Our analytical solution shows that the number of atoms continuously injected into Bose-Einstein condensate from the reservoir depends on the linear gain/loss coefficient, and cannot be controlled by applying the external magnetic field via Feshbach resonance reported by Yuce and Kilic [Phys. Rev. A 74, 033609 (2006)].
In recent experiments on Na Bose-Einstein condensates [S. Inouye et al., Nature 392, 151 (1998); J. Stenger et al., Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of atom pairs that belong to the condensate many-body wave function. A mechanism is offered here to account for the observed losses. It is based on the deactivation of the resonant molecular state by interaction with a third condensate atom, with a deactivation rate coefficient of magnitude $\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.$
We investigate the modulational instability of nonlinear Schrödinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experimentally realizable protocol of Feshbach Resonance Management for Bose–Einstein condensates. We derive the corresponding linear stability equation analytically and we show that it can be reduced to a Kronig–Penney model, which allows the determination of the windows of instability. The results are tested numerically in the absence, as well as in the presence of the magnetic trapping potential.
We consider in detail the situation of applying a time-dependent external magnetic field to a 87 Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Köhler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87 Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.