Alternate orderings: A new tool for the study of phase and photon statistics
M.‐A. Dupertuis · Physical Review A · 1988
A new way to expand an arbitrary boson-field operator into ordered products of creation and annihilation operators is introduced: alternate ordering. A continuous order parameter s characterizes the order and takes the value s=+1 for normal-alternate order, s=0 for symmetric-alternate order, and s=-1 for antinormal-alternate order. All of the alternate moments of a number of well-known states of light are calculated. The expansion of density matrices and operators in terms of alternate products is briefly discussed as well as the relation with the concepts of phase and higher-order phase dependence. Finally, the relevance of the new ordering scheme in the study of photon statistics is outlined and illustrated in the derivation of moment equations for phase-sensitive light amplifiers and absorbers.