Applications and implementation of Fourier multiport devices

Fourier multiport devices in which the creation and annihilation operators at the output are related to those at the input through a finite Fourier transform are studied. A general method for the calculation of the output for arbitrary input states is presented. The case of a squeezed state at one of the inputs and vacua at all other inputs is discussed. In the case of thermal states at the input, the device can be used as a thermometer. A factorization technique inspired by the fast Fourier transform leads to a substantial reduction in the number of beam splitters that are required for the experimental implementation of these devices.