R. Cipolatti | Searcharxiv

arXiv2015

Two-species Bose-Einstein condensate in an optical lattice: analytical approximate formulæ

Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose-Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross-Pitaevkii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom-atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.

cond-mat.quant-gas↗

arXiv2015

Damping of Confined Excitations Modes of 1D Condensates in an Optical Lattice

We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is non-homogeneous and the collective excitations are characterized by a set of discrete confined phonon-like excitations. We derive a general convenient analytical description for the damping rate, which takes into account, the trapping potential and the optical lattice, for the Landau and Beliaev processes at any temperature, $T$. At high temperature or weak spatial confinement, we show that both mechanisms display linear dependence on $T$. In the quantum limit, we found that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of $T$. Our theoretical predictions for the damping rate under thermal regime is in completely correspondence with the experimental values reported for 1D condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a \textit{resonant effect} for the condensate lifetime. Also, we study the influence of the attractive or repulsive non-linear terms on the decay rate of the collective excitations. A general expression of the renormalized Goldstone frequency has been obtained as a function of the 1D non-linear self-interaction parameter, laser intensity and temperature.

cond-mat.quant-gas↗

arXiv2014

Existence of standing waves for the complex Ginzburg-Landau equation

We prove the existence of non-trivial standing wave solutions of the complex Ginzburg-Landau equation $ϕ_t - e^{iθ}(ρI- Δ) φ- e^{iγ} |ϕ|^αφ=0 $ in $\Rn$, where $(N-2)α<4$, $θ,γ\in (-π/2,π/2)$ and $ρ>0$. Analogous result is obtained in a ball $Ω\in\Rn$ for $ρ>-λ_1$, where $λ_1$ is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions.

math.AP↗