SU(2) DISTRIBUTION-FUNCTIONS AND MEASUREMENT OF THE FLUORESCENCE OF A2-LEVEL ATOM

It is well known that two quasi-probability distributions for an optic al mode, the Wigner (W) and Husimi (Q) functions, can be measured by h omodyne and heterodyne detection, respectively. These harmonic oscilla tor distribution functions can be generalized to apply to other algebr as, in particular, the su(2) algebra of a two-level atom. In this pape r I investigate the relationship between these quasi-probability funct ions on the Bloch sphere, and the probability distributions for the in tegrated homodyne and heterodyne photocurrents from the fluorescence o f the atom. While there is no particularly close relation between the su(2) Wigner function and homodyne detection, the su(2) Husimi functio n is simply equal to the heterodyne distribution function multiplied b y a weighting factor. I also show that the two-level atom heterodyne d istribution function can be expressed in a form identical to the corre sponding optical mode distribution function. This correspondence defin es the natural analogue of optical coherent states for a two-level ato m. In deriving these results the theory of effects (positive-operator- valued measures) is essential.