with cubic–quintic nonlinearities. The background of these dark soliton families is different from the one in a common monochromatic linear lattice; namely, the background in our model is composed of two types of Gaussian-like pulses, whereas in the monochromatic linear lattice, it is composed of only one type of Gaussian-like pulses. Such a special background of dark soliton families is convenient for the manipulation of solitons by the parameters of bichromatic and chemical potentials. The dark soliton families in the first, second, and third bandgap in our model are studied. Their stability is assessed by the linear-stability analysis, and stable as well as unstable propagation of these gap solitons are displayed. The profiles, stability, and perturbed evolution of both types of dark soliton families are distinctly presented in this work.
REFERENCES
1.
Y. S.
Kivshar
and B. A.
Malomed
, “Dynamics of solitons in nearly integrable systems
,” Rev. Mod. Phys.
61
, 763
(1989
). 2.
V. V.
Konotop
, J.
Yang
, and D. A.
Zezyulin
, “Nonlinear waves in
-symmetric systems
,” Rev. Mod. Phys.
88
, 035002
(2016
). 3.
H.
Leblond
and D.
Mihalache
, “Models of few optical cycle solitons beyond the slowly varying envelope approximation
,” Phys. Rep.
523
, 61
–126
(2013
). 4.
Y. V.
Kartashov
, G. E.
Astrakharchik
, B. A.
Malomed
, and L.
Torner
, “Frontiers in multidimensional self-trapping of nonlinear fields and matter
,” Nat. Rev. Phys.
1
, 185
–197
(2019
). 5.
D.
Mihalache
, D.
Mazilu
, F.
Lederer
, Y. V.
Kartashov
, L. C.
Crasovan
, L.
Torner
, and B. A.
Malomed
, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation
,” Phys. Rev. Lett.
97
, 073904
(2006
). 6.
X.
Zhu
, F.
Yang
, S.
Cao
, J.
Xie
, and Y.
He
, “Multipole gap solitons in fractional Schrödinger equation with parity-time-symmetric optical lattices
,” Opt. Express
28
(2
), 1631
–1639
(2020
). 7.
J.
Chen
and J.
Zeng
, “Spontaneous symmetry breaking in purely nonlinear fractional systems
,” Chaos
30
, 063131
(2020
). 8.
L.
Zeng
, M. R.
Belić
, D.
Mihalache
, and X.
Zhu
, “Elliptical and rectangular solitons in media with competing cubic-quintic nonlinearities
,” Chaos, Solitons Fractals
181
, 114645
(2024
). 9.
L.
Zeng
, D.
Mihalache
, X.
Zhu
, and J.
He
, “M-shaped solitons in cubic nonlinear media with a composite linear potential
,” Nonlinear Dyn.
112
, 3811
–3822
(2024
). 10.
V. S.
Bagnato
, D. J.
Frantzeskakis
, P. G.
Kevrekidis
, B. A.
Malomed
, and D.
Mihalache
, “Bose-Einstein condensation: Twenty years after
,” Rom. Rep. Phys.
67
, 5
–50
(2015
).11.
Y. V.
Kartashov
and D. A.
Zezyulin
, “Stable multiring and rotating solitons in two-dimensional spin-orbit-coupled Bose-Einstein condensates with a radially periodic potential
,” Phys. Rev. Lett.
122
, 123201
(2019
). 12.
L.
Zeng
, J.
Zeng
, Y. V.
Kartashov
, and B. A.
Malomed
, “Purely Kerr nonlinear model admitting flat-top solitons
,” Opt. Lett.
44
, 1206
–1209
(2019
). 13.
Y. V.
Kartashov
and V. V.
Konotop
, “Stable nonlinear modes sustained by gauge fields
,” Phys. Rev. Lett.
125
, 054101
(2020
). 14.
J.
Chen
and J.
Zeng
, “One-dimensional localized modes of spin-orbit-coupled Bose-Einstein condensates with spatially periodic modulated atom-atom interactions: Nonlinear lattices
,” Commun. Nonlinear Sci. Numer. Simulat.
85
, 105217
(2020
). 15.
J.
Chen
, D.
Mihalache
, M. R.
Belić
, X.
Gao
, D.
Zhu
, D.
Deng
, S.
Qiu
, X.
Zhu
, and L.
Zeng
, “Composite solitons in spin-orbit-coupled Bose-Einstein condensates within optical lattices
,” Chaos, Solitons Fractals
186
, 115325
(2024
). 16.
B. A.
Malomed
, Multidimensional Solitons
(AIP Publishing
, Melville, NY
, 2022
).17.
Y. V.
Kartashov
and V. V.
Konotop
, “Topological star junctions: Linear modes and solitons
,” Chaos, Solitons Fractals
179
, 114461
(2024
). 18.
D.
Mihalache
, “Localized strcutures in optical media and Bose-Einstein condensates: An overview of recent theoretical and experimental results
,” Rom. Rep. Phys.
76
, 402
(2024
).19.
B. J.
Eggleton
, R. E.
Slusher
, C. D.
Sterke
, P. A.
Krug
, and J. E.
Sipe
, “Bragg grating solitons
,” Phys. Rev. Lett.
76
, 1627
(1996
). 20.
B. J.
Eggleton
, C. D.
de Sterke
, and R. E.
Slusher
, “Nonlinear pulse propagation in Bragg gratings
,” J. Opt. Soc. Am. B
14
, 2980
–2993
(1997
).21.
G.
Bartal
, O.
Manela
, O.
Cohen
, J. W.
Fleischer
, and M.
Segev
, “Observation of second-band vortex solitons in 2D photonic lattices
,” Phys. Rev. Lett.
95
, 053904
(2005
). 22.
L.
Zeng
, M. R.
Belić
, D.
Mihalache
, J.
Shi
, J.
Li
, S.
Li
, X.
Lu
, Y.
Cai
, and J.
Li
, “Families of gap solitons and their complexes in media with saturable nonlinearity and fractional diffraction
,” Nonlinear Dyn.
108
, 1671
–1680
(2022
). 23.
L.
Zeng
, J.
Shi
, M. R.
Belić
, D.
Mihalache
, J.
Chen
, J.
Li
, and X.
Zhu
, “Surface gap solitons in the Schrödinger equation with quintic nonlinearity and a lattice potential
,” Opt. Express
31
, 35471
–35483
(2023
). 24.
B.
Eiermann
, T.
Anker
, M.
Albiez
, M.
Taglieber
, P.
Treutlein
, K. P.
Marzlin
, and M. K.
Oberthaler
, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction
,” Phys. Rev. Lett.
92
, 230401
(2004
). 25.
T.
Anker
, M.
Albiez
, R.
Gati
, S.
Hunsmann
, B.
Eiermann
, A.
Trombettoni
, and M. K.
Oberthaler
, “Nonlinear self-trapping of matter waves in periodic potentials
,” Phys. Rev. Lett.
94
, 020403
(2005
). 26.
T. J.
Alexander
, E. A.
Ostrovskaya
, and Y. S.
Kivshar
, “Self-trapped nonlinear matter waves in periodic potentials
,” Phys. Rev. Lett.
96
, 040401
(2006
). 27.
V. A.
Brazhnyi
and M.
Salerno
, “Resonant scattering of matter-wave gap solitons by optical lattice defects
,” Phys. Rev. A
83
, 053616
(2011
). 28.
Y. V.
Kartashov
, B. A.
Malomed
, V. A.
Vysloukh
, and L.
Torner
, “Two-dimensional solitons in nonlinear lattices
,” Opt. Lett.
34
, 770
–772
(2009
). 29.
Y. V.
Kartashov
, B. A.
Malomed
, V. A.
Vysloukh
, and L.
Torner
, “Vector solitons in nonlinear lattices
,” Opt. Lett.
34
, 3625
–627
(2009
). 30.
Y. V.
Kartashov
, B. A.
Malomed
, and L.
Torner
, “Solitons in nonlinear lattices
,” Rev. Mod. Phys.
83
, 247
–305
(2011
). 31.
L.
Zeng
and J.
Zeng
, “One-dimensional solitons in fractional Schrödinger equation with a spatially periodical modulated nonlinearity: Nonlinear lattice
,” Opt. Lett.
44
, 2661
–2664
(2019
). 32.
L.
Zeng
, J.
Shi
, M. R.
Belić
, D.
Mihalache
, J.
Chen
, X.
Lu
, Y.
Cai
, and J.
Li
, “Multipole solitons in saturable nonlinear lattices
,” Nonlinear Dyn.
111
, 3665
–3678
(2023
). 33.
J.
Shi
, L.
Zeng
, and J.
Chen
, “Two-dimensional localized modes in saturable quintic nonlinear lattices
,” Nonlinear Dyn.
111
, 13415
–13424
(2023
). 34.
Y. S.
Kivshar
and B.
Luther-Davies
, “Dark optical solitons: Physics and applications
,” Phys. Rep.
298
, 81
–197
(1998
). 35.
D. J.
Frantzeskakis
, “Dark solitons in atomic Bose-Einstein condensates: From theory to experiments
,” J. Phys. A
43
, 213001
(2010
). 36.
L.
Zeng
and J.
Zeng
, “Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices
,” Adv. Photon.
1
, 046004
(2019
). 37.
Q.
Zhou
, M.
Xu
, Y.
Sun
, Y.
Zhong
, and M.
Mirzazadeh
, “Generation and transformation of dark solitons, anti-dark solitons and dark double-hump solitons
,” Nonlinear Dyn.
110
, 1747
–1752
(2022
). 38.
J.
Chen
and J.
Zeng
, “Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities
,” Chaos, Solitons Fractals
150
, 111149
(2021
). 39.
L.
Zeng
, V. V.
Konotop
, X.
Lu
, Y.
Cai
, Q.
Zhu
, and J.
Li
, “Localized modes and dark solitons sustained by nonlinear defects
,” Opt. Lett.
46
, 2216
–2219
(2021
). 40.
P. J. Y.
Louis
, E. A.
Ostrovskaya
, and Y. S.
Kivshar
, “Matter-wave dark solitons in optical lattices
,” J. Opt. B
6
, S309
–S317
(2004
). 41.
M. A.
Porter
, P. G.
Kevrekidis
, R.
Carretero-González
, and D. J.
Frantzeskakis
, “Dynamics and manipulation of matter-wave solitons in optical superlattices
,” Phys. Lett. A
352
, 210
–215
(2006
). 42.
S. K.
Adhikari
and L.
Salasnich
, “Localization of a Bose-Einstein condensate in a bichromatic optical lattice
,” Phys. Rev. A
80
, 023606
(2009
). 43.
S. K.
Adhikari
, “Localization of a Bose-Einstein-condensate vortex in a bichromatic optical lattice
,” Phys. Rev. A
81
, 043636
(2010
). 44.
P.
Muruganandam
, R. K.
Kumar
, and S. K.
Adhikari
, “Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice
,” J. Phys. B
43
, 205305
(2010
). 45.
Y.
Cheng
and S. K.
Adhikari
, “Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice
,” Laser Phys. Lett.
7
, 824
(2010
). 46.
Y.
Cheng
and S. K.
Adhikari
, “Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice
,” Phys. Rev. A
81
, 023620
(2010
). 47.
Y.
Cheng
, G.
Tang
, and S. K.
Adhikari
, “Localization of a spin-orbit-coupled Bose-Einstein condensate in a bichromatic optical lattice
,” Phys. Rev. A
89
, 063602
(2014
). 48.
K. T.
Xi
, J.
Li
, and D. N.
Shi
, “Localization of a two-component Bose-Einstein condensate in a two-dimensional bichromatic optical lattice
,” Physica B
436
, 149
–156
(2014
). 49.
A.
Nath
and U.
Roy
, “Bose-Einstein condensate in a bichromatic optical lattice: An exact analytical model
,” Laser Phys. Lett.
11
, 115501
(2014
). 50.
T. F.
Xu
, Y. F.
Zhang
, Z. D.
Li
, C.
Zhang
, and R.
Hao
, “Gap solitons in spin-orbit-coupled Bose-Einstein condensates in bichromatic optical lattices
,” Optik
168
, 140
–151
(2018
). 51.
Z.
Oztas
, “Spin orbit coupled Bose-Einstein condensate in a two dimensional bichromatic optical lattice
,” Phys. Lett. A
383
, 504
–508
(2019
). 52.
F.
Kh. Abdullaev
, A.
Gammal
, L.
Tomio
, and T.
Frederico
, “Stability of trapped Bose-Einstein condensates
,” Phys. Rev. A
63
, 043604
(2001
).53.
F. K.
Abdullaev
and M.
Salerno
, “Gap-Townes solitons and localized excitations in low-dimensional Bose-Einstein condensates in optical lattices
,” Phys. Rev. A
72
, 033617
(2005
). 54.
55.
A.
Negretti
and C.
Henkel
, “Enhanced phase sensitivity and soliton formation in an integrated BEC interferometer
,” J. Phys. B
37
, L385
–L390
(2004
). 56.
A.
Negretti
, C.
Henkel
, and K.
Mølmer
, “Quantum fluctuations in the image of a Bose gas
,” Phys. Rev. A
78
, 023630
(2008
). © 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
