What is the diffraction limit of "atom lasers" Due to De Broglie wavelength's behaving differently from photons, the theoretical limit, i.e: not limited by system imperfections, is not clear.
 A: The diffraction limit in optics should correspond to the Heisenberg uncertainty limit for atom lasers. In the ideal scenario, an atom laser will focus a Heisenberg uncertainty limited beam.
For a rough calculation. Consider an atom laser of width $w$ in the $z$-direction propagating with velocity $v_x$ in the $x$-direction. If the atom laser is to be focused at some distance $f$ from a 'lens' (such a lens can be created with optical forces) then the velocity imparted on each atom in the beam at a distance $z$ from the lens center should be
$$v_z=\frac{zv_x}{f}.$$
With an atom of mass $m$, the spread in momentum imparted onto the beam in the $z$-direction can be assumed to be equal to the maximum momentum imparted
$$\Delta p_z=\frac{mwv_x}{2f}.$$
Then, from Heisenberg's uncertainty principle
$$\Delta z=\frac{\hbar}{2\Delta p_z}=\frac{f\hbar}{mwv_x}=\frac{\lambda_x}{2\tan(\theta)},$$
where $\lambda_x=\hbar/mv_x$ and $\theta$ being the half angle subtended by the lens, $2\tan(\theta)=w/f$.
Trying to answer this question I started asking many myself about how to properly formulate the result. For example, the density distribution of the atom laser would have to be considered when properly calculating the deviation $\Delta p_z$. If a BEC is used then atoms can interact, this also might complicate things further.
