Exact Nonlinear Dynamics in Spinor Bose-Einstein Condensates
Jun’ichi Ieda, Miki Wadati
Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we
InTech eBooks•Jan 1, 2010•1 citation