Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction

We report on the first experimental observation of bright matter wave solitons for ${}^{87}\mathrm{Rb}$ 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.

Figure 1

Observation of bright gap solitons. The atomic density in the negative mass regime deduced from absorption images ($430\mu \mathrm{m}\times 125\mu \mathrm{m}$) averaged over four realizations is shown for different propagation times. After approximately 25 ms, a small peak is formed which does neither change in shape nor in amplitude. Excessive atoms are radiated and disperse over time. After 45 ms only the soliton with $\sim 250$ atoms has sufficient density to be clearly observable. The second peak at 15 ms shows the atoms which have been removed by Bragg scattering to generate an initial coherent wave packet consisting of $\sim 900$ atoms. For longer observation times, those atoms move out of the imaged region.

Figure 2

Realization of coherent atomic wave packets with negative effective mass utilizing periodic potentials. (a) Top view of the crossed dipole trap geometry used for Bose-Einstein condensation. (b) A periodic potential is ramped up while the atoms are still trapped in the crossed dipole trap realizing the atomic ensemble at $q_c=0$. (c),(d) The atoms are released into the one-dimensional waveguide and, subsequently, the periodic potential is accelerated to the recoil velocity $v_r=h/\lambda m$. This prepares the atomic wave packet at the band edge of the lowest band. (e) Normal and anomalous (shaded area) dispersion regime in a periodic potential. The single preparation steps are indicated. The shown band structure is calculated for a modulation depth of $V_0=1E_r$.

Figure 3

Characteristic features of the observed gap soliton. (a) Comparison of expansion in the positive and the negative effective mass regime for 300 atoms. While the soliton does not disperse at all over a time of 65 ms, corresponding to more than eight soliton periods (solid circles), a wave packet in the normal mass regime expands significantly (open circles). Each point represents the result of a single realization. The solid line marks the average measured rms width of Gaussian fits to the solitons. Panel (b) shows the position of the soliton in the frame of the periodic potential and reveals that a standing gap soliton has been realized. The dotted lines indicate the positions that correspond to the maximum and the minimum group velocity in the lowest band. (c) Number of atoms in the central peak. The initial atom numbers exhibit large shot to shot fluctuations, which are reduced during the soliton formation. The predicted relation between the number of atoms and the soliton width [Eq. (1)] is indicated by the horizontal bar using the width deduced as shown in (a). Note that this comparison has been done without a free parameter since all contributing parameters are measured independently.

Figure 4

Scaling properties of a gap soliton. The effective mass was varied experimentally by changing the periodic potential depth. The scaling predicted by Eq. (1) is represented by the solid line and is in good agreement with our experimental observations. The error bars represent the variation of the scaling parameter for different realizations.