Atom lens without chromatic aberrations

We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicularly to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity.

Figure 1

Scattering of the wave packet $\Psi =\Psi \left(x\right)$ of a two-level atom by a combination of a standing electromagnetic field formed by two propagating waves of wave vectors ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ and a traveling wave propagating orthogonal to the $x-y$ plane serving as a control field. As the atom propagates along the $y$ axis with the velocity $\mathbf{v}=v_y{\mathbf{e}}_y$, the envelope of the two running waves translates according to the relation $y=v_{y}t$ into the time-dependent function $f_l=f_l\left(v_{y}t\right)$. During the atom-field interaction the effective detuning of the field frequencies from the atomic transition changes its sign due to the control field with an envelope $f_c\left(t\right)$ in the shape of a “top hat.”