Quantum jumps in a system of few trapped ions

Abstract

A theory of quantum jumps in a system of few trapped ions is formulated. The V configuration of the energy levels and incoherent pumping are assumed. The master equation is derived in terms of the SU(3) collective operators for the V system. Numerical results for the intensity-intensity correlations for up to five ions are presented. Analytical results for a system of two ions are derived separating out dynamics at two difference time scales and by eliminating adiabatically the fast variables. From the analytical results, the underlying three-state Markov process that can be used to characterize the quantum jumps in the two-ion system is identified. Probability distributions for various off-on time intervals are presented.