Recurrence formula for generalized optical state truncation by projection synthesis

Abstract

A recent work [Pegg et al., Phys. Rev. Lett. 81, 1604 (1998)] showed how to generate a running-wave superposition of zero- and one-photon field states, ${C}_{0}|0〉{+C}_{1}|1〉,$ by physical truncation of the photon number superposition making up a coherent state. Here we discuss the extension of this device to the case of N components: ${C}_{0}|0〉{+C}_{1}|1〉+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}{+C}_{N}|N〉.$