Bimodal condensates (II) : collective angular momentum model

In the fourth lesson, we compared the physics of bimodal condensates to that of symmetrical sets of spins on the one hand, and to that of coherent states of a field in the presence of the Kerr effect on the other. We recall the definition of the Dicke states of a set of spins as eigenstates of their collective angular momentum. We also introduced coherent and compressed states of angular momentum. We have established the relationship between the notions of spin compression and quadrature compression or photon number compression in quantum optics. We relate spin compression to entanglement. We described methods for preparing compressed states by exploiting collisions between atoms in a bimodal condensate. We showed how this could lead to the transient creation of states with frozen fluctuation of the difference in the number of particles in the two states of the condensate. The second part of the lesson focused on the phenomenon of phase collapse and resurgence in bimodal condensates and the study of bosonic Schrödinger cats in the dynamical regime. We began by describing the two- and multi-component Schrödinger cats generated by the Kerr effect in quantum optics, and showed their similarity to the bosonic cats of a bimodal condensate. We also analyzed the analogy between these bosonic cats and the GHZ-type states recently produced in trapped ion chains (see lecture 2005-2006).