Abstract

Let us consider a superposition | ψ> obtained from ψ₀> by action of some operation T̂(τ_j), where τ_j is complex and N is a normalization constant. The probability distribution for some observable Ậ which commutes with T̂ (τ_j), having eigenstates | n> corresponding to the eigenvalues a_n is where we assume that the eigenvalues of T̂_n(τ_j) are T_n(τ_j) = exp (i λ_n θ_j), for real λ_n and θ_j. For a superposition of N states obtained by regularly transforming | ψ₀>, such that θ_j+1 – θ_j = 2φ, one has where in the interference term of classical diffraction. Besides the interference term, a diffraction term appears, proportional to the square of the overlap between the state | ψ₀> and the eigenstate | n>, and is analogous to the form factor of classical diffraction. The maxima of the function S(N, λ_n φ) occur for λ_n φ = υ π (υ = 0, _±1 _±2, …), thus the distribution Pn has an oscillatory character. We have thus the diffraction grating in phase space.

© 1992 IQEC