Mixed-symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

Cruz, H.; Brazhnyi, V. A.; Alfimov, G. L.; Salerno, Mario

doi:10.1103/physreva.76.013603

Cited by 22 publications

(31 citation statements)

References 32 publications

(36 reference statements)

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“…The existence of dark-bright states of binary BECs mixtures was demonstrated in [15]. On the other hand, the existence of localized states of different symmetry type (mixed symmetry states) was numerically and analytically demonstrated in [16]. Properties of coupled gap solitons in binary BECs mixtures with repulsive interactions were also analyzed in the multidimensional case [17] as well as for combined linear and nonlinear optical lattices [18].…”

Section: Introductionmentioning

confidence: 99%

“…Properties of coupled gap solitons in binary BECs mixtures with repulsive interactions were also analyzed in the multidimensional case [17] as well as for combined linear and nonlinear optical lattices [18]. Although gap-soliton breathers of multicomponent GPE involving periodic oscillations of the two components densities localized on adjacent sites of an optical lattice have been found [16] (in analogy to what was done for single component case in [6], such states can also be seen as matter wave realizations of Josephson junctions), no much numerical and theoretical study has been done until now on AJJ of binary mixtures.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Atomic Josephson junction with two bosonic species

Mazzarella

Moratti

Salasnich

et al. 2009

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We study an atomic Josephson junction (AJJ) in presence of two interacting Bose-Einstein condensates (BECs) confined in a double well trap. We assume that bosons of different species interact with each other. The macroscopic wave functions of the two components obey to a system of two 3D coupled GrossPitaevskii equations (GPE). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODE), for which the coupled pendula represent the mechanic analogous. These differential equations control the dynamical behavior of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and non zero -the macroscopic quantum self-trapping (MQST) -time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPE and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signs the onset of MQST.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Atomic Josephson junction with two bosonic species

Mazzarella

Moratti

Salasnich

et al. 2009

J. Phys. B: At. Mol. Opt. Phys.

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“…Two-site B-B compactons also exist and, similarly to discrete breathers of binary non linear lattices [24], can be of three types: in-phase, out-of-phase and mixed-symmetry type, e.g. with both components symmetric (in-phase), or with both anti-symmetric (out-of phase), or with one component symmetric and the other anti-symmetric (mixedsymmetry) [24], with respect to the middle point between the two sites on which they are localized, respectively.…”

Section: Two-site Compactonsmentioning

confidence: 99%

“…with both components symmetric (in-phase), or with both anti-symmetric (out-of phase), or with one component symmetric and the other anti-symmetric (mixedsymmetry) [24], with respect to the middle point between the two sites on which they are localized, respectively. Two-site B-B compactons directly follow from Eqs.…”

Section: Two-site Compactonsmentioning

confidence: 99%

Binary matter-wave compactons induced by inter-species scattering length modulations

Abdullaev

Hadi

Salerno

et al. 2017

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) in the presence of periodic time modulations of the inter-species scattering length, are investigated. We adopt a mean field description and use the tight binding approximation and the averaging method to derive averaged model equations in the form of two coupled discrete nonlinear Schrödinger equations (DNLSE) with tunneling constants that nonlinearly depend on the inter-species coupling. We show that for strong and rapid modulations of the interspecies scattering length, the averaged system admits exact compacton solutions, e.g. solutions that have no tails and are fully localized on a compact which are achieved when the densities at the compact edges are in correspondence with zeros of the Bessel function (zero tunneling condition). Deviations from exact conditions give rise to the formation of quasi-compactons, e.g. non exact excitations which look as compactons for any practical purpose, for which the zero tunneling condition is achieved dynamically thanks to an effective nonlinear dispersive coupling induced by the scattering length modulation. Stability properties of compactons and quasi-compactons are investigated by linear analysis and by numerical integrations of the averaged system, respectively, and results compared with those from the original (unaveraged) system. In particular, the occurrence od delocalizing transitions with existence of thresholds in the mean inter-species scattering length is explicitly demonstrated. Under proper management conditions, stationary compactons and quasi-compactons are quite stable and robust excitations that can survive on very long time scale. A parameter design and a possible experimental setting for observation of these excitations are briefly discussed.

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“…These studies demonstrated that the stationary state of a BEC mixture depends critically on the intra-and inter-species scattering lengths, as does its stability against excitations [23][24][25][26]. Additional aspects examined involved the static and dynamic properties [27][28][29][30][31], including the excitation spectrum and the nature of low-frequency simultaneous collective excitations, and solitary waves [32][33][34][35][36] (see also references therein).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear from linear states in two-component Bose–Einstein condensates

Karali¹,

Efremidis²

2008

J. Phys. A: Math. Theor.

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In this work, we consider the extension of linear eigenmodes of the harmonic oscillator potential into nonlinear states, for the case of twocomponent Gross-Pitaevskii equations with a parabolic potential, motivated by the context of two interacting hyperfine states of 87 Rb in Bose-Einstein condensates. In particular, we establish that nonlinear continuations of various eigenmode combinations are possible and corroborate this analytical finding with numerical computations for the lowest few eigenmode combinations involving the ground state and the first two excited states. A multitude of nonlinear states can be constructed in this way, some of which spontaneously deform, as the interactions become stronger, into previously obtained nonlinear eigenstates. The Bogolyubov-de Gennes analysis of the excitations on top of such states illustrates that some of them may become unstable beyond a critical threshold (of the chemical potentials associated with the states), while others may be stable within the entire range of chemical potentials considered herein. When the modes are found to be unstable, their evolution is followed, leading to interesting dynamical effects such as spontaneous symmetry breaking or oscillatory growth.

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Mixed-symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

Cited by 22 publications

References 32 publications

Atomic Josephson junction with two bosonic species

Atomic Josephson junction with two bosonic species

Binary matter-wave compactons induced by inter-species scattering length modulations

Nonlinear from linear states in two-component Bose–Einstein condensates

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