Classical Bifurcation and Entanglement Generation in an Internal Bosonic Josephson Junction

Abstract

In this work the dynamical behavior of an internal bosonic Josephson junction is investigated. The junction is realized using two Zeeman sub states of the ground state hyperfine manifold in a Bose-Einstein condensate of 87 Rb . With several hundreds of atoms, the size of the system is at the crossover where its classical description breaks down and quantum mechanical effects become important. The system allows for a high level of control in terms of state preparation, readout and its important parameters. Thus its classical dynamics, which show a striking bifurcating behavior, can be studied by mapping out the full phase space and revealing its topological change. Furthermore the dynamics at the unstable classical fixed point arising in the course of the bifurcation are investigated. The dynamics at this point clearly show the breakdown of the classical description. The dynamical evolution leads to spin squeezing and entanglement and subsequently to macroscopic superposition states. The generation of squeezing is quantitatively analyzed and the generated states are reconstructed in terms of their Wigner functions by tomography. This work is an important step for the understanding of highly entangled macroscopic quantum states.