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arXiv:0709.1938 · Journal of Physics B Atomic Molecular and Optical Physics

Partial delocalization of two-component condensates in optical lattices

Hector Cruz, Valeriy A. Brazhnyi, V. V. Konotop

Published Jan 22, 2008• 10 citations
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Abstract

We study management of localized modes in two-component (spinor) Bose–Einstein condensates embedded in optical lattices by means of changing interspecies interactions. By numerical integration of the coupled Gross–Pitaevskii equations, we find three different regimes of the delocalizing transition: (i) the partial delocalization when the chemical potential of one of the components collapses with a gap edge and the respective component transforms into a Bloch state, while the other component remains localized; (ii) the partial delocalization as a consequence of instability of one of the components; and (iii) the situation where a vector soliton reaches the limits of the existence domain. It is shown that there exists a critical value for the interspecies scattering length, below which solutions can be manipulated and above which one of the components is irreversibly destroyed.

DOI
10.1088/0953-4075/41/3/035304

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We study management of localized modes in two-component (spinor) Bose–Einstein condensates embedded in optical lattices by means of changing interspecies interactions. By numerical integration of the coupled Gross–Pitaevskii equations, we find three different regimes of the delocalizing transition: (i) the partial delocalization when the chemical potential of one of the components collapses with a gap edge and the respective component transforms into a Bloch state, while the other component remains localized; (ii) the partial delocalization as a consequence of instability of one of the components; and (iii) the situation where a vector soliton reaches the limits of the existence domain. It is shown that there exists a critical value for the interspecies scattering length, below which solutions can be manipulated and above which one of the components is irreversibly destroyed.
The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.
We discuss localized ground states of Bose-Einstein condensates (BEC's) in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii equation to the one-dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap solitons) fully characterizing their delocalizing transition. In this context the usual gap solitons appear as a mechanism for arresting the collapse in low-dimensional BEC's in optical lattices with an attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects in gap solitons, and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC's in atomic chips and Tonks-Girardeau gas in optical lattices.
By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method, we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0x=0x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0x=0x=0. In the noninteracting case, the density profiles are symmetric around x=0x=0x=0. We numerically study the breakdown of this symmetry due to interspecies and intraspecies interactions acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.
We consider effects of interspecies attraction on two-component gap solitons (GSs) in the binary BEC with intraspecies repulsion, trapped in the one-dimensional optical lattice (OL). Systematic simulations of the coupled Gross-Pitaevskii equations corroborate an assumption that, because the effective mass of GSs is negative, the interspecies attraction may split the two-component soliton. Two critical values, ${\ensuremath{\kappa}}_{1}$ and ${\ensuremath{\kappa}}_{2}$, of the OL strength $(\ensuremath{\kappa})$ are identified. Two-species GSs with fully overlapping wave functions are stable in strong lattices $(\ensuremath{\kappa}>{\ensuremath{\kappa}}_{1})$. In an intermediate region, ${\ensuremath{\kappa}}_{1}>\ensuremath{\kappa}>{\ensuremath{\kappa}}_{2}$, the soliton splits into a double-humped state with separated components. Finally, in weak lattices $(\ensuremath{\kappa}<{\ensuremath{\kappa}}_{2})$, the splitting generates a pair of freely moving single-species GSs. We present and explain the dependence of ${\ensuremath{\kappa}}_{1}$ and ${\ensuremath{\kappa}}_{2}$ on the number of atoms (total norm), and on the relative strength of the competing interspecies attraction and intraspecies repulsion. The splitting of asymmetric solitons, with unequal norms of the two species, is briefly considered too. It is found and explained that the splitting threshold grows with the increase of the asymmetry.
Critical behavior of solitonic wave forms of Bose-Einstein condensates in optical lattices (OL's) has been studied in the framework of the continuous mean-field equation. In two and three-dimensions OL's bright matter-wave solitons undergo abrupt delocalization as the strength of the OL is decreased below some critical value. A similar delocalizing transition happens when the coefficient of nonlinearity crosses the critical value. As opposed, bright solitons in one-dimensional OL's retain their integrity over the whole range of parameter variations. An interpretation of this phenomenon in terms of quantum bound states in the effective potential is proposed.
We model the nonlinear behavior of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or antiferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multicomponent structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA) frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetization, i.e., intrinsic precession of the local spin. Finally, we demonstrate that nonstationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.