Observing the profile of an atom laser beam

We report on an investigation of the beam profile of an atom laser extracted from a magnetically trapped ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. The transverse momentum distribution is magnified by a curved mirror for matter waves and a momentum resolution of $1∕60$ of a photon recoil is obtained. We find the transverse momentum distribution to be determined by the mean-field potential of the residing condensate, which leads to a nonsmooth transverse density distribution. Our experimental data are compared with a full three-dimensional simulation of the output coupling process and we find good agreement.

Figure 1

(Color online) Left: The combined inverted parabola potential caused by the trapped Bose-Einstein condensate and the gravity potential acting on the $\mid F=1,m_F=0⟩$ atoms in the atom laser beam. The dashed line indicates the region where the resonance condition is fulfilled and output coupling takes place. Right Schematic density profile of the trapped condensate (solid line) and the output coupled atoms (dashed line). The arrows indicate the transverse velocity that the output coupled atoms gain due to roll off from the mean field potential of the remaining condensate.

Figure 2

(a) Atom laser beam extracted from a compressed Bose-Einstein condensate. The double peak structure of the beam is clearly visible. The height of the image is $780\mu \mathrm{m}$. (b) Cut through the atomic density distribution at the position indicated by the arrows.

Figure 3

(a) Atom laser after reflection by the curved mirror. The height of the image is $780\mu \mathrm{m}$ and it is taken $33\mathrm{ms}$ after starting the output coupling process including a $3\mathrm{ms}$ ballistic expansion for the Bose-Einstein condensate. (b) Classical trajectories of atoms being reflected from the curved matter wave mirror. After reflection the atoms laser is beam is focused about $300\mu \mathrm{m}$ below the Bose-Einstein condensate. The evolution is shown up to $30\mathrm{ms}$ after the start of output coupling.

Figure 4

Transverse density distribution of an atom laser beam after momentum magnification by the curved mirror. The profiles correspond to different output coupling regions within the Bose-Einstein condensate [top (a) to bottom (d)]. The difference in the output coupling frequency is $2\mathrm{kHz}$ between each slice [(a)–(d)] corresponding to $1\mu \mathrm{m}$ steps of the vertical extraction point. The density distribution is evaluated $250\mu \mathrm{m}$ below the position of the condensate. (e)–(h) Density profiles from a full three dimensional calculation for various output coupling positions $x_c=x_0-ϵr_{\mathrm{TF}}$, corresponding approximately to the experimental data. The density is averaged along the long axis of the condensate, which takes into account the effect of the absorption imaging. Displayed is the far field density distribution as given by the Fourier transform of the density well below the condensate. The momentum distribution has been converted into position space according to the classical trajectories shown in Fig. 3b.