Physical Society Colloquium

Entanglement, dynamical bifurcations and quantum phase transitions

Gerard Milburn

University of Queensland

From the very beginning semiclassical arguments have been used to help understand the predictions of the quantum theory, and extend the theory in new directions. This has been particularly true in quantum nonlinear dynamics, where such phenomenon as dynamical tunneling in phase space has been related to classical fixed point structures in phase space. In this talk I will show how quantum entanglement in the ground state of interacting quantum systems can arise from dynamical instabilities in the phase space of the corresponding classical system. Using examples such as coupled giant spins and coupled BECs, I will show that, when the fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical parameter. A similar phenomenon occurs in many body systems that undergo a quantum phase transition. Ion traps are the leading experimental context for implementing quantum information processing. I will also discuss how ion traps can be used to implement examples of quantum nonlinear bifurcations and quantum phase transitions in few body systems.