Figure 1

Sketch of the experimental setup. Atoms outcoupled from a BEC at point $A$ are guided by the horizontal beam towards point $B$. In the vicinity of $B$, atoms also experience the attractive force exerted by the LAP (see text) whose center is at a distance $d$ from the guide axis.Reuse & Permissions

Figure 2

(a) Typical trajectory in the weak coupling regime (see text). The interaction with the LAP yields a downstream propagation with a transverse oscillation. (b) An example of trajectory in the strong coupling regime. The complex dynamics may lead to the reflexion of the particle. In both (a) and (b) the LAP potential is represented by the blue shaded area. (c) An example of exponential separation $\Sigma$ of nearby trajectories in phase space revealing the chaotic nature of the potential. The red dotted curve is the best exponential fit. The average over 100 couples of trajectories close to the central one is taken. (d) The amplitude of the transverse excitation as a function of the ratio $P_{\mathrm{LAP}}/P_{\mathrm{G}}$ and the displacement $d$ of the LAP: transmitted (red or dark gray colors) and reflected (blue or light gray colors) particles. A chaotic zone with a complex dynamics can be clearly identified.Reuse & Permissions

Figure 3

(a),(b),(c) Color density plots of the wave function from 2D numerical simulations. The color scale is not linear. Point $B$ is the same as in Fig. 1. Wave packets are prepared in the ground state of the initial trap, and released in the guide at time $t=0$ ($w_{\mathrm{G}}=45\mu \mathrm{m}$ and ${\omega }_{\perp }=2\pi \times 203\mathrm{Hz}$) at $700\mu \mathrm{m}$ from the LAP ($w_{\mathrm{LAP}}=41\mu \mathrm{m}$). The incident mean velocity of the wave packet is $\overline{v}\sim 10\mathrm{mm}·{\mathrm{s}}^{-1}$ close to $B$. (a) $d=2\mu \mathrm{m}$ ($d/w_{\mathrm{LAP}}=0.05$), $P_{\mathrm{LAP}}=0.5\mathrm{W}$ ($P_{\mathrm{LAP}}/P_{\mathrm{G}}=2.78$), propagation time $t=120\mathrm{ms}$; (b) $d=15\mu \mathrm{m}$ ($d/w_{\mathrm{LAP}}=0.37$) and $P_{\mathrm{LAP}}=1\mathrm{W}$ ($P_{\mathrm{LAP}}/P_{\mathrm{G}}=5.56$), $t=120\mathrm{ms}$; (c) $d=20\mu \mathrm{m}$ ($d/w_{\mathrm{LAP}}=0.5$), $P_{\mathrm{LAP}}=1\mathrm{W}$ ($P_{\mathrm{LAP}}/P_{\mathrm{G}}=5.56$), $t=160\mathrm{ms}$; (d) projected distribution (c) on the $z$ axis of the wave function $\int dx|\psi (x,z){|}^2$ (black) and the initially identical classical distribution (red or gray); classical and quantum curves are identical for cases (a) and (b) (data not shown).Reuse & Permissions

Figure 4

Interaction between a guided atom laser and a LAP (experimental results). The absorption image (a) is taken in the weak coupling regime and (b) and (c) in the strong coupling regime after a 15 ms time of flight. (d) Measurement of the displacement $d$ in the weak coupling regime: the ratio $\Delta /\delta$ of the transverse size before and after the interaction is plotted vs $P_{\mathrm{LAP}}/P_{\mathrm{G}}$ ($\overline{v}\simeq 25\mathrm{mm}·{\mathrm{s}}^{-1}$ and ${\omega }_{\perp }/2\pi \simeq 200\mathrm{Hz}$). The dot-dashed curve corresponds to 3D (classical) simulation with $d=4\mu \mathrm{m}$ ($d/w_{\mathrm{LAP}}\approx 0.07$). Most experimental points (disks) are inside the pink or light gray area delimited by the simulated curves (gray lines) for 3.7 and $4.3\mu \mathrm{m}$.Reuse & Permissions

Figure 5

Experimental difference between quantum evolutions for different runs with the same initial conditions (the same parameters as in Fig. 4). (Top) $⟨⟨\sigma ⟩⟩$ (see text) vs $P_{\mathrm{LAP}}/P_{\mathrm{G}}$. The onset of the chaotic regime is clearly visible on both the large value of $⟨⟨\sigma ⟩⟩$ and its error bar. Inset: Examples of these different runs in the weak (left) and strong (right) coupling regimes. (Bottom) $⟨\sigma (z)⟩$ (see text) vs $z$. The solid line is $P_{\mathrm{LAP}}=0.06\mathrm{W}$ ($P_{\mathrm{LAP}}/P_{\mathrm{G}}=0.6$), the dotted line is $P_{\mathrm{LAP}}=0.6\mathrm{W}$ $P_{\mathrm{LAP}}/P_{\mathrm{G}}=6$), the dashed line is $P_{\mathrm{LAP}}=1\mathrm{W}$ $P_{\mathrm{LAP}}/P_{\mathrm{G}}=10$). We observe the amplification of small initial deviations when the beam enters the chaotic zone ($z\sim z_B\sim 0$) as in Fig. 2c.Reuse & Permissions