Quantum state engineering by superpositions of coherent states along a straight line with a single atomic state measurement

A new scheme is proposed for preparation of a type of nonclassical state in cavity QED. In the scheme, an atom either flying through or trapped within a cavity, is controlled by the classical Stark effect; this makes it interact alternately with a (resonant) classical field and with the (dispersive) cavity field. The cavity field, which allows an arbitrary displacement operation during the process, after the detection on the atom, finally collapses to the specific superpositions of coherent states, with their weighting factors controllable. The scheme is also applied for preparation of superpositions of motional coherent states for a trapped ion. The scheme is in contrast to all the previous ones, and thus provides a new perspective for quantum state engineering.