We theoretically investigate an all optical scheme for three-dimensional tr
apping and cooling of atoms in a single bichromatic standing ware with a Ga
ussian transverse intensity profile as: e.g. formed by two different longit
udinal modes of a linear optical cavity. The atoms are cooled through an ef
ficient Sisyphus mechanism and trapped at those anti-nodes (maxima) of the
stronger field where the second weaker field has a node. This generates a l
arge effective atom-field coupling as it is desired in nonlinear optical ex
periments with clouds of atoms. The scheme effects high local densities mod
ulated at the beat frequency of the two involved modes. In the appropriate
parameter regime the results fi om a three-dimensional semi-classical appro
ach are confirmed by a 1D full QMCWF-simulation. Extending our model to a m
ore realistic case, we include loss channels out of the system and repumpin
g. Furthermore, we generalise our approach to Lambda-type level schemes, wh
ich exhibit promising optical nonlinearities. Trapping and cooling of such
atoms is predicted to be compatible with maintaining high cooperativities n
eeded for large nonlinear effects.