Successive oscillatory fields at radio to optical frequencies

The methods of separated or successive oscillatory fields (often called Ramsey methods) are described for radio, microwave and optical coherent radiation. The methods are initially described qualitatively. The quantitative theories of the methods are also given. For a two-level system at radio frequencies exact expressions for the transition probability amplitudes for an arbitrary number of successive oscillatory regions can be found in terms of products of successive transformation matrices. The expressions are greatly simplified if the oscillatory-field regions are very short. If there are only two oscillatory-field regions the situation is similar to a Young's two-slit interference pattern except that the two paths are separated in spin space rather than normal space. Some results from more than two oscillatory regions are discussed. The extensions of the methods and the theories to optical frequencies are described. The advantages and disadvantages of the methods are given as are the many extensions of the method beyond the original concept.I am honored to write an article in celebration of the sixtieth birthday of Herbert Walther. He has established one of the world's best atomic-physics laboratories and has made great contributions to physics, ranging from precision spectroscopy and laser cooling to measurements of fundamental atomic and quantum properties. He has also been a helpful consultant, adviser, and friend to many of us in the field. Happy birthday!!