Accurate one-dimensional effective description of realistic matter-wave gap solitons

Abstract

We consider stationary matter-wave gap solitons realized in Bose-Einstein condensates loaded in onedimensional (1D) optical lattices and investigate whether the effective 1D equation proposed in [Phys. Rev. A 77, 013617 (2008)] can be a reliable alternative to the three-dimensional treatment of this kind of system in terms of the Gross-Pitaevskii equation (GPE). Our results demonstrate that, unlike the standard 1D GPE (which is not applicable in most realistic situations), the above effective model is able to correctly predict the distinctive trajectories characterizing the different gap soliton families as well as the corresponding axial wavefunctions along the entire band gaps. It can also predict the stability properties of the different gap soliton families as follows from both a linear stability analysis and a representative set of numerical computations. In particular, by numerically solving the corresponding Bogoliubov-de Gennes equations we show that the effective 1D model gives the correct spectrum of complex eigenfrequencies responsible for the dynamical stability of the system, thus providing us with a useful tool for the physical description of stationary matter-wave gap solitons in 1D optical lattices.

Shock Waves in a Superfluid with Higher-Order Dispersion

“…This reduces the memory costs by a factor of 4, and is accurate for short times and dynamics in the center of the cloud. Similarly, in some cases, a quasi-1 simulation using techniques like the non-polynomial Schrödinger equation ( ) [33,[45][46][47]] and dynamically rescaled ( ) [48] can quantitatively reproduce the 3 dynamics. However, these are insufficient once features like vortices appear, as shown in [49].…”

Nonlinear waves of Bose-Einstein condensates in rotating ring lattice potentials

“…⊥ , the rescaled wave function is ψ = √ R ψ, and the lattice depth V 0 is measured relative to the ring energy ŝ = V 0 /E R = sM 2 /8, with s = V 0 /E L . It is worth noticing that s, instead of ŝ, is the usual parameter for identifying the dynamical regimes in the presence of the lattice, from the shallow lattice regime (s 1) up to the tight binding limit (s 1) [9][10][11]14]. For later use, we also define an average interaction parameter per lattice site η = ĝN/M .…”

Nonlinear waves of Bose-Einstein condensates in rotating ring-lattice potentials

“…The early studies of BECs in periodic potentials were mainly focused on linear lattices, including one-(1D), two-(2D), and three-dimensional (3D) lattices [3,[6][7][8]. In these settings, the superfluid flow has been demonstrated to support many types of nonlinear waves [9][10][11]. The stability of these is intimately connected with the possibility for breakdown of superfluid flow and has been studied extensively [6,[12][13][14].…”