Abstract

The dynamics in a parametric χ⁽²⁾ crystal is described by the operator U_λ = exp [λ(a^†b^†−ab)] where the ’’gain” λ is proportional to the interaction-time, the nonlinear susceptibility, and the pump intensity. The output state from the downconversion process is given by the twin-beam |ψ〉= (1−ξ²) ${\displaystyle {\sum }_{\text{n=0}}^{\infty }{\text{ξ}}^{\text{n}}\text{|}}\text{n}{〉}_{\text{a}}\otimes \text{ |n}{〉}_{\text{b}}$ where ξ = tanh λ. If one of the two beam is detected by an avalanche on/off photodetector the outcomes ”1”, i.e registering a ’’click” corresponding to one or more incoming photons, occur with probability P₁ = η_Aξ²[1−ξ²(1−η_A)]⁻¹, where η_A is the quantum efficiency. The corresponding conditional output states for the other mode is given by Such density matrix describes a pseudo-thermal state where the vacuum component has been removed by the conditional measurement, and this means that ${\widehat{\varrho }}_1$ describes a highly nonclassical state.

© 2000 IEEE