A generalized Pancharatnam geometric phase formula for three level systems

We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed generalisation of the Poincare sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3)\/ and its generators in the defining representation, and uses geometrical objects and operations in an eight dimensional real Euclidean space. Implications for an n-level system are also discussed.Comment: 12 pages, Revtex, one figure, epsf used for figure insertio

Characterisations of Classical and Non-classical states of Quantised Radiation

A new operator based condition for distinguishing classical from non-classical states of quantised radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum dynamical variables does not in general maintain positivity. It is shown that the approach naturally leads to distinguishing several layers of increasing nonclassicality, with more layers as the number of modes increases. A generalisation of the notion of subpoissonian statistics for two-mode radiation fields is achieved by analysing completely all correlations and fluctuations in quadratic combinations of mode annihilation and creation operators conserving the total photon number. This generalisation is nontrivial and intrinsically two-mode as it goes beyond all possible single mode projections of the two-mode field. The nonclassicality of pair coherent states, squeezed vacuum and squeezed thermal states is analysed and contrasted with one another, comparing the generalised subpoissonian statistics with extant signatures of nonclassical behaviour.Comment: 16 pages, Revtex, One postscript Figure compressed and uuencoded Replaced, minor changes in eq 4.30 and 4.32. no effect on the result