Quantum reflection of bright solitary matter waves from a narrow attractive potential

We report the observation of quantum reflection from a narrow attractive potential using bright solitary matter waves formed from a ${}^{85}\mathrm{Rb}$ Bose-Einstein condensate. We create the attractive potential using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the confinement of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a simple Gaussian potential well. A more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.

Figure 1

(a) Experimental setup. Atoms are cooled in a crossed optical dipole trap (not shown), and then transferred into an optical waveguide. Additional axial confinement is provided by magnetic quadrupole and bias fields. The narrow attractive potential is formed using a high numerical aperture (NA) lens to produce a light sheet, tightly focused in the $x$ direction. (b) Absorption images of solitary wave propagation in the optical waveguide. (c) Schematic showing the position of the narrow attractive potential, relative to the trap center and the initial position of the solitary wave.

Figure 2

Splitting of the solitary wave. Absorption images showing the low velocity propagation of the solitary wave (a) without and (b) with the attractive well present at 1, 250, and 500 ms. (c) In the absence of the well (blue triangles) the atoms oscillate in the waveguide. With the well present the solitary wave splits, with atoms being both transmitted (red circles) and reflected (black squares). Lines indicate classical trajectories for free propagation (solid) and elastic reflection (dashed).

Figure 3

The percentage (a) reflection (R), (b) transmission (T), and (c) confinement (C), of atoms as a function of well depth for an incident solitary wave with a velocity of $1\text{mm}{\mathrm{s}}^{-1}$. These percentages are determined using regions defined in the inset of (a) (see text for details).

Figure 4

Extreme variation in predicted reflection for small changes in spatial structure of the potential. Main panels show calculated reflection coefficients as a function of potential depth for (a) noninteracting wave packets $(a_s=0)$ and (b) bright solitary waves $(a_s=-7a_0)$ in a 1D GPE model. Results are shown for both Gaussian $\left[V_{\mathrm{G}}\left(x\right)\right]$, and truncated diffraction-pattern $\left[V_J^{\left(\mathrm{trunc}\right)}\left(x\right)\right]$ potentials. The inset to (a) shows the large-scale similarity between these potentials. The inset to (b) shows the subsidiary potential wells [zoom of gray area in inset to (a)]; these have $\lesssim 2\%$ the depth of the main well, but strongly influence the reflectivity.

Figure 5

Comparison of 1D GPE predictions for the reflection between potentials $V_J^{\left(\mathrm{trunc}\right)}\left(x\right)$ and $V_J\left(x\right)$ (see text) for (a) noninteracting wave packets $(a_s=0)$ and (b) bright solitary waves $(a_s=-7a_0)$. Also shown in (b) are results of a 3D GPE simulation with equivalent parameters.