Figure 1

(a) A pair of counterpropagating light beams applied to a condensate in magnetic trap. (b) The scattering process: a sequence of standing-wave pulses, containing $s$ intervals with widths ${\tau }_{fi}$ $(i=1,2,...,s$) and $s+1$ light pulses with durations ${\tau }_i$ $(i=1,2,...,s+1$). The incident light’s wavelength is 852 nm and its maximum intensity can reach $120E_R$. (c) The procedure for the experiments. The condensate is exposed to a sequence of standing-wave pulses and then released from the magnetic trap. The absorption images of the condensate can be observed after the free fall. (d) A TOF signal obtained in our experiment.Reuse & Permissions

Figure 2

Single-pulse scattering of condensate: The black dots represent the experiment results. The blue solid line is the theoretical analysis with the Raman-Nath approximation. The red dashed line is the numerical simulation with band structure theory. (a)–(d) correspond to relative populations of the condensates with momenta $0\hslash k$, $\pm 2\hslash k$, $\pm 4\hslash k$, and $\pm 6\hslash k$, respectively.Reuse & Permissions

Figure 3

Two-pulse scattering of the condensate: The relative populations of the stationary condensate, $P_{0\hslash k}$, versus the varied intervals ${\tau }_f$. The parameters of the experiments are described above each figure. The black dots are the experimental results. The blue dashed line is the analysis with the Raman-Nath approximation. The magenta dotted line is the numerical simulation with band structure theory. The red solid line is a numerical simulation taking into account the momentum dispersion. (c) A demonstration of momentum expansion introduced by $s$-wave scattering. The TOF signal (i) corresponds to the dashed curve and pictures the momentum distribution before the lattice pulse. The signal (ii) corresponds to the solid curve and shows the momentum distribution after the pulse. The momentum width along the $Z$ direction (the lattice direction) is evaluated based on the parts in the dashed boxes which include the momenta from $-\hslash k$ to $\hslash k$.Reuse & Permissions

Figure 4

Three-pulse and four-pulse scattering of the condensate: The relative populations of the stationary condensate $P_{0\hslash k}$ versus the varied total intervals $\sum {\tau }_{fi}$. The parameters of the experiments are described above each figure. The black dots are the experimental results. The red solid line is a numerical simulation taking into account the momentum dispersion.Reuse & Permissions

Figure 5

Experimental realization of designed momentum states. The expected momentum state is $\pm 2\hslash k_L$ [(a) and (b)], $\pm 4\hslash k_L$ [(c) and (d)], and $\pm 6\hslash k_L$ [(e) and (f)]. The pulse sequences are shown above each figure. The black circles are experimental results. The blue diamonds are the expectations based on the design. The red squares are the modified design with momentum width included, which agree better with the experiments.Reuse & Permissions