Compression and localization of an atomic cloud in a time dependent optical lattice

We analyze a method of compressing a cloud of cold atoms by dynamic control of a far off resonance optical lattice. We show that by reducing the lattice spacing either continuously or in discrete steps while cooling the atoms with optical molasses large compression factors can be achieved. Particle motion in the time dependent lattice is studied numerically using a three dimensional semiclassical model. Two experimentally realistic models are analyzed. In the first we continuously vary the lattice beam angles to compress atoms initially in a Gaussian distributed cloud with standard deviation of $250 \mu\rm m$ into a single site of a two-dimensional lattice of area $A\sim 35\times 35 \lambda^2$, with $\lambda$ the wavelength of the lattice beams. This results in an optical depth for an on-resonant probe beam $>80$ which is an increase by a factor of about 1800 compared to the uncompressed cloud. In the second approach we use a discrete set of lattice beam angles to decrease the spatial scale of the cloud by a factor of 500, and localize a few atoms to a single lattice site with an area $A\stackrel{<}{\sim} \lambda^2.$