We report on the first experimental observation of bright matter wave solitons for 87Rb atoms with repulsive atom-atom interaction. This counterintuitive situation arises inside a weak periodic potential, where anomalous dispersion can be realized at the Brillouin zone boundary. If the coherent atomic wave packet is prepared at the corresponding band edge, a bright soliton is formed inside the gap. The strength of our system is the precise control of preparation and real time manipulation, allowing the systematic investigation of gap solitons.

The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.

A coherent coupler is proposed to spin a Bose-Einstein condensate composed of ultracold alkali atoms into a vortex state (VS). The proposal is based on a Raman transition induced by two copropagating σ + and σ − polarized LaguerreGaussian laser beams with different frequencies. We show that the transfer of angular momentum of photons to the condensed atoms through a Raman transition leads to a coherent coupling of the ground-state condensate to a rotating condensate in a VS. The detection of such a VS is discussed.It is well-known that VS's play a central role in characterizing the superfluid properties of large-size Bose systems such as superfluid helium (see, e.g., ef.[1]). Recently the experimental realizations of Bose-Einstein condensation in trapped ultracold alkali atomic gases [2] have generated great interest in studying the superfluid aspects of the small-scale trapped Bose gases [3]. To understand how the small-scale Bose-Einstein condensate is related to a superfluid, it is natural to study the rotational properties of the condensate and to examine VS's. Being different from superfluid helium, the trapped Bose gases are not in direct contact to an external container. How to rotate such gases and to create VS's is still an open question.In this letter, we propose to employ a vortex coupler to realize such a goal. The principle for the vortex coupler is illustrated in Fig.1. Two copropagting σ + and σ − polarized laser beams along the z direction (gravity's direction) are used to induce a Raman transition between two hyperfine levels of ground-state alkali atoms. Initially we assume that a Bose-Einstein condensate is prepared in the trapping state |− = |F = 1, M F = −1 . We consider the time evolution of the condensate after the trap is switched off and the Raman laser beams are applied. In addition, gravity effects are excluded here since we are only interested in the rotational motion of the condensates in the x-y plane. To avoid the destructive incoherent heating of the condensate due to spontaneous decay of excited states |j , the two Raman beams are detuned by a frequency ∆ from the optical transition between the ground state and the excited state manifolds. In this case adiabatic elimination of the excited states |j results in a nonlinear Schrödinger equation describing the coherent Raman-type coupling [4] between the condensate wave functions φ − and φ + corresponding to the magnetic sublevel |− and |+ = |F = 1, M F = 1 :wheredenote the positive frequency part of the corresponding Rabi frequencies of the two Raman beams. ∆ω := ω 2 − ω 1 is the frequency difference between the two Raman beams, m the atomic mass, a sc the scattering length, and N the total number of atoms in the initial condensate. µ denotes the chemical potential needed to fix the mean number of atoms. We have normalized the condensate wave functions by the conditionFor the sake of a concise notation we have defined the operator T := p 2 /(2m) for the kinetic energy .The last terms in Eqs.(1) represent the Raman coupling which coh...

We demonstrate the control of the dispersion of matter wave packets utilizing periodic potentials. This is analogous to the technique of dispersion management known in photon optics. Matter wave packets are realized by Bose-Einstein condensates of 87Rb in an optical dipole potential acting as a one-dimensional waveguide. A weak optical lattice is used to control the dispersion relation of the matter waves during the propagation of the wave packets. The dynamics are observed in position space and interpreted using the concept of effective mass. By switching from positive to negative effective mass, the dynamics can be reversed. The breakdown of the approximation of constant, as well as experimental signatures of an infinite effective mass are studied.

Marzlin and Sanders Reply:Here we address Comments by Ma et al. [1] (MZWW) and by Duki et al. [2] (DMN) on our analysis [3] (MS) of problems concerning incautious applications of the adiabatic theorem. These Comments primarily concern our argument of inconsistency, although they differ between each other in conclusions, and MZWW also discuss our counterexample to the sufficiency of the adiabatic condition. The main objections are that MZWW claim our ''proof of inconsistency'' is due to the mathematical error of integrating an approximate differential equation beyond its duration of validity, and DMN provide an alternative explanation of the inconsistency, which is actually similar to our own argument.MZWW agree that our proof of inconsistency is spurious but argue against our explanation of its origin. To understand and refute the MZWW criticism, consider an example for which the adiabatic theorem is valid so the approximate solution to the Schrödinger equation using the adiabatic theorem is close to the exact solution for a large propagation time T A . The adiabatic approximation works on the large time scale T A because perturbations due to coupling to other instantaneous energy eigenstates in the Schrödinger equation [Eq. (1) of Ref.[3] ] oscillate rapidly so their cumulative effect cancels. In contrast application (5) of Ref.[3], which exploits this approximation, yields an inconsistency for large time. Eqs. (7-9) of Ref.[3] reveal that in this particular application the rapidly oscillating phase factors are removed so that the adiabatic approximation cannot be applied on the time scale T A . This inapplicability is the perfunctory use we cautioned against in MS [3]. In the absence of rapidly oscillating phase factors, deviations from the exact solution obviously grow on the ''perturbation'' time scale T p 1=jhE n j _ E m ij T A . MZWW claim our explanation is unrelated to the adiabatic theorem because, in general, a function that only approximately fulfills a differential equation could quickly deviate from the exact solution, but casting the problem in a general context oversimplifies the nature of the inconsistency for adiabatic evolution. The MZWW line of reasoning basically states that deviations generally grow on time scale T p , but this is equivalent to the explanation of the inconsistency we provided in MS and fails to elucidate why the approximation breaks down on time scale T A .