Optically Induced Lensing Effect on a Bose-Einstein Condensate Expanding in a Moving Lattice

We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The experimental results are compared with the numerical predictions of an effective 1D theoretical model. In addition, a precise band spectroscopy of the system is carried out by looking at the real-space propagation of the atomic wave packet in the optical lattice.

Figure 1

Schematics of the experimental procedure. After releasing the condensate from the magnetic trap ($A$), we adiabatically ramp the intensity of an optical lattice moving at velocity $v_L$. We let the condensate expand in the periodic potential and, after 10 ms at the maximum light intensity, we look at the position and dimensions of the atomic cloud by absorption imaging along the radial horizontal direction ($B$).

Figure 2

(a) Velocity of the condensate in the frame of the moving lattice for the lowest two energy bands and two different optical intensities: $s=1.3$ (closed circles) and $s=3.8$ (open circles). The experimental data are obtained from the measured displacements of the condensate center of mass after the expansion inside the lattice. The lines are calculated from band theory. (b) Effective mass of the condensate in the lowest two energy bands for $s=1.3$. The experimental points (closed circles) are obtained by numerically evaluating the incremental ratios $\Delta v/\Delta q$ from the data shown above. The lines are calculated from band theory. We remember that $v_B=q_B/m=\hslash k/m$.

Figure 3

Absorption images of the expanded condensate. From left to right: (a) normal expansion of the condensate without lattice; (b) axial compression in a lattice with $s=2.9$ and $v_L=0.9v_B$; (c) enhanced axial expansion in a lattice with $s=2.9$ and $v_L=1.1v_B$ (where $v_B=q_B/m=\hslash k/m$). In the lower part, we report the axial and radial dimensions of the condensate after expansion in an optical lattice with $s=2.9$ as a function of the quasimomentum. The experimental points (closed and open circles) show the Thomas-Fermi radii of the cloud extracted from a 2D fit of the density distribution. The dotted lines show the dimensions of the expanded condensate in the absence of the optical lattice. The continuous and dashed lines are theoretical calculations obtained from the 1D effective model described in the text.

Figure 4

Ratio of the radial to the axial size (aspect ratio) of the condensate after 13 ms of expansion in an optical lattice with $s=2.9$. The dotted line shows the aspect ratio of the expanded condensate in the absence of the optical lattice. The continuous line is a theoretical calculation obtained from the 1D effective model described in the text.