Generalized Q-functions
نویسنده
چکیده
The modulus squared of a class of wave functions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter λ specifies orderings in a mapping from the operator |ψ〉〈σ| to the corresponding phase space wave function, where σ is a given fiducial vector. The choice λ = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when |σ〉 is the vacuum state. More generally, any choice of λ in the range (−1, 1) corresponds to orderings varying between standard and anti-standard. For all such orderings the generalized Q-functions are non-negative by construction. They are shown to be proportional to the expectation of the system state ρ̂ with respect to a generalized displaced squeezed state which depends on λ and position (p, q) in phase space. Thus, when a system has been prepared in the state ρ̂, a generalized Q-function is proportional to the probability of finding it in the generalized squeezed state. Any such Q-function can also be written as the smoothing of the Wigner function for the system state ρ̂ by convolution with the Wigner function for the generalized squeezed state. PACS: 03.65.Ca; 03.65.Ta
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