Realization scheme for continuous fuzzy measurement of energy and the monitoring of a quantum transition

The continuousfuzzy m easurem entofenergy ofa single two-levelsystem driven by a resonant external eld is studied. An analysis isgiven in the fram ework ofthe phenom enologicalrestricted path integralapproach (RPI)(which reducese ectively to a Schrodingerequation with a com plex Ham iltonian) as wellas with reference to the m icrophysicaldetails ofa class ofconcrete physical realizations.W ithin theRPIapproach itisdem onstrated thatforappropriately adjusted fuzziness, inform ation aboutthe evolution ofthe state ofthesystem j (t)ican be read o from the m easurem ent readout E (t). It is shown furtherm ore how a m easurem ent ofthis type m ay be realized by a series ofweak and short interactions ofthe two-levelsystem with a quantum m echanicalm eter system .Aftereach interaction a m acroscopic m easuring apparatuscausesthe m eterto transitinto one oftwo states. The resultis used to generate the energy readoutE (t). In thisway a com plete agreem entwith theRPIapproach isdem onstrated which thusobtainsan operationalinterpretation.