Making, probing and understanding Bose-Einstein condensates

Contribution to the proceedings of the 1998 Enrico Fermi summer school on Bose-Einstein condensation in Varenna, Italy.Comment: Long review paper with ~90 pages, ~20 figures. 2 GIF figures in separate files (4/5/99 fixed figure

Generating Schr\"{o}dinger-cat states in momentum and internal-state space from Bose-Einstein condensates with repulsive interactions

Resonant Raman coupling between internal levels induced by continuous illumination of non-collinear laser beams can create double-well momentum-space potentials for multi-level ``periodically-dressed'' atoms. We develop an approximate many-body formalism for a weakly interacting, trapped periodically-dressed Bose gas which illustrates how a tunable exchange interaction yields correlated many-body ground states. In contrast to the case of a position-space double well, the ground state of stable periodically-dressed Bose gases with repulsive interactions tends toward a Schr\"{o}dinger cat state in the regime where interactions dominate the momentum-space tunnelling induced by the external trapping potential. The dependence of the momentum-space tunnelling and exchange interaction on experimental parameters is derived. We discuss how real-time control of experimental parameters can be used to create Schr\"{o}dinger cat states either between momentum or internal states, and how these states could be dynamically controlled towards highly sensitive interferometry and frequency metrology.Comment: 7 pages, 3 figures. Submitted to PR

Spontaneously modulated spin textures in a dipolar spinor Bose-Einstein condensate

Helical spin textures in a $^{87}$Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. This evolution is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. This is confirmed by eliminating the dipolar interactions by a sequence of rf pulses and observing a suppression of the formation of the short-range domains. This study confirms the significance of magnetic dipole interactions in degenerate $^{87}$Rb F=1 spinor gases

Long wavelength spin dynamics of ferromagnetic condensates

We obtain the equations of motion for a ferromagnetic Bose condensate of arbitrary spin in the long wavelength limit. We find that the magnetization of the condensate is described by a non-trivial modification of the Landau-Lifshitz equation, in which the magnetization is advected by the superfluid velocity. This hydrodynamic description, valid when the condensate wavefunction varies on scales much longer than either the density or spin healing lengths, is physically more transparent than the corresponding time-dependent Gross-Pitaevskii equation. We discuss the conservation laws of the theory and its application to the analysis of the stability of magnetic helices and Larmor precession. Precessional instabilities in particular provide a novel physical signature of dipolar forces. Finally, we discuss the anisotropic spin wave instability observed in the recent experiment of Vengalattore et. al. (Phys. Rev. Lett. 100, 170403, (2008)).Comment: arXiv version contains additional Section V relevant to the experiment of Vengalattore et. al. (Phys. Rev. Lett. 100, 170403, (2008)

Periodic spin textures in a degenerate F=1 87^{87}Rb spinor Bose gas

We report on the spin textures produced by cooling unmagnetized $^{87}$Rb F=1 spinor gases into the regime of quantum degeneracy. At low temperatures, magnetized textures form that break translational symmetry and display short-range periodic magnetic order characterized by one- or two-dimensional spatial modulations with wavelengths much smaller than the extent of the quasi-two-dimensional degenerate gas. Spin textures produced upon cooling spin mixtures with a non-zero initial magnetic quadrupole moment also show ferromagnetic order that, at low temperature, coexists with the spatially modulated structure.Comment: 6 pages, revised substantially following reviewer comments and further analysi