New s-parametrized quasiprobability distribution for fermion system and its application on fermion-counting

Based on the fermion operators' s-ordered rule, we introduce a new kind of s-ordered quasiprobability distributions (W) over tilde ((alpha) over bar,alpha,s), which is defined by the supertrace different from the other definition introduced by Cahill and Glauber [Phys. Rev. A 59, 1538 (1999)]. We further obtain the s-parametrized operator expansion formula of fermion density operator for multi-mode case. At last, we apply it to deriving new multi-mode fermion-counting formula, which would be convenient to calculate the probability of counting n fermions.