Spin-squeezing and Dicke-state preparation by heterodyne measurement

We investigate the quantum nondemolition (QND) measurement of an atomic population based on a heterodyne detection and show that the induced back-action allows for the preparation of both spin-squeezed and Dicke states. We use a wave-vector formalism to describe the stochastic process of the measurement and the associated atomic evolution. Analytical formulas of the atomic distribution momenta are derived in the weak-coupling regime both for short- and long-time behavior, and they are in good agreement with those obtained by a Monte Carlo simulation. The experimental implementation of the proposed heterodyne detection scheme is discussed. The role played in the squeezing process by the spontaneous emission is considered.