Single-impulse magnetic focusing of launched cold atoms

Abstract

We have theoretically investigated the focusing of a launched cloud of cold atoms. Time-dependent spatially-varying magnetic fields are used to impart impulses leading to a three-dimensional focus of the launched cloud. We discuss possible coil arrangements for a new focusing regime: isotropic 3D focusing of atoms with a single magnetic lens. We investigate focusing aberrations and find that, for typical experimental parameters, the widely used assumption of a purely harmonic lens is often inaccurate. The baseball lens offers the best possibility for isotropically focusing a cloud of weak-field-seeking atoms in 3D.

Double-impulse magnetic focusing of launched cold atoms

“…At the end of [13] there appeared to be a major difference between the parabolic approximation and real lenses. To some extent, this may have been due to the way the lens properties were measured.…”

“…The influence of a magnetic lens can be described by ABCD matrices, as outlined in [12,13]. ) shows the mathematically equivalent thin lens representation that is used in the calculations.…”

“…To some extent, this may have been due to the way the lens properties were measured. In [13], numerical integration of the forces arising from the magnetic fields due to current loops (generated by the Biot-Savart law) was used, to track the trajectories of several (≈1000) simulated atoms. The initial positions and velocities of the atoms were randomly assigned, weighted according to isotropic Gaussian spatial and velocity distributions with 1D standard deviations of σ R = 0.4 mm and σ V = 4.4 cm s −1 (as discussed in the previous section).…”

“…In light of the above discussion, 3D single-impulse focusing outlined in [13] is briefly revisited, in particular Strategy VI: the baseball coil system. This system consisted of a square baseball coil with side lengths w and a coil pair of radius w separated by w that were coaxial with the baseball coil axis.…”

“…Recently, we provided a theoretical analysis of 3D focusing of weak-field-seeking cold atoms using a single magnetic pulse [13]. Lens designs for 1D and 3D were presented that minimize aberrations due to the lens potential's departure from the perfect parabolic case.…”