Developments in cavity QED provide the means to construct non-classica
l light fields which may be regarded as superpositions of coherent sta
tes. These are highly sensitive to dissipation. We examine the evoluti
on of individual realizations of quantum superpositions conditioned by
two distinct measurement schemes: amplitude (heterodyne) measurements
and excitation number (counting) measurements. These two schemes resu
lt in either localization or quantum jumps in phase space, which we il
lustrate for a number of non-classical initial superpositions.