Exact Analysis of Disentanglement for Continuous Variable Systems and Application to a Two-Body System at Zero Temperature in an Arbitrary Heat Bath

We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. Alter reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to the problem of a pair of particles in a correlated Gaussian state. The initial state and its time development are explicitly exhibited. For a single relaxation time bath at zero temperature exact numerical results are given. The criterion of Duan et al. for such states is used to prove that the state is initially entangled and becomes separable after a finite time (entanglement sudden death).